Proof
a play by David Auburn
Study Guide
Freshman Experience
Western Michigan University
Summary
Proof is the story of an enigmatic young woman, Catherine, her manipulative sister,
their brilliant father, and an unexpected suitor.
They are all pieces of the puzzle in the search for the truth behind a mysterious
mathematical proof.
In Proof, the young but guarded Catherine grieves over the loss of her father, a famous
mathematician who had become a legend at the local university for solving complicated
proofs, and for suffering from dementia. Just as Catherine begins to give in to her fear
that she, too, might suffer from her father’s condition, Catherine’s older sister Claire
returns home to help “settle” family affairs and Hal, one of the father’s old students,
starts to poke around the house.What Hal discovers in an old speckle-bound notebook
brings to light a buried family secret.
It tests the sisters’ kinship as well as the romantic feelings growing between Catherine
and Hal.
This poignant drama about love and reconciliation unfolds on the back porch of a house
settled in a suburban university town, that is, like David Auburn’s writing, both simple
and elegant.
-- from the Pulitzer Prize Citation
David Auburn:
Biographical Information on the playwright
David Auburn's play PROOF premiered at the Manhattan Theatre Club in May 2000, and
opened at Broadway's Walter Kerr Theatre on October 24, 2000. He is the recipient of the
Guggenheim Foundation Grant, Helen Merrill Playwrighting Award, and Joseph
Kesselring Prize for Drama.
His other plays include: SKYSCRAPER, performed at the Greenwich House and
published by DPS; FIFTH PLANET, New York Stage and Film; MISS YOU, HBO
Comedy Arts Festival; and THE NEXT LIFE, Juilliard School. His work has been
published in Harper's Magazine and The New England Review. He was a member of the
Juilliard playwrighting program.
Columbia University President George Rupp (left) presents David Auburn with the 2001
Pulitzer Prize for Drama.
-- from www.pulitzer.org
Proof of What Happens When You Just Let Go
by David Auburn
Part of writing a play is letting it go. It’s both exhilarating and a bit frightening when you
turn your script over to the director and the actors who will try to make it live. It’s a
risk—you hope you’ll get lucky. With Proof, I did. But when I let this play go I had no
idea how far it would travel.
The play has been done in London, Tokyo, Manila, Stockholm, Tel Aviv and many other
cities; the definitive New York production, directed by Daniel Sullivan, opens in Beverly
Hills this week at the Wilshire Theatre.
Proof started with two ideas. One was about a pair of sisters: What if, after their father’s
death, they discovered something valuable left behind in his papers? The other, more of a
visual image than anything else, was about a young woman: I saw her sitting up alone,
late at night, worried she might inherit her father’s mental illness.
While trying to see if these ideas fit together, I happened to be reading A
Mathematician’s Apology, the memoir by the great Cambridge mathematician G. H.
Hardy. It’s probably the most famous attempt to explain the pleasures of doing math to a
non-mathematical audience. One passage particularly startled me.
"In a good proof," Hardy wrote, "there is a very high degree of unexpectedness,
combined with inevitability and economy. The argument takes so odd and surprising a
form: the weapons used seem so childishly simple when compared with the far-reaching
consequences; but here is no escape from the conclusions."
That sounded like a definition of a good play, too. Math was alien territory to me—I had
barely made it through freshman calculus in college—but I decided to set my story in
Hardy’s world. A mathematical proof became the "thing" the sisters find: my protagonist,
Catherine, became convinced that she may have inherited her father’s talent—he was a
legendary mathematician—as well as his illness. With these elements in place, and
feeling inspired by the meetings with the mathematicians I’d begun to have, I was able to
finish a draft of the play quickly, in about six weeks.
My first play, Skyscraper, had been commercially produced off-Broadway in 1997. Its
run was short, but long enough for the literary staff at Manhattan Theater Club to catch a
performance. They had invited me to submit my next play—a good break for me, since
MTC is the best venue for new work in the city. I sent Proof to them. A few weeks later,
it had a star, Mary Louise Parker, a director, Daniel Sullivan, and an opening date for
what I assumed would be a six-week run.
Proof has now been running for two years. In that time, I’ve often been surprised at the
responses it has generated. At a New York University conference on the play, a panel of
women mathematicians used it to discuss questions of sexism and bias in their
professions. After a performance on Broadway I got a note from an audience member
backstage: "My daughter is just like Catherine," it said. "I can’t communicate with her.
Can you help me?"
In Chicago, a woman confronted me after a book signing. She told me her father had
been a mathematician who’d lost his mind and she’d spent her whole life caring for him.
"This is the story of my life," she said. "How did you know?"
The answer, of course, is that I didn’t, any more than I intended the play to speak directly
to the concerns of female academics, or could tell a stranger how to break through to his
daughter. When you let a play go, you also take the risk that it will take on associations
for people that you didn’t intend and can’t account for.
That risk is the prerogative of art, however, and of the theater in particular. The theater
affects us more directly, and unpredictably, than any of the other arts, because the actors
are right there in front of us, creating something new every night. "Unexpected and
inevitable." Which makes it all work the risk.
-- from the Los Angeles Times, 4 June 2002
PBS NewsHour:
an Interview with David Auburn
TERENCE SMITH: The prize for drama went to David Auburn for his play "Proof". It's
a family drama that unfolds against the backdrop of mathematical theory. The play is a
hit at the Walter Kerr theater on Broadway. It's the second full-length play Auburn has
written and his first Broadway production. Auburn, who is 31, was born in Chicago and
lives in Williamstown. Massachusetts. David, welcome and congratulations.
DAVID AUBURN: Thanks very much.
SMITH: It must be quite a thrill. Tell me how you heard about the prize and how you felt
about it.
AUBURN: I was minding my own business at home talking to my wife about what we
were going to have for dinner and call waiting deep beeped so I beeped over and they
said congratulations you've won the Pulitzer Prize. So I beeped back -SMITH: How did you feel. I'm sorry, go ahead?
AUBURN: I went back to my wife and told her we won. And we decided to go out to
dinner.
SMITH: I would think so. This was only your second full length play. That is, frankly,
amazing.
AUBURN: Right. My first play was done in '97 off Broadway. The people from the
theater that eventually produced "Proof" saw that and encouraged me to submit to them.
So that first play did lead pretty much directly to this one.
SMITH: Tell us a little about "Proof," what it deals with.
AUBURN: It's the story of a young woman, Katherine, who has spent years caring for
her father who is a brilliant mathematician, and her father began having various kinds of
mental illness problems. She gave up her life to care for him. When the play begins the
father died. She is sitting alone on the 25th birthday and wondering is this going to
happen to me. How much of my father's mental illness have I inherited and have I
inherited any of his talent as well? So the play is about a weekend in other life where she
is trying to sort that out and she is trying to deal with her sister, who's flown in from New
York and she has some plan's for Katherine's life. There is also a character who is a grad
student who is a protégé of the father's who is upstairs in the house looking through the
dad's papers hoping to find something he left behind. He also kind of has designs on
Katherine.
SMITH: David, why did you -- this is a four person play. Three of them are
mathematicians, why? Why mathematicians?
AUBURN: Well, I didn't start with the idea about writing about math but I had this idea
that the sisters who would start finding over something they found left behind after their
dad's death. Since I also had this idea about someone who was worried that they would
inheriting their parent's mental illness, I kind of went looking for the thing that the sisters
would find, and it seemed to me that a scientific document or a mathematical document
could be really interesting. I thought - you know -- its authorship could be called into
question in some interesting ways and the historical fact that a number of famous
mathematicians have suffered from mental illness kind of gave me the bridge to the other
idea about someone worried about their own mental state. So it just seemed to fit the
story that I wanted to tell.
SMITH: Did you feel any special burden to explain or make accessible the world of the
mathematician to the audience?
AUBURN: The real trick of writing the play was figuring out how much math to put in it.
This ended up being constrained by the story. Since there is a mystery as to who wrote
the mathematical proof, I sort of had to withdraw information when I could so that I
didn't give away the solution to the mystery but I did try to get in as much kind of lore
about the mathematical profession as I could. In that I was helped a lot by reading
popular books and spending time with mathematicians. We even had some come in to
meet and talk with the cast and talk to them, so that was really the fun part of doing the
play, getting as much of the kind of world of mathematics into the play as possible and
putting it up on stage.
SMITH: As you suggested earlier the essential tension is between the daughter and her
late father and her fear, if that is the right word, is it, that along with his possible, his
insanity she may have inherited his brilliance?
AUBURN: Sure, I think in a way the play is dealing in a heightened way with emotions
that a lot of people feel about their families - that I think everyone in some ways both
worries and hopes to be like their family, to inherit traits they admire and also to avoid
being in some ways -- following in patterns that may be they don't like as much. So,
"Proof" kind of deals with that question in a slightly exaggerated or heightened way. But
I think if there is a reason why the play is connected with audiences, that might be the
reason.
SMITH: How did you get in the business of writing plays?
AUBURN: I started in college. I didn't know I wanted to be a writer but I got into a
student troupe that did comedy reviews. We did sketch reviews in the style of Second
City kind of thing. and I started writing sketches, and I found out I liked doing it and I
could do it. And the sketches kind of gradually got longer and longer. And pretty soon I
had written a play. I kept going from there. I moved to New York and started trying to
writing plays and getting them put on in tiny theaters and eventually I got into the Julliard
play writing program which was a great kind of incubator - when you're starting out -- it
enabled me to write some write plays and have them read by wonderful actors at Julliard.
And, you know, just gradually developed enough material and met enough people that by
the time I had written a full-length play, I could -- someone could help me put it on.
SMITH: Did this play come easily or was it a long labor?
AUBURN: It was a little bit of both. The first draft came very fast and the whole plot and
structure of the play was there from the beginning. I knew what was going to happen in
the story and what was going to happen in every scene. So that came quickly then going
back through it and really figuring out the relationship between the characters and sort of
putting some meat on the bones of the play that I -- the first draft that I had written that
took a long time. I probably -- it was probably about nine months or something like that
before I had a draft that's substantially like the draft that is in performance now.
SMITH: What is next for you? Is it another play? A screenplay, what is next?
AUBURN: Well, right now I'm doing a screen play adaptation of a novel for a movie
company, which is interesting work, but it's not my story. And I hope in months I'll write
a new play. With any luck that will happen.
SMITH: So we'll get to see a little more of David Auburn on the stage.
AUBURN: That's my hope.
SMITH: That's great. Thank you very much, David Auburn and congratulations again.
AUBURN: Thanks a lot.
-- from http://www.pbs.org/newshour/bb/media/jan-june01/auburn_04-20.html#
Robert Osserman, of the Mathematical Association of
America, interviews David Auburn
By Gerald L. Alexanderson
The play Proof, as everyone associated with mathematics must know by now, has been
an enormous success on Broadway. Now it has begun a national tour at the Curran
Theatre in San Francisco. To mark the occasion the Mathematical Sciences Research
Institute (MSRI) at Berkeley arranged to have the playwright, David Auburn, interviewed
by Robert Osserman on stage at the theatre two days after the play opened its month-long
San Francisco run, on November 29. The San Francisco Chronicle reported a $2 million
advance ticket sale. Not bad for a play about mathematics and mental illness!
