Women in Mathematics
Snezana Lawrence
MEI conference, July 2008
University of Hertfordshire
http://women.timesonline.co.uk/tol/life_and_styl
e/women/the_way_we_live/article4099034.ece
The four women
mathematicians
•
•
•
•
Emilie du Chatelet (1706-1749)
Maria Gaetana Agnesi (1718-1799)
Caroline Herschel (1750-1848)
Marie-Sophie Germain (1776-1831)
• And what is so special about women
doing mathematics…
Emilie du
Chatelet
• Gabrielle Emilie Le
Tonnelier de Breteuil,
marquise du Chatelet
• Born 17 Dec 1706 in
Paris
• Died 10 Sept 1749 in
Lunéville, France
• Remarkable upbringing
– as a child she learnt Latin and later Italian and
English, studied mathematics and was given
lessons in fencing, riding and gymnastics
• Married at 19 to Marquis Florent-Claude
Chatelet
• Prettly unremarkable marriage apart from the
fact that her husband not only didn’t mind
her having a very public affair with Voltaire,
but accepted Voltaire’s money to refurbish
the mansion at Cirey where Voltaire and
Emilie lived last ten years of her life.
• Voltaire wrote of their life together
I found in 1733 a young lady who felt more or less
as I did, and who resolved to spend several years
in the country to cultivate her mind, far from the
tumult of the world. It was the marquise Du
Châtelet, the woman who in all France had the
greatest disposition for all the sciences. ... Seldom
has so fine a mind and so much taste been united
with so much ardour for learning; but she also
loved the world and all the amusements of her age
and sex. Nevertheless she left all this to go and
bury herself in a dilapidated house on the frontiers
of Champagne and Lorraine, where the land was
very fertile and very ugly. She beautified the
house, to which she added pleasant gardens. I built
a gallery, in which I created a very fine collection
of scientific instruments. We had a large library.
• The relationship with the husband…
I also stopped at Cirey. It is a
rare sight. The two of them are
there alone, plunged in gaiety. One
writes verse in his corner, the
other triangles in hers.
writing to a friend upon return from
visiting Emilie and Voltaire
• Had three children, a daughter and a son - for
whom she later wrote popular treatise on
Newton’s Principia. After the birth of her
third child, a daughter, she died (was 43). At
the birth of the child, her husband, Voltaire
and her then lover, Jean-Francois de SaintLambert were all present. As the daughter
was born, she was
‘laid on a quarto book of geometry’
(reported by Voltaire)
• Chatelet on prejudice
I feel the full weight of the prejudice
which so universally excludes us from
the sciences; it is one of the
contradictions in life that has always
amazed me, seeing that the law allows
us to determine the fate of great
nations, but that there is no place
where we are trained to think ... Let
the reader ponder why, at no time in
the course of so many centuries, a good
tragedy, a good poem, a respected tale,
a fine painting, a good book on physics
has ever been produced by a woman…
Why these creatures whose understanding
appears in every way similar to that of
men, seem to be stopped by some
irresistible force, but until they do, women
will have reason to protest against their
education. ... I am convinced that many
women are either unaware of their talents
by reason of the fault in their education or
that they bury them on account of
prejudice for want of intellectual courage.
My own experience confirms this. Chance
made me acquainted with men of letters
who extended the hand of friendship to
me. ... I then began to believe that I was a
being with a mind ...
• Major work - translation of Newton’s
Principia (third edition 1731) into French
• Her remains the standard translation
• Wrote an extensive commentary in which she
gave her own description of the System of the
World, and analytical solutions to key
disputed aspects of Newton’s theory of
universal gravitation.
• Included mathematical summaries that
clarified and confirmed Newton’s application
of his theory to observed phenomena: AlexisClaude Clairaut’s on the shape of the Earth,
and Daniel Bernoulli’s on the effects of the
Sun and Moon on the tides.
