Abu Al-Khwarizmi by Rebecca Shoyket
Abu al- Khwarizmi was a famous Islamic mathematician. He was born in Baghdad,
ca 780 AD, which is a city now in Iraq. He died around 850 AD, but there is very little
information on the life of al- Khwarizmi. He was given the name “father of algebra”
because he was the first of many to teach algebra in an elementary way. Along with many
other scholars, Abu al- Khwarizmi studied at the House of Wisdom. The House of Wisdom
is very similar to the colleges that we have now. It was a key institution in the Translation
Movement and considered to have been a major intellectual center of the Islamic Golden
Age. The House was an unrivalled center for the study of humanities and for Islamic
science, Islamic mathematics, Islamic astronomy, Islamic medicine, Islamic chemistry,
zoology and Islamic geography. His first step to earning the name of “the father of
algebra”, was writing a book. The title of the book is translated to “The book on
calculations by completion and balancing”.
In Al-Khwarizmi’s book, he starts with a discussion of algebra of the first and
second degree, today known as linear and quadratic terms. It wasn’t until many years later
when Cardano solved equations of the cubic, or third degree terms. The second part of his
book, he focuses on the aspect of business and the applications involved. Al-Khwarizmi
was probably the greatest mathematician of his time. He wrote and gave examples of linear
and quadratic equations, into six standard forms: 1. Squares equal to roots 10x2 = 20x; 2.
Squares equal to numbers 10x2 = 25; 3. Roots equal to numbers 10x = 20; 4. Squares and
roots equal to numbers x2 + 10x = 39; 5. Squares and numbers equal to roots x2 + 39 =
10x; 6. Roots and numbers equal to squares 10x + 39 = x2 .
Not only is Abu al- Khwarizmi known as the “father of algebra”, but also he was
also successful in other things. He also founded some basic concepts to areas like
astronomy, and geography. Al- Khwarizmi was also successful in developing
trigonometric tables containing the sine function, which he did in great detail. His
discoveries also helped many mathematicians. From his development of trigonometric
tables, they helped to form the tangent function.
I believe that Abu al–Khwarizmi was very successful in his career, discoveries in
math, and in life. He was successful in many of his discoveries, because we use those in
our lives still to this day. I recently learned how to find the tangent and how to use the
Pythagorean theorem in my math class. If I ever had to think of who developed the theory
to finding the tangent, I would have never thought it was from a man who lived a long time
ago. This is why Abu al–Khwarizmi was greatly affected by the time period that he lived
in. technology back then wasn’t as advanced as it is today, so it would have taken a lot
more effort, and hard work to figure out something like that, compared to modern day
discoveries and inventions. It also affected him greatly because he lived in a time period
where the atmosphere around him provided him with very little institutional support.
Although very little is known about the life of Abu al- Khwarizmi, we do know that
he discovered and came up with many theories that we still use in our everyday lives. He
will always be known as the “father of algebra” for his success as a mathematician, and in
many other subjects.
Charles Babbage by Joseph DiGiovanni
Charles Babbage was a 19th century mathematician, philosopher, and inventor. He
is credited with designing the first working mechanical computer, even though it was never
fully constructed during his lifetime.
Charles Babbage was born in London, England in 1791. His father was a banker,
who was responsible for his early education. Charles Babbage went to private schools and
had his own tutors. He was eventually accepted into Cambridge University, where he
eventually graduated top in his class of mathematics. As an undergraduate, he formed the
Analytical Society with fellow mathematicians John Herschel and George Peacock in
1812. In 1814 he married Georgiana Whitmore, with whom he had 8 children, though
only 3 survived to adulthood. In his early career he worked as a mathematician, mainly in
the area of the calculation of functions. He spent his professional and academic career at
Cambridge, where he became Lucasian Professor of Mathematics (the same post that Isaac
Newton held).
The thing that Charles Babbage is remembered for the most is his work on
mechanical computing. He felt that it was possible to create machines that were able to
perform mathematical operations faster and with greater accuracy then humans can. His
first design was something called a “difference machine”, which was designed to do
mathematical computations. Babbage received some funding from his university to build
a working model, but after years of effort it was never completed. He also designed a
printer for his machine, which like the difference machine, was never built in his lifetime.
It was not known exactly why the machines weren't completed (as they would be after his
lifetime), but finances, impatience, and his own difficult personality probably all
contributed. Always with a restless mind, Babbage moved on to the next challenge of
designing and building an “Analytical Engine”, which would have been able to program
using paper punch cards. This machine, like his difference machine was never fully
constructed, though a program was written for it by fellow mathematician Ada Lovelace.