MSRI has arranged events of this kind before, an interview with George V. Coyne, S.J.,
Director of the Vatican Observatory, and the actor Michael Winters, on the occasion of a
Bay Area production of Brecht's Galileo, and an interview with Tom Stoppard about his
play Arcadia. Previous settings for these interviews have been the Berkeley Repertory
Theatre and Hertz Hall on the UC Berkeley campus. The Curran is quite another matter, a
large and elegant house, built in the 1920's, and home traditionally to traveling companies
of Broadway musicals. Never before has there been so much mathematical talk heard in
the lobby and in the auditorium.
Auburn is not a well-known name in the theatre like Brecht or Stoppard, at least not until
Proof, which was his second full-length play. From an initial off-Broadway run at the
Manhattan Theatre Club it moved up Broadway to the Walter Kerr Theatre and now to a
national tour, after picking up the Joseph Kesselring Prize, the Pulitzer Prize, the Drama
Desk Award, and the Tony Award for Best Play of 2001. The New York run continues.
One of Osserman's opening questions concerned Auburn's background. He attended the
University of Chicago where he studied political philosophy and where his formal
mathematical education ended with calculus. But he had an interest in theatre and wrote
sketches in the tradition of Second City and a one-act play while still in college. After
graduating he went to New York and worked for a chemical company writing copy for
labels for a carpet shampoo! And then he attended Juilliard, acting and writing until he
decided to give up acting.
Proof is a play about a young woman who had taken care of her mathematician-father for
several years prior to his death that came after a long bout with mental illness. Auburn
was asked whether he had planned from the beginning to write about a mathematician.
He did not. He started out by being interested in the question of whether mental illness, as
well as talent, can be inherited — the mathematical connections came later.
As part of the interview Osserman and Auburn read two provocative and very amusing
passages from the play (Osserman played Catherine, the young woman, and Auburn
played Hal, a young protégé of Catherine's father). The passages touched on various
misconceptions (or are they?) about mathematicians — (1) that it is a young man's
profession (and here we emphasize the word "man"), (2) that there is something that
predisposes mathematicians to mental instability, and (3) that only brilliant results count
in mathematics and that less exalted research and teaching (high school teaching is
referred to as a sign of failure) are lesser activities, to be eschewed by those in the lofty
realms of the highest level of mathematical research.
Catherine in the play has been trained (up to a certain point) as a mathematician, so a
question is raised and tackled in the play — can a woman really do highly original work?
The lack of a woman on the list of Fields Medalists and the appearance only a few years
ago of the first woman to place among the top five in the Putnam Competition — both of
these were cited in the discussion. Clearly, in this area at least, perceptions have changed
in the last decade or two. Then the question arose: whether the mathematical life is really
all over at the age of 40 (as is implied by the tradition in awarding Fields Medals).
Osserman pointed out that though great original breakthroughs might be seen more often
in the young, mathematicians continue to carry on productive lives into their 50s, 60s and
70s. The idea that what really matters in mathematics is the highest level research
probably still dominates the thinking in many circles.
Auburn touched on all of these questions. He described mathematics as a remarkable
subculture. But how did he find out so much about the culture without having seriously
studied mathematics? It became clear that he has read a lot and has considerable
familiarity with the biographies of Erdos, Nash, Ramanujan, and others. He was asked
why the principal character is a woman and he responded that a man would not be
expected to stay home to take care of an ailing father.
There are a few claims made in the play that one might question — the level of drug use
among mathematicians, for example, obviously something suggested by one of the Erdos
biographies. Occasionally there are bits of mathematics. At the mention of Sophie
Germain, Hal recalls, after a slight hesitation, Germain primes and Catherine blurts out
"92,305 x 216,998 + 1". Hal is startled that she seems to know this, but then Catherine
claims that it is the largest one known — not so, though it may have been at the time of
the action of the play, which is left ambiguous in the printed version. (According to the
web page, http://www.utm.edu/research/primes/lists/top20/SophieGermain.html, the
largest Germain prime is 109433307 x 266452 – 1.)
Osserman raised the question of whether Auburn was consciously aware of the parallel
between Arcadia and Proof. In both plays there is a very clever young woman who has
remarkable insights into mathematics and is "mentored," in a way, by a slightly older
man who is well-trained in mathematics but much less original in his thinking. Auburn
appeared unaware of the parallel but admitted to being an admirer of Stoppard and his
plays. But when asked whether he was strongly influenced by Stoppard, he said that he
was more influenced by the people who wrote sketches years ago, like Mike Nichols and
Elaine May, and by John Guare and David Mamet.
A much discussed aspect of Proof has been made even more interesting of late with the
imminent appearance of the film, A Beautiful Mind, based, we understand, quite loosely
on the biography of John Forbes Nash by Sylvia Nasar. What about this connection
between insanity and mathematics? Is it really true that a special kind of person is drawn
to mathematics? Auburn had said earlier that he was fascinated by the "romantic quality
of mathematical work," the solitary worker in an attic somewhere (obviously an idea
inspired by Andrew Wiles) working on a problem and coming up with something entirely
original. He also said that mathematicians have rather edgy personalities and they make
leaps of the mind that most people just cannot make. So he thinks there may be some
kind of causal relationship between being a mathematician and suffering from a mental
breakdown. Osserman cited four people whom he considers to be "romantic" figures in
mathematics: Hypatia, Galois, Turing and van Heijenoort. Their stories are well-known
to a mathematical audience — but others could be added to this short list: Abel and
Ramanujan (if Hardy was a good judge) come to mind. But not one of these could be
viewed as being insane — eccentric in one or two cases, maybe, but not insane.
Osserman cited a study that ranked various professions by the numbers of adherents to
the field who have also suffered from mental illness. Poets ranked at the top of the list.
People in the creative arts are two or three times as likely to suffer from psychosis as
scientists (mathematicians were not cited separately), according to K. R. Jamison in
Touched with Fire. Auburn said he had read of enough cases to justify writing his play
about mathematicians. Besides, people are used to hearing about mad scientists. Who
would want to read about a perfectly sane scientist? Osserman responded by saying they
might want to read about mad poets.
Those who have seen the excerpts of Proof on the Tony Awards or the interview on the
Charlie Rose Show with the Tony Award winning star, Mary-Louise Parker, from the
New York cast, may not realize how funny this play is. The excerpts at the Curran were
read to a very receptive audience. They picked up every joke.
So what will the author do next? He said he has decided not to follow Proof with another
mathematical play. He's working on two projects, one on the Spanish Civil War and the
other on twentieth-century spiritualism, including Houdini!
Meanwhile, until he produces another mathematical play, watch the MSRI website for the
next event in this series, an interview with Michael Frayn, author of Copenhagen, the
play about Niels Bohr and Werner Heisenberg which won the Tony Award for Best Play
the previous year. That play opens at the Curran in San Francisco in January.
--from http://www.maa.org/features/proof.html
David Auburn: Broadway’s Rising Star
by Jennifer Kiger
Just over two years ago most theatergoers had not heard of David Auburn, but that all
changed in the blink of an eye because of one play—Proof. In May 2000 the Manhattan
Theatre Club premiered what was only Auburn’s second full-length play. Proof was an
instant hit with audiences and critics. The production was transferred quickly to
Broadway, where it earned award after award, including the 2001 Tony for Best Play and
the Pulitzer Prize for Drama. Pretty good for someone writing only his second full-length
play, but as is the case in most success stories, Auburn did not reach the top overnight.
Born in Chicago, David Auburn was reared in the Midwest, moving from Ohio to
Arkansas. He returned to the University of Chicago where he earned a degree in English
Literature while working with a group that performed improvisational and sketch
comedy. Auburn began writing short comic scenes for the group. Eventually, the sketches
got longer and Auburn produced a one-act with the help of his friends at school. In his
final year at the University of Chicago, Auburn applied for a writing fellowship with
Steven Spielberg’s Amblin Entertainment. He had not planned on a career in writing, but
he won the fellowship and soon he was off to Los Angeles to write screenplays.
Once the fellowship ended, Auburn was faced with a choice. Should he stay in L.A. as a
struggling screenwriter, or should he make a go of it in New York? The theatre held more
interest for Auburn, and as he relocated to New York, he made a commitment to be a
playwright. A succession of “boring day jobs” followed as Auburn formed a theater
company with friends and continued to write.
After producing his own work in small venues, he joined the playwriting program at
Juilliard. For the first time, he received professional feedback on his work from worldclass mentors like Christopher Durang and Marsha Norman. “In the eight years it took to
begin to earn any money from playwriting, there was always a lot of doubt. I had all the
troubles that most writers have trying to build a career, trying to figure it out. I thought,
‘Can I do this? Am I going to wind up sorry that I did this, in ten years?’”
Juilliard provided the young writer with support and validation. It also gave him the
opportunity to develop his work with the help of strong actors. “Having actors as good as
those at Juilliard do your work forces you to think seriously about how professional
actors will approach the material you write. That was one of the best things about the
program—learning what kinds of questions actors ask when they approach a new script
and being able to think through those problems before you get into rehearsal. That was
invaluable.”
His first full-length play, Skyscraper, was produced Off-Broadway in 1997. The
production had a short run, but representatives from the Manhattan Theatre Club caught
it. They invited Auburn to submit his next play. That play was Proof.
Auburn had written Skyscraper as a student at Juilliard. It was more of an abstract piece,
one that focused on form and concept. As he prepared to write Proof, Auburn decided to
try a different kind of writing. He wanted to concentrate on character and work in a more
naturalistic palette. “I don’t know if the cliché of ‘finding your voice’ is true, but I felt
like the direction I wanted to work in was a less absurd, more realistic mode, which is
what Proof is. Once I arrived at that, it felt very good. It felt like the right direction for
me.”
He wrote Proof while in London in 1998. He had moved there with his future wife,
Frances Rosenfeld, who was researching her doctorate in history. Although three of the
four characters in Proof are mathematicians and the plot concerns the authorship of a
scientific document, the play did not begin there. “I started with the idea of two sisters
fighting over something that a parent had left behind after [his] death and the idea of a
character worried about inheriting [her] parent’s mental illness.”
Auburn searched for the subject of the sisters’ conflict. He wanted an item whose
authorship could be called into question and decided that a mathematical proof would
serve the drama nicely. When he started writing the play, math was foreign to him. He
read biographies and surveys on the history of mathematics, and he consulted with
mathematicians. “The most challenging part of the play was finding a balance between
the math and the story. I would probably have liked to add more mathematical
information, but that was really constrained by the plot. Catherine is so reluctant to reveal
herself. There’s a limit to how much she can talk about her work. I wanted to find the
right amount so that [the math] was convincing and plausible, but not so much that
Catherine’s motivations no longer made sense.” The result is an utterly accessible,
poignant drama that navigates the passions of the human heart with humor and
intelligence.