• She worked on Newton’s translation from
1745 to her death in 1749
• Final version of the translation appeared only
in 1759
• Because she was writing for the young and
inexperienced researcher, her translation
contains explanation for all terms however
simple (for example orbit and ellipse)
• She refers to experiments and annotates her
explanations with citations to Newton’s
writings or others upon which she had drawn
What must be one of the first
mathematical jokes…
‘A Jesuit had told his Superior that he
had discovered spots on the Sun; the
Superior responded in a grave manner,
that is impossible, I have read Aristotle
two or three times, and I found nothing
like that in his book…’
• Well respected by her contemporaries
• In 1746, in the Journal Universel it was
noted that Emilie has been elected to the
Bologna Academy, and was described as
‘notre infatigable Marquise’
• Respect shown to her by the three men she
was surrounded with at her death also shows
unusual position she was in - genius is
forgiven the social trespasses
Description in contemporary
literature on Chatelet
‘Alone, after dinner. Through the long window
leading on to her terrace the low hills of eastern
France were barely visible in the dusk. She’d loved
this house, her home, but after a decade spent
with Francois, the man she’d lived for above all
others, their life together had begun to shatter.
In his place she’d thought she’d found a better
man, younger and more handsome, but then he
too had turned cool to her. She’d tried to avoid
admitting it at first… but his coldness never
ended: she was experienced with men, and knew
when passion was over…’
Maria Gaetana
Agnesi
• Born 16 May 1718
in Milan
• Died 9 Jan 1799
Milan
• Father Pietro, links with the University of
Bologna but not a professor as sometimes
reported, but silk merchant
• Pietro had twenty-one children with three
wives (not at the same time), Maria eldest.
• Education from young age, at 9 knew Latin
and published a discourse on the higher
education of women
• Cultural salon - Maria presents thesis on
various subjects and defends them in
disputation
• Maria Teresa her sister, meanwhile plays the
harpsichord (she became a composer)
• Parallels with Mozart?
• When 20 (1738) published Propositiones
Philosophicae - a series of essays on
philosophy and natural sciences. Contains 191
theses defeneded by Agnesi.
• Agnesi’s views on woman’s ability and fitness
to study sciences and the arts Propositiones’s main theme.
• Her thesis that woman are able to develop
faculties and practices involved in the
scientific enterprise as exemplified by the
notion of ‘attention’.
• Mathematics as only science and one in which
one can contemplate truths derived with
absolute certainty
• Teaching girls at the church of Santa
Caterina and in San Calimero
• Eventually became Priora della Dottrina
Cristiana (school director)
• Run a hospital for poor and ‘fallen’ women
until her death (increasingly devoted to this
and away from mathematics)
• Her major work adaptation of Newton’s work
Instituzioni analytiche ad uso della
gioventu italiana (analytic institutions for
the use of young Italians) published in 1748,
written in Italian.
• Agnesi’s translation of Newton
• Early systematisation of the techniques of
calculus
• Clearly written and as such in use for many
years
• Conceptually soon superseded
• Aimed at popular public
• First woman to publish a mathematical
book - and not any book - on an
esoteric branch of the mathematical
sciences
• Pope Benedict XIV appointed Agnesi
professor of mathematics at the
University of Bologna in 1750. Never
taught there.
• John Colson
(1680-1760)
Origin of the
‘Witch of Agnesi’
The Witch of Agnesi
This curve was known to Fermat (1601-1665)
and Luigi Guido Grandi (1671-1742), who
called it versiera (from Latin vertere - to
turn). Agnesi explained it, but the Italian
word ‘la versera’ was taken for ‘l’aversiera’
(meaning female devil, devil’s wife, or shedevil in Italian) was used by John Colson who
translated Principia into English from the
original in 1736 and from Agnesi’s Italian
version in 1760, translated it ‘witch’, ‘and the
mistake is lovingly preserved in most texts in
English language.
• The Witch of Agnesi
x = 2a tan ! , y = 2a cos 2 !
or
8a 3
y= 2
x + 4a 2
• several conclusions about it
• as
x ! ±", y ! 0
• Area between the curve and x is 4! a (or 4 x
the area of the generating circle)
2
• Later Agnesi became symbol of feminine
wisdom and as such
– Symbol of Catholic Enlightenment
– Heroine of counterrevolution and political
restoration
– A prophet of the national unification of
Italy
– A Catholic modernist
– A proto-feminist
– The ideal fascist woman
– Potential saint of the church (recent
invitations to canonize her).