Babbage also had accomplishments in other fields such as, cryptography
(decrypting several codes in his time), mechanical engineering, philosophy, and economics
(investigated work theories which later became used in assembly-line production
methods). He is credited with helping forming the British Association for the
Advancement of Science through his paper titled "Reflections on the Decline of Science in
England". He is also invented the 'cow catcher' (the steel cage on the front of trains
designed to remove any obstructions on the tracks) and the ophthalmoscope (a device to
study the retina).
In modern times, two of his designs were completed and functioned fully as he
intended them to. This is proof that his ideas were correct, but he lacked either the means
or the patience to see them through in his own time. He is considered to be the father of
mechanical computer theory, and someone who is certainly ahead of his time. After his
death in 1871, one of his sons, Henry Prevost Babbage, continued on his work and
constructed working versions of his 'Difference Machines”, some of which survive to this
day. He is buried Kensal Green Cemetery in London, England. His brain however, was
saved for study, and is now in London's Hunterian Museum in the Royal College of
Surgeons.
Mr. Babbage worked as a designer for computers in a time when there was no
electronics or working electrical machines. His designs used the only materials that were
available to him, such as gears, steam, and paper, to build his inventions. Even though the
finished product weighed several tons, the fact that it did work proved that he was a
genius. If he lived today, he would probably be doing great things with modern electronic
computers.
The Bernoullis by India Shore
The Bernoulli family produced several exceptional mathematicians during the 17th
and 18th centuries. Many important mathematical and physical principles were developed
by members of this family during that time. Several of the family members also had very
strong personalities, which led to competition and conflict between them.
The first important mathematician was Jacob Bernoulli. Jacob was the son of
Nikolaus, a wealthy Swiss merchant. He originally studied to be a minster, but fell in love
with mathematics and studied with many of the important mathematicians and scientists of
his age, including Hudde, Robert Boyle and Robert Hooke, and Gottfried Leibniz. He
became the chair of mathematics at the University of Basel, and held that post until his
death in 1705. His conflicts with his brother Johann and the University authorities (whom
we didn't feel supported him as much as they should), made his stay there interesting. The
Bernoulli distribution, the Bernoulli theorem of statistics and probability, The Bernoulli
numbers, and Bernoulli polynomials were all named after Jacob Bernoulli. Jacob
Bernoulli also made great contributions and calculus and differential equations. He is most
well known for his book the Ars conjectandi, which was published after his death by his
nephew. Jacob had the logarithmic spiral and the inscription “Eadem Mutata Resurgo” (I
shall arise the same though changed) put on his tombstone.
Johann Bernoulli was Jacob's younger brother and, like his brother, went against his
father's wishes when he started to study mathematics. His father wanted him to go into the
family business, but with his brother's help he took up mathematics instead. Johann
became a mathematics professor at the University of Groningen, and ended up succeeding
his brother at the University of Basel when he died in 1705. Even though it was his
brother that helped him get started, they ended up as rivals during the time when they were
both alive together. Johann, who had a reputation of being prideful, often bragged that he
was the better mathematician, with his brother responding that Johann had copied his
results. His competition also extended to that of his own son Daniel, with whom he
backdated a paper in order for it to appear that it came out earlier than his son's did.
Johann did create some important works of his own including important discoveries in
calculus and differential equations.
He entered an agreement with Guillaume L'Hopital in which Johann agreed to gift
credit to L'Hopital for any discoveries that he had while working for him. For that reason
L'Hopital's rule was not named after Johann Bernoulli, even though he was the one that
developed it. His other accomplishments include the Catenary solution, Bernoulli's
identity, and Bernoulli's rule. Johann died in 1748 at the age of 80 years old, and had the
inscription “The Archimedes of our Age” on his tombstone.
Johann's son Daniel was also an important mathematician of the age. Once again,
he didn't start out studying mathematics, and, at his father's urging, took up medicine first.
An important turning point in his life came after he finished his doctorate in medicine and
applied for the chair of anatomy and botany at the University of Basel, which was decided
by drawing lots. Daniel lost, and moved to Venice where he started to study mathematics.
He also studied at the Saint Petersburg Academy in Russia with his brother Nicolaus, who
unfortunately drowned while they were both there together. He ended up returning to
Basel, where he counting studying and teaching. In 1734, he entered a competition Paris
Academy which he ended up co-winning with his father. Unfortunately, his father was so
prideful at his son being considered his equal, that their relationship disintegrated after this
point. His accomplishments include the Petersburg paradox, moral expectation, and
principles of hydrodynamics called Bernoulli's Principle. Daniel died in 1782 at the age of
82 years old.