Proof will be the most produced contemporary play this year (29 productions are planned
throughout the US, nine in Canada and more are planned around the globe). Meanwhile,
David Auburn is grateful for the success of Proof, but he is not resting on his laurels. He
is currently working on a new play, a screenplay and a libretto for an opera. Also, he and
his wife recently welcomed an addition to their family: their first child, a daughter. “I try
not to ask broader questions about the shape of my career at this point. I am grateful to
have the opportunity to do the work I want to do with a certain amount of freedom. I
think that is an unusual blessing, and I’m just trying to do that work.”
From SCR's January 2003 SubSCRiber Newsletter.
Quotes excerpted from "A Conversation with David Auburn, Moderated by Christian
Parker" published in The Dramatist Magazine, May-June 2002 and from a telephone
interview with David Auburn conducted by Jennifer Kiger in December 2002.
The Winner’s Circle:
some of the awards that “Proof” has won to date
•
2001 Tony Awards®:
2001 Tony Award®, Best Play -- Written by David Auburn; Produced by
Manhattan Theatre Club (Lynn Meadow, Artistic Director; Barry Grove,
Executive Producer), Roger Berlind, Carole Shorenstein Hays, Jujamcyn
Theaters (James H. Binger: Chairman; Rocco Landesman: President; Paul
Libin: Producing Director; Jack Viertel: Creative Director), OSTAR
Enterprises, Daryl Roth, Stuart Thompson
2001 Tony Award®, Best Actress in a Play -- Mary-Louise Parker
2001 Tony Award®, Best Direction of a Play -- Daniel Sullivan
2001 Tony Award® Nominees, Best Featured Actor in a Play -- Larry
Bryggman, Ben Shenkman
2001 Tony Award® Nominee, Best Featured Actress in a Play -- Johanna
Day
•
2001 Pulitzer Prize for Drama – David Auburn
•
2001 Drama Desk Awards:
Outstanding Play
Proof
Best Actress in a Play
Mary-Louise Parker, Proof
•
2001 New York Drama Critics Circle Awards:
Best American Play: Proof by David Auburn
•
2000–2001 Outer Critics Circle Awards:
Broadway Play -- Proof
Actress in a Play -- Mary-Louise Parker, Proof
John Gassner Playwrighting Award -- David Auburn, Proof
HISTORY OF THE PRIZES
In the latter years of the 19th century, Joseph Pulitzer stood out as the very embodiment
of American journalism. Hungarian-born, an intense indomitable figure, Pulitzer was the
most skillful of newspaper publishers, a passionate crusader against dishonest
government, a fierce, hawk-like competitor who did not shrink from sensationalism in
circulation struggles, and a visionary who richly endowed his profession. His innovative
New York World and St. Louis Post-Dispatch reshaped newspaper journalism. Pulitzer
was the first to call for the training of journalists at the university level in a school of
journalism. And certainly, the lasting influence of the Pulitzer Prizes on journalism,
literature, music, and drama is to be attributed to his visionary acumen. In writing his
1904 will, which made provision for the establishment of the Pulitzer Prizes as an
incentive to excellence, Pulitzer specified solely four awards in journalism, four in letters
and drama, one for education, and four traveling scholarships. In letters, prizes were to go
to an American novel, an original American play performed in New York, a book on the
history of the United States, an American biography, and a history of public service by
the press. But, sensitive to the dynamic progression of his society Pulitzer made provision
for broad changes in the system of awards. He established an overseer advisory board and
willed it "power in its discretion to suspend or to change any subject or subjects,
substituting, however, others in their places, if in the judgment of the board such
suspension, changes, or substitutions shall be conducive to the public good or rendered
advisable by public necessities, or by reason of change of time." He also empowered the
board to withhold any award where entries fell below its standards of excellence. The
assignment of power to the board was such that it could also overrule the
recommendations for awards made by the juries subsequently set up in each of the
categories. Since the inception of the prizes in 1917, the board, later renamed the Pulitzer
Prize Board, has increased the number of awards to 21 and introduced poetry, music, and
photography as subjects, while adhering to the spirit of the founder's will and its intent.
The board typically exercised its broad discretion in 1997, the 150th anniversary of
Pulitzer's birth, in two fundamental respects. It took a significant step in recognition of
the growing importance of work being done by newspapers in online journalism.
Beginning with the 1999 competition, the board sanctioned the submission by
newspapers of online presentations as supplements to print exhibits in the Public Service
category. The board left open the distinct possibility of further inclusions in the Pulitzer
process of online journalism as the electronic medium developed. The other major
change was in music, a category that was added to the Plan of Award for prizes in 1943.
The prize always had gone to composers of classical music. The definition and entry
requirements of the music category beginning with the 1998 competition were broadened
to attract a wider range of American music. In an indication of the trend toward bringing
mainstream music into the Pulitzer process, the 1997 prize went to Wynton Marsalis's
"Blood on the Fields," which has strong jazz elements, the first such award. In music, the
board also took tacit note of the criticism leveled at its predecessors for failure to cite two
of the country's foremost jazz composers. It bestowed a Special Award on George
Gershwin marking the 1998 centennial celebration of his birth and Duke Ellington on his
1999 centennial year.
Over the years the Pulitzer board has at times been targeted by critics for awards made or
not made. Controversies also have arisen over decisions made by the board counter to the
advice of juries. Given the subjective nature of the award process, this was inevitable.
The board has not been captive to popular inclinations. Many, if not most, of the honored
books have not been on bestseller lists, and many of the winning plays have been staged
off-Broadway or in regional theaters. In journalism the major newspapers, such as The
New York Times, The Wall Street Journal, and The Washington Post, have harvested
many of the awards, but the board also has often reached out to work done by small,
little-known papers. The Public Service award in 1995 went to The Virgin Islands Daily
News, St. Thomas, for its disclosure of the links between the region's rampant crime rate
and corruption in the local criminal justice system. In letters, the board has grown less
conservative over the years in matters of taste. In 1963 the drama jury nominated Edward
Albee's Who's Afraid of Virginia Woolf?, but the board found the script insufficiently
"uplifting," a complaint that related to arguments over sexual permissiveness and rough
dialogue. In 1993 the prize went to Tony Kushner's "Angels in America: Millennium
Approaches," a play that dealt with problems of homosexuality and AIDS and whose
script was replete with obscenities. On the same debated issue of taste, the board in 1941
denied the fiction prize to Ernest Hemingway's For Whom the Bell Tolls, but gave him
the award in 1953 for The Old Man and the Sea, a lesser work. Notwithstanding these
contretemps, from its earliest days, the board has in general stood firmly by a policy of
secrecy in its deliberations and refusal to publicly debate or defend its decisions. The
challenges have not lessened the reputation of the Pulitzer Prizes as the country's most
prestigious awards and as the most sought-after accolades in journalism, letters, and
music. The Prizes are perceived as a major incentive for high-quality journalism and have
focused worldwide attention on American achievements in letters and music.
The formal announcement of the prizes, made each April, states that the awards are made
by the president of Columbia University on the recommendation of the Pulitzer Prize
board. This formulation is derived from the Pulitzer will, which established Columbia as
the seat of the administration of the prizes. Today, in fact, the independent board makes
all the decisions relative to the prizes. In his will Pulitzer bestowed an endowment on
Columbia of $2,000,000 for the establishment of a School of Journalism, one-fourth of
which was to be "applied to prizes or scholarships for the encouragement of public,
service, public morals, American literature, and the advancement of education." In doing
so, he stated: "I am deeply interested in the progress and elevation of journalism, having
spent my life in that profession, regarding it as a noble profession and one of unequaled
importance for its influence upon the minds and morals of the people. I desire to assist in
attracting to this profession young men of character and ability, also to help those already
engaged in the profession to acquire the highest moral and intellectual training." In his
ascent to the summit of American journalism, Pulitzer himself received little or no
assistance. He prided himself on being a self-made man, but it may have been his
struggles as a young journalist that imbued him with the desire to foster professional
training.
JOSEPH PULITZER, 1847–1911
Joseph Pulitzer was born in Mako, Hungary on April 10, 1847, the son of a wealthy grain
merchant of Magyar-Jewish origin and a German mother who was a devout Roman
Catholic. His younger brother, Albert, was trained for the priesthood but never attained it.
The elder Pulitzer retired in Budapest and Joseph grew up and was educated there in
private schools and by tutors. Restive at the age of seventeen, the gangling 6'2" youth
decided to become a soldier and tried in turn to enlist in the Austrian Army, Napoleon's
Foreign Legion for duty in Mexico, and the British Army for service in India. He was
rebuffed because of weak eyesight and frail health, which were to plague him for the rest
of his life. However, in Hamburg, Germany, he encountered a bounty recruiter for the
U.S. Union Army and contracted to enlist as a substitute for a draftee, a procedure
permitted under the Civil War draft system. At Boston he jumped ship and, as the legend
goes, swam to shore, determined to keep the enlistment bounty for himself rather than
leave it to the agent. Pulitzer collected the bounty by enlisting for a year in the Lincoln
Cavalry, which suited him since there were many Germans in the unit. He was fluent in
German and French but spoke very little English. Later, he worked his way to St. Louis.
While doing odd jobs there, such as muleteer, baggage handler, and waiter, he immersed
himself in the city's Mercantile Library, studying English and the law. His great career
opportunity came in a unique manner in the library's chess room. Observing the game of
two habitues, he astutely critiqued a move and the players, impressed, engaged Pulitzer in
conversation. The players were editors of the leading German language daily, Westliche
Post, and a job offer followed. Four years later, in 1872, the young Pulitzer, who had
built a reputation as a tireless enterprising journalist, was offered a controlling interest in
the paper by the nearly bankrupt owners. At age 25, Pulitzer became a publisher and
there followed a series of shrewd business deals from which he emerged in 1878 as the
owner of the St. Louis Post-Dispatch, and a rising figure on the journalistic scene.
Earlier in the same year, he and Kate Davis, a socially prominent Washingtonian woman,
were married in the Protestant Episcopal Church. The Hungarian immigrant youth - once
a vagrant on the slum streets of St. Louis and taunted as "Joey the Jew" - had been
transformed. Now he was an American citizen and as speaker, writer, and editor had
mastered English extraordinarily well. Elegantly dressed, wearing a handsome, reddishbrown beard and pince-nez glasses, he mixed easily with the social elite of St. Louis,
enjoying dancing at fancy parties and horseback riding in the park. This lifestyle was
abandoned abruptly when he came into the ownership of the St. Louis Post-Dispatch.