Caroline Herschel
• Born 16 March
1750 Hannover,
Germany
• Died 9 Jan 1848
Hannover,
Germany
• Sister of William Herschel (1738-1822),
astronomer, musician, and
mathematician
• In 1766 William becomes organist in
Bath
• Caroline joins him in 1772
• Both had fond memories of their
father…
... on a clear frosty night into the
street, to make me acquainted with
several of the beautiful
constellations, after we had been
gazing at a comet which was then
visible
• Studied mathematics, music and astronomy
together.
• Caroline pursued a somewhat successful
singing career:
‘As first treble in the Messiah, Judas Macabaeus,
etc., she sang at Bath or Bristol sometimes five
nights in the week, but declined an engagement for
the Birmingham festival, having resolved to
appear only where her brother conducted.’ (DOB)
• Interested in applied mathematics.
• Astronomy a hobby for both of them when in
1781 William discovered Uranus.
• Employment with George III ensued,
Herschels moving to few places around
London before finally to Clay Hall near
Windsor.
• William on a pay from GIII, £200 p.a.
• In 1786 moved to Observatory House in
Slough where on 1 August 1786 Caroline
discovered her first comet - called by some
‘first lady’s comet’.
• 1787 Caroline on GIII pay - £50 p.a.
• Discovered eight comets between 1768 and
1797 when she began cross-referencing and
correcting the star catalogue produced by
Flamsteed.
• Returned to Hanover after William’s
death in 1822.
• Completed the catalogue of 2500
nebulae and in 1828 Royal Astronomical
Society awarded her its gold medal.
• Became something of a celebrity, visited
by Gauss.
• Together with Mary Somerville she was
elected to honorary membership of the
Royal Society in 1835. First women
honorary members.
MarieSophie
Germain
• Born 1 April
1776 in Paris
• Died 27 June
1831 in Paris
• Middle daughter of a silk merchant. Her
parents’ home meeting place for those
interested in liberal reforms.
• Defining moment of interest when she
read the account of Archimedes’ death.
Parents didn’t approve at first, so
studying hiding.
• Obtained notes from many courses at
the Ecole Polytechnique
• Submitted a paper to Lagrange at the
end of his course on analysis under the
pseudonym M LeBlanc.
• Corresponded with Lagrange and later
Gauss (began with the same
pseudonym).
• Worked on Fermat’s Last Theorem
using modular arithmetic. Came to
what has became known as Germain’s
Theorem.
• Probably the most frustrating life history • In 1808 The Institute of France set a prize
competition with the challenge:
• Formulate a mathematical theory of elastic
surfaces and indicate just how it agrees with
empirical evidence.
• A deadline set for two years.
• No one submitted apart from Germain
• Lagrange’s opinion was that the mathematical
modesl available were not adequate to solve
the problem
• She did not win the reward, but Lagrange
who was a judge in the contest corrected the
errors in Germain’s equation and came up
with what he believed was a good description.
• The contest deadline extended for two years,
and Germain again the only entrant.
• She worked on Lagrange’s amendments and
was able to show that Lagrange’s equation
did yield some results but could not give a
satisfactory derivation of equation from
physical principles.
• For this work she received an
honourable mention.
• The contest reopened in 1813 and
Germain was awarded a gold medal, but
did not come to collect it.
Germain’s primes
• A theorem and prime numbers bearing
her name
• If number is a prime p, and 2p+1 is also
a prime, then p is Germain prime
• Theorem states that if p and 2p+1 are
both primes, then there are no integers
x, y, and z for which xp + yp = zp
Conclusions?
• Perception of whether women can do
mathematics
• How many women have done
mathematics?
• Is there anything to contribute?
• How do we really treat women/girls
through the popular culture? And how
do we treat maths?
Some of the things we can do
• Inspire in different ways
– History of mathematics
– Learning fantasies
• Empower (Garden of Knowledge not
teacher preacher concept)
• Involve young people
• Show the ways of making a contribution
Thank you for listening!
snezana@mathsisgoodforyou.com