The interesting thing about all three of these great mathematicians was that none of
their fathers wanted them to be mathematicians; even Daniel’s who was a mathematician
himself. All three became mathematicians because they loved the subject and had the talent
to succeed. I think that the times that they lived in also helped them with their passion –
great discoveries were being made in mathematics and science at this time, with great
names such as Newton, Leibniz, and Hooke becoming famous with them. Jacob’s father
wanted him to become a merchant, but this age that he lived in made him a mathematician.
Georg Cantor by Mohammad Ullah
Georg Ferdinand Ludwig Philipp Cantor was born on March 3rd, 1845 and died on
January 6th, 1918. He was best known for his invention of set theory. He was born in a
western merchant colony in Saint Petersburg, Russia, and brought up in the city until he
was eleven.
Cantor was the eldest of six children and was an outstanding violinist. He had
apparently inherited his parents' considerable musical and artistic talents. When Cantor’s
father became ill, his family moved to Germany in 1856, first to Wiesbaden then
to Frankfurt, seeking milder winters than those of Saint Petersburg. In 1860, Cantor
graduated with excellence from the Realschule in Darmstadt. His exceptional skills in
mathematics, in particular trigonometry were noted. In 1862, Cantor entered the Federal
Polytechnic Institute in Zürich, today the ETH Zurich. After receiving a sizeable
inheritance upon his father’s unfortunate death in 1863, Cantor shifted his studies to
the University of Berlin, attending lectures by Leopold Kronecker, Karl
Weierstrass and Ernst Kummer. He spent the summer of 1866 at the University of
Göttingen, then at a very important center for mathematical research. In 1867, Berlin
granted him the PhD for a thesis on number theory.
In 1874, Cantor married Vally Guttmann and had six children. Cantor was able to
support a family despite modest academic pay, thanks to his inheritance from his father.
During his honeymoon in the Harz Mountains, Cantor spent much time in mathematical
discussions with Richard Dedekind, whom he befriended two years earlier while
on Swiss holiday. Cantor was promoted to Extraordinary Professor in 1872 and made full
Professor in 1879. To attain the latter rank at the age of 34 was a remarkable
accomplishment, but Cantor wanted a job at a more prominent university. At that time,
Berlin was the leading German university. However, his work was too controversial for
that to happen. Kronecker, who headed mathematics at Berlin until his death in 1891, was
gradually becoming uncomfortable with the possibility of having Cantor as a
colleague. This is due to the fact that Kronecker viewed Cantor as a "corrupter of youth"
for teaching his ideas to the younger generation of mathematicians. Worse yet, Kronecker,
a well-established figure within the mathematical community and Cantor's former
professor, fundamentally disagreed with the thrust of Cantor's work.
As stated before, Cantor was the inventor of set theory. Set theory is the branch
of mathematics that studies sets, which are collections of objects. Although any type of
object can be collected into a set, set theory is applied most often to objects that are
relevant to mathematics. Set theory is used in nearly every mathematical subject, such as
Venn and Euler diagrams.
Cantor was gradually becoming more and more depressed as criticism of his work
increased. It got so bad that he went to a lecture on philosophy, rather than mathematics.
He also studied Elizabethan literature to get his mind off mathematics for a while. This
break helped him. In 1899, however, his youngest son, Rudolph, died while Cantor was
delivering a lecture on his views on Baconian Theory and William Shakespeare. This
tragedy drained much of Cantor’s passion for mathematics. In 1904, Cantor was outraged
and agitated by a paper presented by Julius König at the Third International Congress of
Mathematicians. The paper attempted to prove that the basic tenets of transfinite set theory
were false. Since it had been read in front of his daughters and colleagues, Cantor
perceived himself as having been publicly humiliated.
Although Ernst Zermelo demonstrated less than a day later that König's proof had
failed, Cantor remained shaken. Cantor suffered from chronic depression for the rest of his
life. Cantor retired in 1913, and suffered from poverty, even malnourishment,
during World War I. The public celebration of his 70th birthday was canceled because of
the war. He died on January 6, 1918 in the sanatorium where he had spent the final year of
his life.
Paul Erdos by Stephanie Thomas
Paul Erdos was born March 26, 1913 to a Hungarian family. Paul Erdos parents
Lajos and Anna had two daughters, both of which had died of scarlet fever a few days
before Paul was born. This had a major effect on how his parents treated him. Paul Erdos
parents were extremley protective of him and they introduced mathematics to him, both
Lajos and Anna were teachers of mathematics.
While Lajos was captured by the Russian army, Pauls mother kept him home with a
tutor to teach him for the earlier years of his life being the over protective mother she was.