James Wyman Barrett, the last city editor of The New York World, records in his
biography Joseph Pulitzer and His World how Pulitzer, in taking hold of the PostDispatch, "worked at his desk from early morning until midnight or later, interesting
himself in every detail of the paper." Appealing to the public to accept that his paper was
their champion, Pulitzer splashed investigative articles and editorials assailing
government corruption, wealthy tax-dodgers, and gamblers. This populist appeal was
effective, circulation mounted, and the paper prospered. Pulitzer would have been pleased
to know that in the conduct of the Pulitzer Prize system which he later established, more
awards in journalism would go to exposure of corruption than to any other subject.
Pulitzer paid a price for his unsparingly rigorous work at his newspaper. His health was
undermined and, with his eyes failing, Pulitzer and his wife set out in 1883 for New York
to board a ship on a doctor-ordered European vacation. Stubbornly, instead of boarding
the steamer in New York, he met with Jay Gould, the financier, and negotiated the
purchase of The New York World, which was in financial straits. Putting aside his serious
health concerns, Pulitzer immersed himself in its direction, bringing about what Barrett
describes as a "one-man revolution" in the editorial policy, content, and format of The
World. He employed some of the same techniques that had built up the circulation of the
Post-Dispatch. He crusaded against public and private corruption, filled the news
columns with a spate of sensationalized features, made the first extensive use of
illustrations, and staged news stunts. In one of the most successful promotions, The
World raised public subscriptions for the building of a pedestal at the entrance to the New
York harbor so that the Statue of Liberty, which was stranded in France awaiting
shipment, could be emplaced.
The formula worked so well that in the next decade the circulation of The World in all its
editions climbed to more than 600,000, and it reigned as the largest circulating newspaper
in the country. But unexpectedly Pulitzer himself became a victim of the battle for
circulation when Charles Anderson Dana, publisher of The Sun, frustrated by the success
of The World launched vicious personal attacks on him as "the Jew who had denied his
race and religion." The unrelenting campaign was designed to alienate New York's
Jewish community from The World. Pulitzer's health was fractured further during this
ordeal and in 1890, at the age of 43, he withdrew from the editorship of The World and
never returned to its newsroom. Virtually blind, having in his severe depression
succumbed also to an illness that made him excruciatingly sensitive to noise, Pulitzer
went abroad frantically seeking cures. He failed to find them, and the next two decades of
his life he spent largely in soundproofed "vaults," as he referred to them, aboard his
yacht, Liberty, in the "Tower of Silence" at his vacation retreat in Bar Harbor Maine, and
at his New York mansion. During those years, although he traveled very frequently,
Pulitzer managed, nevertheless, to maintain the closest editorial and business direction of
his newspapers. To ensure secrecy in his communications he relied on a code that filled a
book containing some 20,000 names and terms. During the years 1896 to 1898 Pulitzer
was drawn into a bitter circulation battle with William Randolph Hearst's Journal in
which there were no apparent restraints on sensationalism or fabrication of news. When
the Cubans rebelled against Spanish rule, Pulitzer and Hearst sought to outdo each other
in whipping up outrage against the Spanish. Both called for war against Spain after the
U.S. battleship Maine mysteriously blew up and sank in Havana harbor on February 16,
1898. Congress reacted to the outcry with a war resolution. After the four-month war,
Pulitzer withdrew from what had become known as "yellow journalism." The World
became more restrained and served as the influential editorial voice on many issues of the
Democratic Party. In the view of historians, Pulitzer's lapse into "yellow journalism" was
outweighed by his public service achievements. He waged courageous and often
successful crusades against corrupt practices in government and business. He was
responsible to a large extent for passage of antitrust legislation and regulation of the
insurance industry. In 1909, The World exposed a fraudulent payment of $40 million by
the United States to the French Panama Canal Company. The federal government lashed
back at The World by indicting Pulitzer for criminally libeling President Theodore
Roosevelt and the banker J.P. Morgan, among others. Pulitzer refused to retreat, and The
World persisted in its investigation. When the courts dismissed the indictments, Pulitzer
was applauded for a crucial victory on behalf of freedom of the press. In May 1904,
writing in The North American Review in support of his proposal for the founding of a
school of journalism, Pulitzer summarized his credo: "Our Republic and its press will rise
or fall together. An able, disinterested, public-spirited press, with trained intelligence to
know the right and courage to do it, can preserve that public virtue without which popular
government is a sham and a mockery. A cynical, mercenary, demagogic press will
produce in time a people as base as itself. The power to mould the future of the Republic
will be in the hands of the journalists of future generations."
In 1912, one year after Pulitzer's death aboard his yacht, the Columbia School of
Journalism was founded, and the first Pulitzer Prizes were awarded in 1917 under the
supervision of the advisory board to which he had entrusted his mandate. Pulitzer
envisioned an advisory board composed principally of newspaper publishers. Others
would include the president of Columbia University and scholars, and "persons of
distinction who are not journalists or editors." In 2000 the board was composed of two
news executives, eight editors, five academics including the president of Columbia
University and the dean of the Columbia Graduate School of Journalism, one columnist,
and the administrator of the prizes. The dean and the administrator are nonvoting
members. The chair rotates annually to the most senior member. The board is selfperpetuating in the election of members. Voting members may serve three terms of three
years. In the selection of the members of the board and of the juries, close attention is
given to professional excellence and affiliation, as well as diversity in terms of gender,
ethnic background, geographical distribution, and in the choice of journalists and size of
newspaper.
THE ADMINISTRATION OF THE PULITZER PRIZES
More than 2,000 entries are submitted each year in the Pulitzer Prize competitions, and
only 21 awards are normally made. The awards are the culmination of a year-long
process that begins early in the year with the appointment of 102 distinguished judges
who serve on 20 separate juries and are asked to make three nominations in each of the
21 categories. By February 1, the Administrator's office in the Columbia School of
Journalism has received the journalism entries -in 2004, typically 1,423. Entries for
journalism awards may be submitted by any individual from material appearing in a
United States newspaper published daily, Sunday, or at least once a week during the
calendar year. In early March, 77 editors, publishers, writers, and educators gather in the
School of Journalism to judge the entries in the 14 journalism categories. From 19641999 each journalism jury consisted of five members. Due to the growing number of
entries in the public service, investigative reporting, beat reporting, feature writing and
commentary categories, these juries were enlarged to seven members beginning in 1999.
The jury members, working intensively for three days, examine every entry before
making their nominations. Exhibits in the public service, cartoon, and photography
categories are limited to 20 articles, cartoons, or pictures, and in the remaining categories,
to 10 articles or editorials - except for feature writing, which has a maximum of five
articles. In photography, a single jury judges both the Breaking News category and the
Feature category. Since the inception of the prizes the journalism categories have been
expanded and repeatedly redefined by the board to keep abreast of the evolution of
American journalism. The cartoons prize was created in 1922. The prize for photography
was established in 1942, and in 1968 the category was divided into spot or breaking news
and feature. With the development of computer-altered photos, the board stipulated in
1995 that "no entry whose content is manipulated or altered, apart from standard
newspaper cropping and editing, will be deemed acceptable."
These are the Pulitzer Prize category definitions for the 2004 competition:
1. For a distinguished example of meritorious public service by a newspaper through the
use of its journalistic resources which may include editorials, cartoons, and photographs,
as well as reporting.
2. For a distinguished example of local reporting of breaking news.
3. For a distinguished example of investigative reporting by an individual or team,
presented as a single article or series.
4. For a distinguished example of explanatory reporting that illuminates a significant and
complex subject, demonstrating mastery of the subject, lucid writing and clear
presentation.
5. For a distinguished example of beat reporting characterized by sustained and
knowledgeable coverage of a particular subject or activity.
6. For a distinguished example of reporting on national affairs.
7. For a distinguished example of reporting on international affairs, including United
Nations correspondence.
8. For a distinguished example of feature writing giving prime consideration to high
literary quality and originality.
9. For distinguished commentary.
10. For distinguished criticism.
11. For distinguished editorial writing, the test of excellence being clearness of style,
moral purpose, sound reasoning, and power to influence public opinion in what the writer
conceives to be the right direction.
12. For a distinguished cartoon or portfolio of cartoons published during the year,
characterized by originality, editorial effectiveness, quality of drawing, and pictorial
effect.
13. For a distinguished example of breaking news photography in black and white or
color, which may consist of a photograph or photographs, a sequence or an album.
14. For a distinguished example of feature photography in black and white or color,
which may consist of a photograph or photographs, a sequence or an album.
While the journalism process goes forward, shipments of books totaling some 800 titles
are being sent to five letters juries for their judging in these categories:
• For distinguished fiction by an American author, preferably dealing with American
life.
• For a distinguished book upon the history of the United States.
• For a distinguished biography or autobiography by an American author.
• For a distinguished volume of original verse by an American author.
• For a distinguished book of non-fiction by an American author that is not eligible for
consideration in any other category.
The award in poetry was established in 1922 and that for non-fiction in 1962. Unlike the
other awards which are made for works in the calendar year, eligibility in drama extends
from March 2 to March 1, and in music from January 16 to January 15. The drama jury of
four critics and one academic attend plays both in New York and the regional theaters.
The award in drama goes to a playwright but production of the play as well as script are
taken into account.
The music jury, usually made up of four composers and one newspaper critic, meet in
New York to listen to recordings and study the scores of pieces, which in 2004
numbered 82. The category definition states:
For distinguished musical composition by an American that has had its first performance
or recording in the United States during the year.
The final act of the annual competition is enacted in early April when the board
assembles in the Pulitzer World Room of the Columbia School of Journalism. In prior
weeks, the board had read the texts of the journalism entries and the 15 nominated books,
listened to music cassettes, read the scripts of the nominated plays, and attended the
performances or seen videos where possible. By custom, it is incumbent on board
members not to vote on any award under consideration in drama or letters if they have
not seen the play or read the book. There are subcommittees for letters and music whose
members usually give a lead to discussions. Beginning with letters and music, the board,
in turn, reviews the nominations of each jury for two days. Each jury is required to offer
three nominations but in no order of preference, although the jury chair in a letter
accompanying the submission can broadly reflect the views of the members. Board
discussions are animated and often hotly debated. Work done by individuals tends to be
favored. In journalism, if more than three individuals are cited in an entry, any prize goes
to the newspaper. Awards are usually made by majority vote, but the board is also
empowered to vote 'no award,' or by three-fourths vote to select an entry that has not been
nominated or to switch nominations among the categories. If the board is dissatisfied with
the nominations of any jury, it can ask the Administrator to consult with the chair by
telephone to ascertain if there are other worthy entries. Meanwhile, the deliberations
continue.
Both the jury nominations and the awards voted by the board are held in strict confidence
until the announcement of the prizes, which takes place about a week after the meeting in
the World Room. Towards three o'clock p.m. (Eastern Time) of the day of the
announcement, in hundreds of newsrooms across the United States, journalists gather
about news agency tickers to wait for the bulletins that bring explosions of joy and
celebrations to some and disappointment to others. The announcement is made precisely
at three o'clock after a news conference held by the administrator in the World Room.
Apart from accounts carried prominently by newspapers, television, and radio, the details
appear on the Pulitzer Web site. The announcement includes the name of the winner in
each category as well as the names of the other two finalists. The three finalists in each
category are the only entries in the competition that are recognized by the Pulitzer office
as nominees. The announcement also lists the board members and the names of the jurors
(which have previously been kept confidential to avoid lobbying.)
A gold medal is awarded to the winner in Public Service. Along with the certificates in
the other categories, there are cash awards of $10,000, raised in 2002 from $7,500. Four
Pulitzer fellowships of $7,500 each are also awarded annually on the recommendation of
the faculty of the School of Journalism. They enable three of its outstanding graduates to
travel, report, and study abroad and one fellowship is awarded to a graduate who wishes
to specialize in drama, music, literary, film, or television criticism. For most recipients of
the Pulitzer prizes, the cash award is only incidental to the prestige accruing to them and
their works. There are numerous competitions that bestow far larger cash awards, yet
which do not rank in public perception on a level with the Pulitzers. The Pulitzer
accolade on the cover of a book or on the marquee of a theater where a prize-winning
play is being staged usually does translate into commercial gain.
The Pulitzer process initially was funded by investment income from the original
endowment. But by the 1970s the program was suffering a loss each year. In 1978 the
advisory board established a foundation for the creation of a supplementary endowment,
and fund raising on its behalf continued through the 1980s. The program is now
comfortably funded with investment income from the two endowments and the $50 fee
charged for each entry into the competitions. The investment portfolios are administered
by Columbia University. Members of the Pulitzer Prize Board and journalism jurors
receive no compensation. The jurors in letters, music, and drama, in appreciation of their
year-long work, receive honoraria, raised to $2,000, effective in 1999.
Unlike the elaborate ceremonies and royal banquets attendant upon the presentation of
the Nobel Prizes in Stockholm and Oslo, Pulitzer winners receive their prizes from the
president of Columbia University at a modest luncheon in May in the rotunda of the Low
Library in the presence of family members, professional associates, board members, and
the faculty of the School of Journalism. The board has declined offers to transform the
occasion into a television extravaganza.
The Who's Who of Pulitzer Prize Winners is more than simply a roster of names and
biographical data. It is a list of people in journalism, letters, and music whose
accomplishments enable researchers to trace the historical evolution of their respective
fields and the development of American society. We are indebted to Joseph Pulitzer for
this and an array of other contributions to the quality of our lives.
Seymour Topping was Administrator of The Pulitzer Prizes and Professor of
International Journalism at the Graduate School of Journalism of Columbia University
from 1993 to 2002. After serving in World War II, Professor Topping worked for 10
years for The Associated Press as a correspondent in China, Indochina, London, and
Berlin. He left The Associated Press in 1959 to join The New York Times, where he
remained for 34 years, serving as a foreign correspondent, foreign editor, managing
editor, and editorial director of the company's 32 regional newspapers. In 1992-1993 he
served as president of the American Society of Newspaper Editors. He is a graduate of
the School of Journalism at the University of Missouri.
Adapted from Who's Who of Pulitzer Prize Winners by Elizabeth A. Brennan and
Elizabeth C. Clarage, copyright 1999 by The Oryx Press. Used with permission from The
Oryx Press, 4041 N. Central Ave., Suite 700 Phoenix, AZ 85012, 800 279-6799.
www.oryxpress.com.
Math's Hidden Woman
the true story of Sophie Germain, an 18th-century woman who
assumed a man's identity in order to pursue her passion -attempting to prove Fermat's Last Theorem
From FERMAT'S ENIGMA: The Epic Quest to Solve the World's Greatest Mathematical
Problem
by Simon Singh
Published by Walker and Company
Pythagoras' theorem leads to one of the best understood equations in mathematics:
x2 + y2 = z2
There are many whole number solutions to this equation, e.g.,
32+ 42= 52
In the 17th century the French mathematician Pierre de Fermat set a challenge for future
generations of mathematicians -- prove that there are no whole number solutions for the
following closely related family of equations:
x3 + y3 = z3
x4 + y4 = z4
x5 + y5 = z5
x6 + y6 = z6
etc.
Although these equations appear similar to Pythagoras' equation, Fermat's Last Theorem
claims that these equations have no solutions. The difficulty in proving that this is the
case revolves around the fact that there are an infinite number of equations, and an
infinite number of possible values for x, y, and z. The proof has to prove that no solutions
exist within this infinity of infinities. Nonetheless, Fermat claimed he had a proof. The
proof was never written down, so the challenge has been to rediscover the proof of
Fermat's Last Theorem.
Monsieur Le Blanc
By the beginning of the 19th century, Fermat's Last Theorem had already established
itself as the most challenging problem in number theory. Mathematicians had merely
succeeded in showing that there are no solutions to the following equations:
x3 + y3 = z3
x4 + y4 = z4
An infinite number of other equations remained, and mathematicians still had to
demonstrate that none of these had any solutions. There was no progress until a young
French woman reinvigorated the pursuit of Fermat's lost proof.
Sophie Germain was born on April 1, 1776 the daughter of a merchant, AmbroiseFrancois Germain. Outside of her work, her life was to be dominated by the turmoil of
the French Revolution. The year she discovered her love of numbers, the Bastille was
stormed, and her study of calculus was shadowed by the Reign of Terror.
Although her father was financially successful, Sophie's family members were not of the
aristocracy. Had she been born into high society, her study of mathematics might have
been more acceptable. Although aristocratic women were not actively encouraged to
study mathematics, they were expected to have sufficient knowledge of the subject in
order to be able to discuss the topic should it arise during polite conversation.
To this end, a series of text books were written to help young women understand the
latest developments in mathematics and science. Francesco Algarotti was the author of
Sir Isaac Newton's Philosophy Explain'd for the Use of Ladies. Because Algarotti
believed that women were only interested in romance, he attempted to explain Newton's
discoveries through the flirtatious dialogue between a Marquise and her interlocutor. The
interlocutor outlines the inverse square law of gravitational attraction, whereupon the
Marquise gives her own interpretation on this fundamental law of physics. "I cannot help
thinking ... that this proportion in the squares of the distances of places ... is observed
even in love. Thus after eight days absence, love becomes 64 time less than it was the
first day."
Not surprisingly, this gallant genre of books was not responsible for inspiring Sophie
Germain's interest in mathematics. The event that changed her life occurred one day
when she was browsing in her father's library and chanced upon Jean-Étienne Montucla's
book History of Mathematics. The chapter that caught her imagination was Montucla's
essay on the life of Archimedes. His account of Archimedes' discoveries was
undoubtedly interesting, but what particularly kindled her fascination was the story
surrounding his death.
Archimedes had spent his life at Syracuse studying mathematics in relative tranquillity,
but when he was in his late 70s, the peace was shattered by the invading Roman army.
Legend had it that, during the invasion, Archimedes was so engrossed in the study of a
geometric figure in the sand that he failed to respond to the questioning of a Roman
soldier. As a result, he was speared to death.
Germain concluded that if somebody could be so consumed by a geometric problem that
it could lead to their death, then mathematics must be the most captivating subject in the
world. She immediately set about teaching herself the basics of number theory and
calculus, and soon she was working late into the night studying the works of Euler and
Newton. But this sudden interest in such an unfeminine subject worried her parents and
they tried desperately to deter her. A friend of the family, Count Guglielmo LibriCarrucci dalla Sommaja, wrote how Sophie's father confiscated her candles and clothes
and removed any heating in order to discourage her.
Only a few years later in Britain the young mathematician Mary Somerville would also
have her candles confiscated by her father who maintained that "we must put a stop to
this, or we shall have Mary in a straitjacket one of these days." In Germain's case, she
responded by maintaining a secret cache of candles and wrapping herself in bed-clothes.
Libri-Carrucci claimed that the winter nights were so cold that the ink froze in the
inkwell, but Sophie continued regardless. She was described by some people as shy and
awkward, but undoubtedly she was also immensely determined. Eventually, her parents
relented and gave Sophie their blessing.
Germain never married and throughout her career her father funded her research and
supported her efforts to break into the community of mathematicians. For many years,
this was the only encouragement she received. There were no mathematicians in the
family who could introduce her to the latest ideas and her tutors refused to take her
seriously.
In 1794, the Ecole Polytechnique opened in Paris. It was founded as an academy of
excellence to train mathematicians and scientists for the nation. This would have been an
ideal place for Germain to develop her mathematical skills, except for the fact that it was
an institution reserved only for men. Her natural shyness prevented her from confronting
the academy's governing body, so instead she resorted to covertly studying at the Ecole
by assuming the identity of a former student at the academy, Monsieur Antoine-August
Le Blanc.
The academy's administration was unaware that the real Monsieur Le Blanc had left
Paris, and continued to print lecture notes and problems for him. Germain managed to
obtain what was intended for Le Blanc, and each week she would submit answers to the
problems under her new pseudonym.
Everything was going according to plan until the supervisor of the course, Joseph-Louis
Lagrange, could no longer ignore the brilliance of Monsieur Le Blanc's answer sheets.
Not only were Monsieur Le Blanc's solutions marvelously ingenious but they showed a
remarkable transformation in a student who had previously been notorious for his
abysmal mathematical skills. Lagrange, who was one of the finest mathematicians of the
nineteenth century, requested a meeting with the reformed student and Germain was
forced to reveal her true identity. Lagrange was astonished and pleased to meet the young
woman, and became her mentor and friend. At last Sophie Germain had a teacher who
could inspire her, and with whom she could be open about her skills and ambitions.
Germain grew in confidence and she moved from solving problems in her course work to
studying unexplored areas of mathematics. Most importantly, she became interested in
number theory and inevitably she came to hear of Fermat's Last Theorem. She worked on
the problem for several years, eventually reaching the stage where she believed she had
made an important breakthrough. She needed to discuss her ideas with a fellow number
theorist and decided that she would go straight to the top and consult the greatest number
theorist in the world, the German mathematician Carl Friedrich Gauss.
Gauss is widely acknowledged as being the most brilliant mathematician who has ever
lived. Germain had first encountered his work through studying his masterpiece
Disquisitiones arithmeticae, the most important and wide-ranging treatise since Euclid's
Elements. Gauss's work influenced every area of mathematics, but strangely enough he
never published anything on Fermat's Last Theorem.
In one letter he even displayed contempt for the problem. His friend the German
astronomer Heinrich Olbers had written to Gauss encouraging him to compete for a prize
which had been offered by the Paris Academy for a solution to Fermat's challenge: "It
seems to me, dear Gauss, that you should get busy about this." Two weeks later Gauss
replied, "I am very much obliged for your news concerning the Paris prize. But I confess
that Fermat's Last Theorem as an isolated proposition has very little interest for me, for I
could easily lay down a multitude of such propositions, which one could neither prove
nor disprove."