Then chaos arose by the end of World War I. Anna still worked as a teacher because she
didn’t want to see the childrens education suffer. By 1920 Paul Erdos father returned home
from captivity. While in captivity he learned english but did not know how to pronounce
the words but was still determined to teach Paul. This will give Paul a weird english accent
being a defining character in his life.
In the year 1930, even though there were restictions over Jewish people entering
the universities Paul Erdos was allowed to enter because he was the winner of the national
examination. In 1934 Paul received his doctorate from the University Pázmány Péter in
Budapest. He eventually was forced out of Hungary for being Jewish and travelled in the
United Kingdom. In 1938 Erdős was on his way to the United States where he took up a
fellowship at Princeton. He hoped for his fellowship to be renewed for another 6 months
but Paul Erdos did not meet Princeton's standards or specified qualities so he was given
only a six month extension instead of the year he expected. Princeton believed that Paul
Erdos uncouth and unconventional. Erdos’ friend Ulam asked him to visit Madison to help
them out.
Paul Erdos devoted the rest of his live to solving seemingly unsolvable math
problems. By the age of 20 Paul had discovered an intriguing proof for Chebyshev's
theorem which was famous within the number theory that for each number greater than
one, there is always at least one prime number between it and its double. Paul himself
founded the amazing field of discrete mathematics, solving math problems in number
theory the area of number theory or , and the foundation of computer science. Paul has
wrote 1500 papers of working. An Erdos number was the “collaborative distance” between
Paul Erdos and a mathematician. It became an honor to collaborate with Paul Erdos by
other mathematicians.
Paul Erdos devoted his entire life to mathematics. Paul never had much he
considered property a nuisance and refused settling down in fear that it would mess up his
ability to focus on difficult problems and collaborating with distant collegues. He lived
with other mathematians, sharing his ideas from one place to the next.
Paul Erdos lived in a time of discrimination and hate. He was sent out of the
country he was born in. Paul opted to immigrate to the United States because of the
political tensions from WWII, and this didn’t alow him to further himself in mathematic
achievement in any way possible. Also in the later years he was denied to return back to
his homeland because he was Jewish. Paul Erdos was an bizarre man, even though he was
a genius he had social flaws and never really attached to anything but his numbers.Paul
then worked on mathematics more thoroughly and spent the remainder of his life doing so.
Pierre de Fermat by Julia Zubrovich
"I have a truly marvelous demonstration of this proposition which this margin is
too small to contain." -Pierre de Fermat
Pierre de Fermat was born on August 17, 1601 in Beaumont-de-Lomange, France.
Fermat’s father and uncle were wealthy merchants and his mother’s family was involved
with legal professions. He had one brother and two sisters. It is not certain, but he probably
attended the Franciscan monastery in his hometown. In the 1620s, Fermat attended the
University of Toulouse. He then moved to Bordeaux, and after that he moved to Orleans to
study law. He gained a Bachelor’s Degree in law in 1631. Fermat went on to practice law,
as well as get married in 1631 and have five children. He and his children were very
involved in the Catholic religion. Fermat also became a government official. He rose in
government office very quickly. He had to change his name from Pierre Fermat to Pierre
de Fermat because of the office he held. Apart from his impressive career, he was also
known as an excellent linguist. He spoke Latin, Basque, Greek, Italian, and Spanish.
Fermat is considered one of the greatest mathematicians of the seventeenth century.
Fermat never wanted any of his math published, for it was more of a hobby to him. Fermat
only published his work once, and it was published anonymously. Fermat sent many of his
theories to famous French mathematicians. He did not want to let his love of math take
over the little time he had besides work. He, along with his good friend Blaise Pascal, is
considered to be one of the founders of the probability theory. He, along with Rene
Descartes, is considered as a founder of analytic geometry. Fermat discovered a simpler
method of quadrating parabolas, which were originated by Archimedes. He also provided a
law on light travel, as well as finding a way to calculate the greatest and smallest ordinates
of curved lines.
His most important and most memorable work was done in the development of a
modern number theory. His theory (known as Fermat’s Last Theorem) states that xn + yn =
zn has no non-zero integer solutions for x, y, and z when n is greater than two. Fermat
provided little to no proof of the procedures for reaching his conclusions, including his
theorems. Even the theorem above was not proven until 1993 because he didn’t leave any
proof on the original document. Andrew J. Wiles proved it. Fermat was dubbed the “Prince
of Amateurs” because of his great achievements in mathematics.
In the 1650s, there was a plague that broke out that killed many older men. Fermat
caught this sickness and someone assumed he died of the plague. His death was wrongly
reported in 1653. It was later corrected that he was in fact, alive and that they no longer
feared for his health. Fermat gained little recognition for his discoveries in his time. The
only reason he is recognized today is because the letters he sent to other famous
mathematicians were saved.