Gauss was entitled to his opinion, but Fermat had clearly stated that a proof existed.
Historians suspect that, in the past, Gauss had tried and failed to make any impact on the
problem, and his response to Olbers was merely a case of intellectual sour grapes.
Nonetheless, when he received Germain's letters, he was sufficiently impressed by her
breakthrough that he temporarily forgot his ambivalence towards Fermat's Last Theorem.
Germain had adopted a new approach to the problem which was far more general than
previous strategies. Her immediate goal was not to prove that one particular equation had
no solutions, but to say something about several equations. In her letter to Gauss she
outlined a calculation which focused on those equations in which n is equal to a particular
type of prime number.
Prime numbers are those numbers which have no divisors. For example, 11 is a prime
number because 11 has no divisors, i.e. nothing will divide into 11 without leaving a
remainder (except for 11 and 1). On the other hand, 12 is not a prime number because
several numbers will divide into 12, i.e., 2, 3, 4, and 6. Germain was interested in those
prime numbers p such that 2p + 1 is also a prime number. Germain's list of primes
includes 5, because 11 (2 x 5 + 1) is also prime, but it does not include 13, because 27 (2
x 13 + 1) is not prime.
For values of n equal to these Germain primes, she could show that there were probably
no solutions to the equation:
xn + yn = zn
By "probably" Germain meant that it was unlikely that any solutions existed, because if
there was a solution, then either x, y, or z would be a multiple of n. This put a very tight
restriction on any solutions. Her colleagues examined her list of primes one by one,
trying to prove that x, y, or z could not be a multiple of n, therefore showing that for that
particular value of n there could be no solutions.
Germain's work on Fermat's Last Theorem was to be her greatest contribution to
mathematics, but initially she was not credited for her breakthrough. When Germain
wrote to Gauss she was still in her 20s, and, although she had gained a reputation in Paris,
she feared that the great man would not take her seriously because of her gender. In order
to protect herself Germain resorted once again to her pseudonym, signing her letters as
Monsieur Le Blanc.
Her fear and respect for Gauss is shown in one of her letters to him: "Unfortunately, the
depth of my intellect does not equal the voracity of my appetite, and I feel a kind of
temerity in troubling a man of genius when I have no other claim to his attention than an
admiration necessarily shared by all his readers." Gauss, unaware of his correspondent's
true identity, attempted to put Germain at ease and replied: "I am delighted that
arithmetic has found in you so able a friend."
Germain's contribution would have been forever wrongly attributed to the mysterious
Monsieur Le Blanc were it not for the Emperor Napoleon. In 1806, Napoleon was
invading Prussia and the French army was storming through one German city after
another. Germain feared that the fate that befell Archimedes might also take the life of
her other great hero Gauss, so she sent a message to her friend, General Joseph-Marie
Pernety, asking that he guarantee Gauss's safety. The general was not a scientist, but even
he was aware of the world's greatest mathematician, and, as requested, he took special
care of Gauss, explaining to him that he owed his life to Mademoiselle Germain. Gauss
was grateful but surprised, for he had never heard of Sophie Germain.
The game was up. In Germain's next letter to Gauss she reluctantly revealed her true
identity. Far from being angry at the deception, Gauss wrote back to her with delight:
But how to describe to you my admiration and astonishment at seeing my esteemed
correspondent Monsieur Le Blanc metamorphose himself into this illustrious personage
who gives such a brilliant example of what I would find it difficult to believe. A taste for
the abstract sciences in general and above all the mysteries of numbers is excessively
rare: one is not astonished at it: the enchanting charms of this sublime science reveal
only to those who have the courage to go deeply into it. But when a person of the sex
which, according to our customs and prejudices, must encounter infinitely more
difficulties than men to familiarize herself with these thorny researches, succeeds
nevertheless in surmounting these obstacles and penetrating the most obscure parts of
them, then without doubt she must have the noblest courage, quite extraordinary talents
and superior genius.
Sophie Germain's correspondence with Carl Gauss inspired much of her subsequent work
but, in 1808, the relationship ended abruptly. Gauss had been appointed Professor of
Astronomy at the University of Göttingen, his interest shifted from number theory to
more applied mathematics, and he no longer bothered to return Germain's letters. Without
her mentor, her confidence began to wane and within a year she abandoned pure
mathematics.
Although she made no further contributions to proving Fermat's Last Theorem, others
were to build on her work. She had offered hope that those equations in which n equals a
Germain prime could be tackled, however the remaining values of n remained intractable.
After Fermat, Germain embarked on an eventful career as a physicist, a discipline in
which she would again excel only to be confronted by the prejudices of the
establishment. Her most important contribution to the subject was "Memoir on the
Vibrations of Elastic Plates," a brilliantly insightful paper which was to lay the
foundations for the modern theory of elasticity.
As a result of this research and her work on Fermat's Last Theorem, she received a medal
from the Institut de France and became the first woman, who was not a wife of a
member, to attend lectures at the Academy of Sciences. Then, towards the end of her life,
she re-established her relationship with Carl Gauss, who convinced the University of
Göttingen to award her an honorary degree. Tragically, before the university could
bestow the honor upon her, Sophie Germain died of breast cancer.
H.J. Mozans, an historian and author of Women in Science, said of Germain:
All things considered, she was probably the most profoundly intellectual woman that
France has ever produced. And yet, strange as it may seem, when the state official came
to make out her death certificate, he designated her as a "rentière-annuitant" (a single
woman with no profession) -- not as a "mathématicienne." Nor is this all. When the Eiffel
Tower was erected, there was inscribed on this lofty structure the names of seventy-two
savants. But one will not find in this list the name of that daughter of genius, whose
researches contributed so much toward establishing the theory of the elasticity of metals
-- Sophie Germain. Was she excluded from this list for the same reason she was ineligible
for membership in the French Academy -- because she was a woman? If such, indeed,
was the case, more is the shame for those who were responsible for such ingratitude
toward one who had deserved so well of science, and who by her achievements had won
an enviable place in the hall of fame.
http://www.pbs.org/wgbh/nova/proof/germain.html
Theater Review:
A Common Heart and Uncommon Brain
By Bruce Weber
Published: May 24, 2000
Have you noticed how many well-educated characters are holding forth on New York
stages?
The physicists of ''Copenhagen,'' the accomplished playwright of ''The Real Thing,'' the
literati of ''The Designated Mourner'' -- all are challenging, and charming, audiences with
the force of intellect. Lyman Felt, the self-justifying bigamist of ''The Ride Down Mount
Morgan,'' makes his case with the well-reasoned eloquence of a philosopher, and even in
a romantic comedy like ''Dirty Blonde,'' the lead male character is a film historian. Forrest
Gumpism may still be alive in the land, but one thing this spate of excellent plays
reminds us is that learning is desirable, not least because it enriches the emotions. In case
you've forgotten, intellectuals are people too.
Happily, this trend is being perpetuated with ''Proof,'' an exhilarating and assured new
play by David Auburn that turns the esoteric world of higher mathematics literally into a
back porch drama, one that is as accessible and compelling as a detective story. The play,
which opened yesterday at the Manhattan Theater Club, is fundamentally a mystery about
the authorship of a particularly important proof, a mystery that is solved in the end; it is
also, however, about the unravelable enigma of genius, and the toll it can take on those
who are beset with it, aspire to it or merely live in its vicinity.
In that service, the play takes great pains to depict the study of mathematics as a painful
joy, not as the geek-making obsession of stereotype, but as human labor, both ennobling
and humbling, by people who, like musicians or painters (or playwrights), can envision
an elusive beauty in the universe and are therefore both enlivened by its pursuit and
daunted by the commitment. It does this not by showing them at work but by showing
them trying to live and cope when they can't, won't or simply aren't, and in so doing
makes the argument that mathematics is a business for the common heart as well as the
uncommon brain.
As directed by Daniel Sullivan and performed by an exemplary cast, ''Proof'' has the pace
of a psychological thriller, and if its resolution (''lumpy'' rather than elegant, to use a word
that one character uses to describe the titular proof) tilts toward the sentimental, the
characters deserve to be hopeful. As one woman exiting the theater ahead of me said to
her companion, ''It's like 'Copenhagen' with a happy ending,'' an oversimplified review,
perhaps, but in spirit, close enough.
At the center of the play is Catherine, a young woman who is about to bury her father, a
once-great mathematician at the University of Chicago whose final years were beset by
madness. Played with stirring unsettledness by Mary-Louise Parker, Catherine has
inherited her father's handwriting, his humor and, to an indeterminate degree, both his
genius and illness.
''A taste for the mysteries of numbers is excessively rare,'' the German mathematician
Karl Friedrich Gauss wrote to Sophie Germain, a gifted young French woman, some 200
years ago. Catherine has the letter memorized. Its acknowledgment that such a
predilection is particularly rare in women is a source of pride and inspiration to her, but it
makes her fearful as well; she has witnessed firsthand the jumble that mathematics can
make of a working brain. Having quit her own studies years earlier to care for her father,
she is, as we see her first on the eve of the funeral -- and her 25th birthday -- at the
intersection of a haunting past and blank future. Drinking cheap champagne from the
bottle on the back porch of the house she now lives in alone -- to anyone who knows
Chicago, John Lee Beatty's staunch, brick set will locate the play precisely -- she is
disheveled, bitter, immobilized by depression.
Ms. Parker is immediately vivid as Catherine, a woman whose sense of defeat is both
circumstantial and self-imposed, someone who is aware she has both brain power and sex
appeal in spades but trusts neither enough to exhibit them.
She is herself only with her father (Larry Bryggman), who appears intermittently in both
flashbacks and dreams, dramatically risky scenes that are skillfully integrated into the
narrative by Mr. Auburn and performed by Mr. Bryggman and Ms. Parker with the sad -and occasionally droll -- resignation of people holding onto a lifeline of mutual
understanding.
Eloquently snappish in her self-pity, Catherine is, with everyone else, an intimidating
presence, except that her body language, in Ms. Parker's performance, can't help but be a
fetching plea for salvation. Her inner conflict determinedly keeps at bay her wellmeaning sister, Claire, a nonmathematician (she didn't get the family's more troublesome
genes) who, as played with a fine blend of anger and concern by Johanna Day, is
understandably exasperated by her sister's obstinate antics and wants to sell the house and
bring Catherine back with her to New York where she won't be alone with her demons.
Fortunately for Catherine, she is being courted, shyly but insistently, by Hal Dobbs (Ben
Shenkman), a former student of her father's who has been going through the great man's
notebooks hoping to find unpublished revelations that may be masked by deranged
scribbling. Perhaps conditioned by his chosen profession, Hal doesn't accede to rejection
readily, or maybe he doesn't recognize it; he is moved by Catherine as much as he was by
her father. In a role written both to acknowledge and debunk the stereotype of the socially
inept math nerd, Mr. Shenkman wonderfully evokes the hesitant charm of a young man
whose self-awareness tells him that he is more than brainy but less than suave.