Pierre de Fermat died in Toulouse on January 12th, 1665. His son, Samuel de
Fermat, edited his father’s works.
Sophie Germain by Julia Zubrovich
Sophie Germain was born in Paris, France on April 1st, 1776. Her father,
Ambroise-Fransois, was a wealthy silk merchant who became the Bank of France's director
later. Her mother was Marie Madeleine Gruguelin. Sophie also had two sisters, MarieMadeleine and Angelique-Ambroise.
Sophie took an interest in mathematics when she was 13 years old. She was staying
at home because there was unrest in Paris during the French Revolution. Sophie started
teaching herself math by reading her father’s books after she felt inspired by a story of
Archimedes’ death. According to the story, he was killed while reading geometry. Her
family considered math to be an inappropriate subject for a girl and didn't support her
studies at first. Sophie’s parents wanted her to stop studying so they took away her light,
her fire, and her clothes. She would wrap herself in covers and still study. She taught
herself math, Latin, and Greek by reading the books from her father's library.
The Ecole Polytechnique was founded in Paris in 1795. Sophie was not able to
attend because women weren't accepted into that school. She gained the notes from the
lectures and studied from them. Sophie took an identity of M. LeBlanc and submitted a
paper under his name to J. L. Lagrange who taught in the school. The teacher was very
impressed with her work and even though she was a girl from the middle class family, he
became her mentor, and even included some of her work in the second edition of his book
"Theorie".
In 1804, Sophie started writing to German mathematician Carl Friedrich Gauss.
She sent him her work on number theory and once again she used the identity of M.
LeBlanc. Gauss praised her work and found out several years later that M. LeBlanc was
really a gifted woman. He also mentioned that Sophie Germain was one of the reasons he
restarted his own work on number theory.
In 1808, the Institute de France announced a competition where the challenge was
to explain a theory of Elasticity. Sophie German spent next several years working on it
and she was the only person to enter the contest in 1811. She didn't win the award because
there were errors in her calculations. Two years later, she was once again the only entrant
to that competition, and she now got the honorable mention. Third time she submitted the
work, she finally won the medal in 1815.
She continued her research until her death. She never married and didn’t have any
children. Germain’s father supported her for the most of her life. Before she died of breast
cancer in 1831, she wrote papers on number theory, proving that for prime exponents that
are smaller than 100, there was no solution relatively prime to the exponent. Her studies
made progress towards proving Fermat's Last Theorem. Another important achievement of
hers is a theorem that was named after her. She also wrote a philosophy essay that was
published after her death.
Today, a street, la rue Germain, and a school in Paris, L’Ecole Sophie Germain, are
named after her. She is an important figure in math history, because even though she lived
at the times when women weren’t allowed to enroll in the university and only aristocratic
women were able to study math and sciences privately, she was a woman who taught
herself and continued her research and worked on something she truly loved - Math!
G. H. Hardy by Edmond Loi
G.H. (Godfrey Harold) Hardy was an eccentric and shy man, but nevertheless he
was a brilliant mathematician. Born on February 7th, 1877, Hardy considered his work to
be “pure mathematics.” (In other words, this math is not done to be applied elsewhere.)
But, in 1908, Hardy offered a law stating that the dimensions of dominant and recessive
traits would be reproduced in a large population, which was important for blood group
distribution. Let’s take a closer peek into this English mathematician’s life, shall we?
G.H. Hardy was born in Cranleigh, Surrey, England and both of his parents were
teachers. They were also really good at math. Speaking of being really good at math,
Hardy was a gifted child. For example, at age two he could write numbers up to millions.
However, Godfrey Harold simply wanted to beat the other kids in math, he wasn’t
passionate about it. Godfrey went to Cranleigh School until he was twelve years of age.
In 1889, Hardy was awarded a scholarship to Winchester College. This was a
brilliant school, and yet the man disliked it except for the learning. G.H. Hardy entered
Trinity College in Cambridge in 1896. He received fourth place on the Mathematics Tripos
test after only studying for two years. He took part II of the Tripos in 1900 and was
awarded a prize. Three years later Hardy earned an M.A, at that time being the highest
academic degree given at English universities. Then, starting in the year 1906, he became a
lecturer. In 1919 he left Cambridge to Oxford, where he was a geometry professor. In 1931
he returned to Cambridge to be a professor until 1942.