Do Catherine and Hal belong together? That, pardon the expression, is a complex
equation for any two people to solve. As their mutual affection and trust waxes and
wanes over the course of an autumn weekend, the issue of genius -- who has it and what
does it portend? -- turns out to be the elusive variable.
But ultimately this is emotional math, the sort that everyone and no one understands.
Without any baffling erudition -- if you know what a prime number is, there won't be a
single line of dialogue you find perplexing -- the play presents mathematicians as both
blessed and bedeviled by the gift for abstraction that ties them achingly to one another
and separates them, also achingly, from concrete-minded folks like you and me. And
perhaps most satisfying of all, it does so without a moment of meanness. ''Proof'' reaches
into remote cerebral terrain and finds -- guess what? -- good people. Intelligence a virtue?
Q.E.D.
PROOF
By David Auburn; directed by Daniel Sullivan; sets by John Lee Beatty; costumes by
Jess Goldstein; lighting by Pat Collins; sound by John Gromada; production stage
manager, James Harker; production manager, Michael R. Moody; associate artistic
director, Michael Bush; general manager, Harold Wolpert. Presented by Manhattan
Theater Club, Lynne Meadow, artistic director; Barry Grove, executive director. At City
Center, Stage 1, 131 West 55th Street, Manhattan.
WITH: Larry Bryggman (Robert), Mary-Louise Parker (Catherine), Ben Shenkman (Hal)
and Johanna Day (Claire).
http://theater2.nytimes.com/mem/theater/treview.html?html_title=&tols_title=PROOF%2
0(PLAY)&pdate=20000524&byline=By%20BRUCE%20WEBER&id=1077011431186
Upcoming Movie
a film adaptation of “Proof”
Based on the Pulitzer Prize-winning play by David Auburn, “Proof” follows a devoted
daughter (Paltrow) who comes to terms with the death of her father (Hopkins) a brilliant
mathematician whose genius was crippled by mental insanity -- and is forced to face her
own long-harbored fears and emotions. She adjusts to his death with the help of one of
her father’s former mathematical students (Gyllenhaal) who searches through her father’s
notebooks in the hope of discovering a bit of his old brilliance. While coming to terms
with the possibility that his genius, which she has inherited, may come at a painful price,
her estranged sister (Davis) arrives to help settle their father’s affairs.
Genres: Drama
Running Time:
MPAA Rating: PG-13 for some sexual content, language and drug references.
Distributor: Miramax Films
Cast and Credits
Starring:
Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal, Hope Davis, Gary Houston
Directed by:
John Madden
Produced by:
John N Hart, Jeffrey Sharp, Alison Owen
A Mathematician’s Apology
by G.H. Hardy
As David Auburn was writing Proof, he ran across G.H. Hardy’s A Mathematician’s
Apology (Cambridge University Press, 1967). A layman’s guide to the world of
mathematics, the book provides insight into the creativity of mathematicians. Like artists,
mathematicians often work in isolation, and they hold themselves and their work up to
high aesthetic standards. They find beauty in patterns while searching for truth. The
following passages are excerpts from Hardy’s book.
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more
permanent than theirs, it is because they are made with ideas. A painter makes patterns
with shapes and colors, a poet with words.... A mathematician on the other hand, has no
material to work with but ideas, so his patterns are likely to last longer, since ideas wear
less with time than with words.
In [proofs] there is a very high degree of unexpectedness, combined with inevitability and
economy. The arguments take so odd and surprising a form; the weapons used seem so
childishly simple when compared with the far-reaching results; but there is no escape
from the conclusions. …A mathematical proof should resemble a simple and clear-cut
constellation, not a scattered cluster in the Milky Way....
I have never done anything ‘useful.’ No discovery of mine has made, or is likely to make,
directly or indirectly, for good or ill, the least difference to the amenity of the world. I
have helped to train other mathematicians, but mathematicians of the same kind as
myself, and their work has been, so far at any rate as I have helped them to do it, as
useless as my own. Judged by all practical standards, the value of my mathematical life is
nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a
verdict of complete triviality, that I may be judged to have created something worth
creating. And that I have created something is undeniable: the question is about its
value....
The case for my life, then, or for that of any one else who has been a mathematician in
the same sense in which I have been one, is this: that I have added something to
knowledge, and helped others to add more; and that these somethings have a value which
differs in degree only, and not in kind, from that of the creations of the great
mathematicians, or of any of the other artists, great or small, who have left some kind of
material behind them.
(From SCR’s January 2003 SubSCRiber Newsletter)
http://www.scr.org/season/02-03season/studyguides/proof/apology.html
A Mathematical Glossary
Prime number
A prime number is a natural number that has no integer factors other than itself and 1.
The smallest prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41.
An integer is a real number that does not include a fractional part. The natural numbers
are also called positive integers, and the integers smaller than zero are called negative
integers. …, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, …
Imaginary number
An imaginary number is the form ni, where n is a real number that is being multiplied by
the imaginary number i, and i is defined by the equation i2 = -1.
Since the product of any two real numbers with the same sign will be positive (or zero),
there is no way that you can find any real number that, when multiplied by itself, will
give you a negative number. Therefore, the imaginary numbers need to be introduced to
provide solutions for equations that require taking the square roots of negative numbers.
Imaginary numbers are needed to describe certain equations in some branches of
physics, such as quantum mechanics. However, any measurable quantity, such as energy,
momentum, or length, will always be represented by a real number.
Game theory
This area of mathematics is applied to fields such as economics and military strategy in
which conflicting interests work against each other based on potential gains and losses.
Algabraic geometry
Algebra is the study of the properties of operations carried out on sets of numbers.
Algebra is a generalization of arithmetic in which symbols, usually letters, are used to
stand for numbers. The structure of algebra is based upon axioms (or postulates), which
are statements that are assumed to be true. The axioms are then used to prove theorems
about the properties of operations on numbers.
Euclidian geometry describes the geometry of our everyday world. One postulate of
Euclidian geometry describes the behavior of parallel lines and says that if two parallel
lines were extended forever, they would never intersect. This postulate seems intuitively
clear, but nobody has been able to prove it after several centuries of trying. Since we
cannot travel to infinity to verify that the two seemingly parallel lines never intersect, we
cannot tell whether this postulate really is satisfied in our universe.
Some mathematicians decided to investigate what would happen to geometry if they
changed the parallel postulate. They found that they were able to prove theorems in their
new type of geometry. These theorems were consistent because no two theorems
contradicted each other, but the geometry that resulted was different from the geometry
developed by Euclid.
Non-Euclidian geometries play an important role in the development of relativity theory.
They are also important because they shed light on the nature of logical systems.
Algebraic geometry is the branch of mathematics that uses the tools of both geometry
and algebra to address questions such as the famous Fermat’s Last Theorem.
Fermat’s Last Theorem states that there is no solution for the equation an + bn = cn
where a,b,c and n are all positive integers, and n >2
The theorem acquired its name because Fermat mentioned the theorem and claimed to
have discovered a proof of it, but did not have space to write it down. Nobody has ever
discovered a counter-example, but it has turned out to be very difficult to prove this
theorem. Over the years several proofs have been proposed, but closer analysis has
revealed they have flaws. Prior to being proved, this statement should more properly be
called a conjecture rather than a theorem. In 1993 Andrew Wiles proposed a proof,
which started a worldwide effort to verify that the proof was correct.
Sophie Germain
This 18th century French mathematician attended school and wrote proofs under a man’s
name, Monsieur Le Blanc, because women were not regarded as scholars at that time.
One of her most notable accomplishments is the discovery of a new set of prime
numbers which are now known as Germain primes.
Germain primes
The next number member of this set of primes discovered by Sophie Germain can be
found by doubling the previous prime and adding one. For example, 2 is prime, 2 double
equals four, plus one equals five, which is also a prime.
Proof
A proof is a sequence of statements that show a particular theorem to be true. In the
course of a proof it is permissible to use only axioms (postulates) or theorems that have
been previously proved.
According to Hardy (1999, pp. 15-16), "all physicists, and a good many quite respectable
mathematicians, are contemptuous about proof. I have heard Professor Eddington, for
example, maintain that proof, as pure mathematicians understand it, is really quite
uninteresting and unimportant, and that no one who is really certain that he has found
something good should waste his time looking for proof.... [This opinion], with which I
am sure that almost all physicists agree at the bottom of their hearts, is one to which a
mathematician ought to have some reply."
To prove Hardy's assertion, Feynman is reported to have commented, "A great deal more
is known than has been proved" (Derbyshire 2004, p. 291).
There is some debate among mathematicians as to just what constitutes a proof. The fourcolor theorem is an example of this debate, since its "proof" relies on an exhaustive
computer testing of many individual cases which cannot be verified "by hand." While
many mathematicians regard computer-assisted proofs as valid, some purists do not.
http://mathworld.wolfram.com/Proof.html
Infinity
Infinity represents a limitless quantity. It would take you forever to count an infinite
number of objects. There is an infinite number of numbers. The opposite of infinite is
finite.
Lithium
This powerful medication is often used in the treatment of manic depression.
Elliptical curves
A component of algebraic geometry, this field is connected to several different areas,
including number theory.
Number theory
Number theory is the study of properties of the natural numbers. One aspect of number
theory focuses on prime numbers. For example, it can be easily proven that there are an
infinite number of prime numbers. Suppose, for example, that p was the largest prime
number. Then, form a new number equal to one plus the product of all the prime
numbers from 2 up to p. This number will not be divisible by any of these prime
numbers (and, therefore, not by any composite number formed by multiplying these
primes together) and will therefore be prime. This contradicts the assumption that p is
the largest prime number. There are still unsolved problems involving the frequency of
occurrence of prime numbers.
The introduction of computers has made it possible to verify that a proposition works for
very large numbers, but no computer can count all the way to infinity so the computer is
no substitute for a formal proof if you need to know that a theorem is always true.
Gauss
Carl Freidrich Gauss (1777 to 1855) was a German mathematician and astronomer who
studied errors of measurement (so the normal curve is sometimes called the Gaussian
error curve); developed a way to contruct a 17-sided regular polygon with geometric
construction; developed a law that says the electric flux over a closed surface is
proportional to the charge inside the surface (this law is now included as one of
Maxwell’s equations); and studied the theory of complex numbers. The Gauss-Jordan
Elimination is a method for solving a system of linear equations.
http://www.scr.org/season/02-03season/studyguides/proof/glossary.html
Mathematical Quotes
"We arrive at truth, not by reason only, but also by the heart."
Blaise Pascal (1623-1662)
"Mathematics is often erroneously referred to as the science of common sense. Actually,
it may transcend common sense and go beyond either imagination or intuition. It has
become a very strange and perhaps frightening subject from the ordinary point of view,
but anyone who penetrates into it will find a veritable fairyland, a fairyland which is
strange, but makes sense, if not common sense."