For 35 years, starting in 1911, he collaborated with John Edensor Littlewood,
working in topics such as the mathematical analysis and number theory. Some of the stuff
they did included the proving results in the prime number theory. This was one of the most
successful mathematical collaborations in history! G.H. Hardy also collaborated with
Srinivasa Ramanujan, after Ramanujan sent Hardy mathematical papers from India in
1913. (They started work in 1914) In Cambridge the duo wrote five math papers together!
Godfrey calls this collaboration,” his greatest contribution to math.” Collaborating came
naturally to Godfrey Harold, and he also wrote papers with mathematicians like Edmund
Landau. Another one of Godfrey’s passions was cricket, and he befriended C.P. Snow for
this common interest.
G.H. Hardy lived through two world wars, so the time in which he lived most
defiantly affected him. He volunteered for World War 1, but was not healthy enough. He
also did not believe in the fighting, but greatly respected Germany. (That opinion made it
hard for G.H. to make friends) Both wars were painful for Godfrey Harold (he suffered a
heart attack in 1939, age 62) and after 1945 he started to lose his intelligence and ability to
play the sports. Also, this mathematician was involved in political groups like the “Union
of Democratic Control” during WW1.
This mathematician’s work was greatly appreciated. Some of his honors include
receiving the Sylvester Medal of Society in 1940 and the Copley Medal of Royal Society
in 1947. “A mathematician’s apology”, written in 1940, was Hardy’s book describing a
mathematician’s mind and math pleasures. Its power moved many towards math. The book
and Hardy showed true rigor, not common in British mathematics. Also, many of his
papers have been published by the Oxford University Press, in seven volumes! Of course
these are not all the details about his life, but some truly significant ones. Godfrey Harold
Hardy passed away on December 1st, 1947. Hardy never married and his sister looked over
him for the last few years he was alive. As you can see, we can remember G.H. Hardy with
respect and fascination.
Joseph-Louis Lagrange by Mohammad Ullah
Joseph-Louis Lagrange was born on January 5, 1736 in Turin, Sardinia-Piedmont.
Lagrange was a mix; his mother’s side was Italian and his father’s side was French. He
was the oldest of his ten siblings and one of the 2 that survived to become an adult. He was
mostly self-taught and was not interested in mathematics until his late teens. He went to
college at Turin and joined the Berlin Academy at age 23.
Lagrange published his first mathematical work in 1754 (an analogy between the
binomial theorem and the successive derivatives of the product of functions). Lagrange
made his first important discovery at age nineteen, by solving the isoperimetric problem.
He sent a letter to Euler that was about a more efficient way of solving the problem. In
1766, Lagrange was chosen by Euler to be the director of the Berlin Academy.
In 1758, Lagrange and his students created the Royal Academy of Science of Turin
and wrote Miscellanea Taurinesia, five volumes of transactions. While working at the
Berlin Academy for 20 years, he became good friends with Lambert. During those 20
years, Lagrange regularly won the prize from the Académie des Sciences of Paris. Only in
1772, he shared the prize with Euler. In addition to working on mathematics, Lagrange
also worked on science in the Berlin Academy (he mostly worked on science).
In 1770, Lagrange proved that every positive integer is the sum of four squares.
During the same year, he also created a fundamental investigation of why equations of
degrees up to 4 could be solved by radicals. In 1771, Lagrange proved Wilson’s theorem to
be true (n is prime if and only (n-1)! + 1 is divisible by n).
In 1787, Lagrange left Berlin because the death of his wife made him less happy (in
1792, Lagrange got married again, to Renée-Françoise-Adélaide Le Monnier and still had
no children). He became a member of the Académie des Sciences of Paris and remained
one for the rest of his life. Later on, Lagrange wrote Mécanique analytique to define his
contributions to mechanics (because he did not write anything yet that discussed his
contributions). This work made mechanics a branch of mathematical analysis. In 1790,
Lagrange and other members of the committee of Académie des Sciences worked on the
metric system and supported a decimal base. After this, some people referred to Lagrange
as the founder of the metric system.
In 1794, Ecole Polytechnique was founded and Lagrange became its first professor
of analysis. In 1797, he published the first theory of functions with a real variable in
Théorie des fonctions analytique. Later on, Lagrange gained the respect of Napoleon and
was named to the Legion of Honour and Count of the Empire in 1908. In 1910, Lagrange
started to make revisions of Mécanique analytique but was not able to finish due to his
death. He died on April 10, 1813.
Lagrange did not make many enemies while working with other mathematicians.
He was lucky to survive the French Revolution and be able to work more in the field of
mathematics (and science). Although Lagrange did not spend most of his life working in
the field of mathematics, the contributions he made were important.
Ada Lovelace by Lester Lee
Augusta Ada Byron, famously known as Ada Lovelace, was a mathematician
during the nineteenth century. She was born on December 10, 1815 and died on November
27, 1852. Her father was Lord Bryon, a famous British poet. Her mother was Anne Isabella
Byron, who was highly talented in mathematics. Lord Bryon left the family a month after
Augusta was born and died when she was eight. Lord Byron was the only one who called
Augusta, Ada.
Ada was not allowed to walk the same path as her father because of her mother’s
hatred towards her father. Therefore, Lady Byron forced Ada to have tutors in math. She
was also forced to learn music, because her mother felt that music was something that can
teach a girl her social skills. Personally, Ada’s favorite subject was geography, but when
her mother found out, she replaced Ada’s geography classes with more math. She wanted
her daughter to work hard and long on her lessons. Punishments were: being locked in,
staying still, and writing apologies. People in the family were afraid that Lady Byron
pushed Ada too hard. From a young age, Ada was often very ill. She had terrible
headaches at 8 that blocked some of her vision. At age 13, she was paralyzed from
measles. From that, she had to rest for a year and walk in crutches.
One of Ada's tutors, William King, complemented on how Ada excelled his own
mathematical studies. Another tutor, the mathematician Augustus De Morgan, also
predicted that Ada might be a real mathematician later on in life. At the age of seventeen,
Ada met Mary Somerville. She sent math books to her, and nourished Ada into loving
mathematics. She was a friend of Charles Babbage, so she introduced him to her at a party.
Ada became fascinated by Babbage's invention of the difference engine. They became
great friends after that.
The two developed a working relationship between themselves. A memoir was
written about Babbage's Analytical Engine, and she was the one to translate it. Along with
translating it, from Babbage's suggestion, Ada even added her own comments and notes to
it. It became three times as long as the original memoir filled with her notes. They even
exchanged letters about Babbage's invention. Ada even personally created a way for it to
calculate Bernoulli numbers becoming the first computer programming language. Charles
Babbage gave her the nickname, “Enchantress of Numbers.” From that, Ada started
becoming famous. Her notes were published through the initials of AAL. Back then, it was
not encouraged for women to work on such complicated studies. She was even lucky for
being able to have her papers published despite the fact that she was a woman.
In her personal life, Ada married William King. When he became the Earl of
Lovelace, Ada became the Countess of Lovelace. People often relate to her as Ada
Lovelace. They had three children together. The family was mainly dominated by her
mother, Lady Byron. If only her husband was as good as being a leader as she was smart
with numbers, family problems wouldn't have occurred from her mother's ruling.
With all the pressure, Ada Lovelace flirted with some of the males around her. Her
husband got furious and destroyed many of her letters to her friends. Ada started drinking
wine excessively. She went from drinking wine with meals to drinking wine instead of
meals. Then she even took up gambling. She sold her jewels to get money for horse races.
By the time of her death, Lovelace was in debt of £2000 from gambling.
Throughout her years, Ada Lovelace became weaker and weaker because of her
cancer. At the young age of thirty-six, she died from uterine cancer and bloodletting by her
doctors. Ada Lovelace was buried next to the father she never knew.
Srinivasa Ramanujan by Mohammad Ullah
Srinivasa Ramanujan was born on December 22, 1887 in Erode, British India, in
the house of his mother’s parents. Ramanujan lived in a traditional house in India called
Kumbakonam, and the house is now a museum. When Srinivasa was only two years old,
he suffered a case of smallpox, notorious at the time for causing many deaths, but he
miraculously recovered from it. His mother gave birth a few times, but he was the only one
who made it passed infancy. Ramanujan moved back and forth from his house in
Kumbakonam to his maternal grandparents’ house in/near Madras. His father was at work
most of the day, so Srinivasa’s mother had a close relationship with him. She taught him
traditions and cultural activities.
When he enrolled in the Kangayan Primary School, he excelled, and generated the
best score in his district. This achievement brought him to Town Higher Secondary School,
where he began learning true mathematics. He understood it fully, and began to even create
theorems of his own. In the years following, he received many awards and recognitions for
his outstanding skill, and completed exams with plenty of time to spare. He was awed by
his classmates for his amazing knowledge and understanding of complex mathematics. He
was offered a scholarship from his school, but lost it because of his failures in any other
subjects.