E. and Newman, J. Kasner. Mathematics and the Imagination, New York: Simon and
Schuster, 1940.
"Mathematics is not a careful march down a well cleared highway, but a
journey into a strange wilderness, where explorers often get lost."
W. S. Anglin
http://gateways2learning.com/Quotes.htm
Dictionary Definitions
m-w.com – Main Entry: proof
Pronunciation: 'prüf
Function: noun
Etymology: Middle English, alteration of preove, from Old French preuve, from Late
Latin proba, from Latin probare to prove -- more at PROVE
1.
a: the cogency of evidence that compels acceptance by the mind of a truth or a fact
b: the process or an instance of establishing the validity of a statement especially
by derivation from other statements in accordance with principles of reasoning
2. obsolete : EXPERIENCE
3. something that induces certainty or establishes validity
4. archaic : the quality or state of having been tested or tried; especially : unyielding
hardness
5. evidence operating to determine the finding or judgment of a tribunal
6.
a: plural proofs or proof : a copy (as of typeset text) made for examination or
correction
b: a test impression of an engraving, etching, or lithograph
c: a coin that is struck from a highly-polished die on a polished planchet, is not
intended for circulation, and sometimes differs in metallic content from coins of identical
design struck for circulation
d: a test photographic print made from a negative
7. a test applied to articles or substances to determine whether they are of standard or
satisfactory quality
8.
a: the minimum alcoholic strength of proof spirit
b : strength with reference to the standard for proof spirit; specifically: alcoholic
strength indicated by a number that is twice the percent by volume of alcohol present
<whiskey of 90 proof is 45% alcohol>
oed.com: proof
A. Illustration of Forms.
() 3 preoue, 4 proeue, prieve, 4-5 pref, preef, 4-6 prefe, preve, Sc. preiff, 5 proef,
preff(e, preeff, preyf, prewe, 5-6 prief(e, preif, 6 preife, pryef, preeue, pryve, Sc.
prieff; 8-9 arch. prief, dial. preef, prief, preif.
() 4-5 prooff, 4-5 prof, proff, Sc. pruf(f, 4-6 proue, profe, Sc. prowe, 5-6 proufe, ffe, prove, prooue, 5-7 proofe, proffe, Sc. prufe, 6 prooffe, 7 Sc. pruife, 5- proof. (Sc.
pruife, etc. (Y, ø).) pl. proofs; also 4-7 proues, 5 prouves, 5-7 proves, 6-7 prooves.
B. Signification.
I. From PROVE v. in the sense of making good, or showing to be true.
1.
a. That which makes good or proves a statement; evidence sufficient (or
contributing) to establish a fact or produce belief in the certainty of something. to make
proof: to have weight as evidence (obs.).
b. Law. (generally) Evidence such as determines the judgement of a tribunal. Also
spec. (a) A written document or documents so attested as to form legal evidence. (b)
A written statement of what a witness is prepared to swear to. (c) The evidence which
has been given in a particular case, and entered on the court records. (See also 3.)
c. A person who gives evidence; a witness: = EVIDENCE n. 7. Obs. (After 1500
only Sc.)
2. The action, process, or fact of proving, or establishing the truth of, a statement; the
action of evidence in convincing the mind; demonstration.
3. Sc. Law. Evidence given before a judge, or a commissioner representing him, upon a
record or an issue framed in pleading; the taking of such evidence by a judge in order to a
trial; hence, trial before a judge instead of by a jury. This distinctive development of
sense has gradually taken place since the introduction of trial by jury into Scotland in
1815.
II. From PROVE v. in the sense of trying or testing.
4.
a. The action or an act of testing or making trial of anything, or the condition of
being tried; test, trial, experiment; examination, probation; assay. Often in phrases to
bring, put, set, etc. (something) in, on, to (the, a) proof.
b. Arith. An operation serving to test or check the correctness of an arithmetical
calculation.
(Sometimes understood as in sense 2.)
5. The action or fact of passing through or having experience of something; also,
knowledge derived from this; experience. Obs.
6. A trial, attempt, essay, endeavour. Obs.
7. That which anything proves or turns out to be; the issue, result, effect, fulfilment; esp.
in phrase to come to proof. Obs.
8. esp. The fact, condition, or quality of proving good, turning out well, or producing
good results; thriving; good condition, good quality; goodness, substance. Now only dial.
9.
a. The testing of cannon or small fire-arms by firing a heavy charge, or by
hydraulic pressure. proof of (gun) powder, the testing of the propulsive force of
gunpowder.
b. A place for testing fire-arms or explosives.
10.
a. The condition of having successfully stood a test, or the capability of doing so;
proved or tested power; orig. of armour and arms, whence transf. and fig.:
impenetrability, invulnerability. arch. Often in phrase armour (etc.) of proof: cf.
PROOF a. 1; at the proof, so as to be proof; to the proof, to the utmost, in the highest
degree. proof of lead or shot (cf. PROOF a. 1), the quality of being proof against leaden
bullets.
b. Proof armour. Hist.
c. The process of stiffening hats and rendering them waterproof. Cf. PROOF v. 2.
11. a. The standard of strength of distilled alcoholic liquors (or of vinegar); now, the
strength of a mixture of alcohol and water having a specific gravity of 0·91984, and
containing 0·495 of its weight, or 0·5727 of its volume, of absolute alcohol. Also transf.
Spirit of this strength.
b. In sugar-boiling: The degree of concentration at which the syrup will
successfully crystallize.
c. The aeration of dough by leaven before baking. Cf. PROVE v. 1g.
III. That which is produced as a test; a means or instrument for testing.
12. Typog. A trial or preliminary impression taken from composed type, in which
typographical errors may be corrected, and alterations and additions made. Applied esp.
to the first proof; a second or later one being called a revise: see REVISE n. 3; see also
quot. 1842.
13. a. Engraving. Originally, An impression taken by the engraver from an engraved
plate, stone, or block, to examine its state during the progress of his work; now applied to
each of a limited or arbitrary number of careful impressions made from the finished plate
before the printing of the ordinary issue, and usually before the inscription is added (in
full, proof before letter(s)). artist's or engraver's proof, a proof taken for examination or
alteration by the artist or engraver; signed proof, an early proof signed by the artist. letter
or lettered proof, a proof with the signatures of the artist and engraver, and the
inscription. marked, remarque, touched, trial, wax proof: see these words.
b. Photogr. A first or trial print taken from a plate; also used as equivalent to
PRINT (n. 13).
14. A coin or medal struck as a test of the die (obs.); also, one of a limited number of
early impressions of coins struck as specimens. These often have their edges left plain
and not milled; they may also be executed in a metal different from that used for the
actual coin.
15. An instrument, vessel, or the like for testing.
a. A surgeon's probe. Obs. rare0.
(Perhaps only an etymologizing invention of Cotgrave.)
b. (a) A test-tube. (b) An apparatus for testing the strength of gunpowder.
16. Typog. A definite number of ems placed in the composing-stick as a pattern of the
length of the line. Obs.
[The width of pages is expressed according to the number of ‘ems’. Encycl. Brit. 1888.]
17. Bookbinding. The rough uncut edges of the shorter or narrower leaves of a book, left
in trimming it to show that it has not been cut down.
IV.
18. attrib. and Comb.
a. General Combs. in senses 1-4, as proof needle, object, paper, passage, patch,
piece, test, text; proof-producing, proof-proof adjs.; in sense 4, as proof-test vb.; in sense
9, as proof-butts, -charge, -ground, -house, -master, -mortar (MORTAR n.1), -sleigh; in
senses 12-14, as proof coin, copy, proof-correct vb., to correct in proof, proofcorrecting, -correction, -corrector, -galley, impression, -plate (PLATE n. 6b), print, printer, -puller, -pulling, set, stage, state.
b. Special Combs.: proof-arm v. nonce-wd. [?back-formation from proof armour],
trans. to arm in or as in armour of proof; proof-favour, favour or goodwill strong as
armour of proof; proof-gallon, a gallon of proof-spirit; proof-glass, a deep cylindrical
glass for holding liquids while under test; proof-leaf, = PROOF-SHEET; also, the sheet
of paper by means of which coloured designs are transferred from the engraved plate to
the biscuit in pottery-making; proof-letter, a letter cast to test the accuracy of the typemould; proof load Mech., a load which a structure must be able to bear without
exceeding specified limits of deformation; loosely, proof stress; proof-man (Sc.), one
whose profession is to estimate the content of corn-stacks; proof-mark, (a) in testing
powder, a mark made on the ribbon by which the recoil is measured, showing the
strength of powder of the standard quality (obs.); (b) a mark impressed on a fire-arm to
show that it has passed the test; proof-plane, a small flat or disk-shaped conductor fixed
on an insulating handle, used in measuring the electrification of any body; proof-plug:
see quot.; proof-press, a press or machine used for taking proofs of type; proof-read v.
trans., to read (printer's proofs) and mark errors for correction; hence proof-read ppl. a.;
proof-reader, one whose business is to read through printer's proofs and mark errors for
correction; = READER 2b; so proof-reading vbl. n. and ppl. a.; proof-slip Typog. =
PROOF-SHEET; proof-sphere: see quot.; proof-staff, a metal straight-edge for testing
or adjusting the ordinary wooden instrument (Knight Dict. Mech. 1875); proof-stick, a
rod by means of which a sample of the contents of a vacuum sugar-boiler may be taken
without admitting air; proof strain Mech., the strain produced by the proof stress;
loosely, proof stress; proof strength, = sense 11; proof stress Mech., the stress required
to produce a specified permanent deformation of a material or structure; proof theory
(see quot. 1942); hence proof-theoretic a., of or pertaining to proof theory; prooftheoretically adv., in a proof-theoretic manner; proof timber: see quot.; proof vinegar,
vinegar of standard strength.
dictionary.com -- proof
( P ) Pronunciation Key (prf) n.
1. The evidence or argument that compels the mind to accept an assertion as true.
2.
a. The validation of a proposition by application of specified rules, as of
induction or deduction, to assumptions, axioms, and sequentially derived conclusions.
b. A statement or argument used in such a validation.
3.
a. Convincing or persuasive demonstration: was asked for proof of his identity;
an employment history that was proof of her dependability.
b. The state of being convinced or persuaded by consideration of evidence.
4. Determination of the quality of something by testing; trial: put one's beliefs to the
proof.
5. Law. The result or effect of evidence; the establishment or denial of a fact by
evidence.
6. The alcoholic strength of a liquor, expressed by a number that is twice the percentage
by volume of alcohol present.
7. Printing.
a. A trial sheet of printed material that is made to be checked and corrected. Also
called proof sheet.
b. A trial impression of a plate, stone, or block taken at any of various stages in
engraving.
8.
a. A trial photographic print.
b. Any of a limited number of newly minted coins or medals struck as specimens
and for collectors from a new die on a polished planchet.
9. Archaic. Proven impenetrability: “I was clothed in Armor of proof” (John Bunyan).