He ran away from home, and enrolled in a school near Madras. Here, he was also
outstanding in mathematics, but he again suffered in other subjects, leaving him in
desperate poverty. When he was 21, he married a 9- year old girl, Janaki Ammal. After he
married, he developed a condition in his body that required a surgery. His family couldn’t
afford the operation, but a kind doctor agreed to perform the operation for free. After the
surgery, Ramanujan searched for a job, and ended up tutoring college students in math. In
March, 1914, he took a ship from Madras to England, where he worked with Hardy and
Littlewood. Ramanujan went to England because he sent his results to G. H. Hardy, who
was amazed by the work. Hardy arranged a trip for Srinivasa to go to Cambridge, England,
so Hardy could see proof of Ramanujan’s work. After living in England for awhile,
Srinivasa then became homesick, sick of the war’s effect on England, and literally sick. He
died soon after he returned on April 26, 1920, from tuberculosis and a vitamin deficiency.
Ramanujan started his interest in mathematics very early in his life, and progressed
through many types of it. He mastered general math skills in his primary school, mastered
formal mathematics in secondary school, and mastered the trigonometry book he was lent.
He wrote down hundreds of theorems he created in his notebook, many experimenting
with pi and radicals. Ramanujan also worked on continued fractions and integrals. When
he moved to England, Srinivasa received a PhD for highly composite numbers research.
His last major study before he died was elliptic functions.
One thing that may have affected Ramanujan’s life during his time would be World
War I. Towards the end of his life, the Great War took place, and since England controlled
India, there was much involvement in his life. It was said that one reason he became ill was
the scarcity of vegetarian food during the war. Also, he lived in a time where there was
much sickness. He died young (age 32) because of tuberculosis, liver infection and a
severe vitamin deficiency. He also spent a large amount of time in Madras, which was
determined to be the source of his liver problems, because amoebiasis was a common
parasitic infection of the liver in that area. He also suffered from poverty after he ran away
from home, due to the economy at the time.
John von Neumann by Ilana Kelmanskiy
John von Neumann was born on December 28, 1903 in Budapest, Hungary.
Throughout the course of his short life, he made multiple discoveries that revolutionized
mathematics. His presence can be felt in almost every branch of mathematics. He made
sizable contributions to the fields of geometry, game theory, economics, and quantum
theory, and his involvement was instrumental in the ending of World War II. To this day,
he is still regarded as one of the best mathematicians of his time.
He was a banker’s son, and his father realized John’s talent at an early age.
Although he recognized his son was a genius with incredible skills of memorization, he did
not believe he could make a living as a mathematician. Instead of encouraging his son to
continue his studies of mathematics, he asked his son to memorize pages of the phone
book to amuse guests at parties. He attempted to get his son to study something more
practical than math, and as a result John began to study chemistry. At 23, he received his
PhD in mathematics, and he never had to resort to chemistry to make money ever again.
Neumann became a professor at Princeton in 1933 as a teacher at the Institute for
Advanced Studies. He was one of the first six math teachers there, alongside some other
brilliant people (most notably Albert Einstein). He quickly became known as an incredible
pure mathematician, collaborating with people like Howard Aiken and Alan Turing.
Von Neumann is considered to be the founder of game theory. He improved the minimax
theorem, among other things. The minimax theorem states that in a game where all
information is revealed, there is always a method with which each player can minimize
their maximum losses in a game. He applied the theorem to games with more than two
players and games where not all the information was revealed.
He continued his work solely in the field of pure mathematics until 1940. With the
onset of World War II, von Neumann's areas of interest changed towards applied
mathematics. He became one of the few mathematicians to be skilled with explosions, and
his talent led to him being selected to assist with the Manhattan Project (the project that led
to the creation of the atomic bomb). He is responsible for the so-called “explosive lens”
design of the atomic bomb, and was on the committee deciding where to launch the bomb.
To help with his work at Los Alamos, he needed to work with computers. He used an early
digital computer to run simulations, and as a result needed to create a basic random number
generator of sorts. He proposed the middle-square method. The method would multiply a
six-digit seed number to the power of two, take the middle six digits, and make that the
new seed number. His work with the middle-square method eventually led to the creation
of the Monte Carlo method.
He married Mariette Kovesi in 1930, and with her he had his only daughter, Marina
von Neumann Whitman. (She later followed in her father’s footsteps and became a
mathematician.) Later, after his wife’s death in 1938, he married Klara Dan. He always
wore a grey flannel suit, no matter what the situation. He once wore one while riding a
camel! He also was a notoriously bad driver, often reading a book at the wheel and
consequently crashing into the trees.
In 1955, he was diagnosed with cancer. Upon being informed of this, he was forced
to realize that he would soon cease to exist, and as a result cease to think. His close friends
who visited him during his time said that watching him struggle was heartbreaking. He
suffered for a year and a half under military custody (he feared he might reveal state
secrets while medicated) and died on February 8, 1957. The number of advancements he
made in the field of mathematics is immeasurable, and to this day he remains one of the
greatest mathematicians of the 1900s.