Famous Mathematicians

1. AdaLovelace
A giftedmathematician,AdaLovelaceisconsideredtohave written
instructionsforthe firstcomputerprograminthe mid-1800s.
Augusta Ada King-Noel, Countess of Lovelace (née Byron; 10
December 1815 – 27 November 1852) was an English
mathematician and writer, chiefly known for her work on Charles
Babbage's proposed mechanical general-purpose computer, the
Analytical Engine. She was the first to recognise that the machine
had applications beyond pure calculation, and created the first
algorithmintendedtobe carriedout by such a machine. As a result,
she isoftenregarded as the first to recognise the full potential of a
"computing machine" and the first computer programmer.
Ada Lovelace was the only legitimate child of the poet George, Lord Byron, and his wife Anne Isabella
Milbanke ("Annabella"),LadyWentworth.All Byron'sother children were born out of wedlock to other
women. Byron separated from his wife a month after Ada was born and left England forever four
monthslater,eventuallydyingof disease inthe Greek War of Independence when Ada was eight years
old. Her mother remained bitter towards Lord Byron and promoted Ada's interest in mathematics and
logic in an effort to prevent her from developing what she saw as the insanity seen in her father, but
Ada remainedinterestedin him despite this (and was, upon her eventual death, buried next to him at
herrequest).Oftenill,she spentmostof herchildhoodsick.AdamarriedWilliam King in 1835. King was
made Earl of Lovelace in 1838, and she became Countess of Lovelace.
Her educational and social exploits brought her into contact with scientists such as Andrew Crosse, Sir
DavidBrewster,CharlesWheatstone,Michael Faraday and the author Charles Dickens, which she used
to furtherhereducation.Adadescribedherapproachas"poetical science"andherself asan "Analyst (&
Metaphysician)".
When she was a teenager, her mathematical talents led her to a long working relationship and
friendshipwithfellowBritishmathematicianCharlesBabbage, also known as 'the father of computers',
and inparticular,Babbage'sworkon the Analytical Engine.Lovelace first met him in June 1833, through
theirmutual friend,and her private tutor, Mary Somerville. Between 1842 and 1843, Ada translated an
article by Italian military engineer Luigi Menabrea on the engine, which she supplemented with an
elaborate set of notes, simply called Notes. These notes contain what many consider to be the first
computerprogram—thatis,analgorithmdesignedtobe carried out by a machine. Lovelace's notes are
importantinthe earlyhistoryof computers.She also developed a vision of the capability of computers
to go beyond mere calculating or number-crunching, while many others, including Babbage himself,
focusedonlyonthose capabilities.Hermindsetof "poetical science" led her to ask questions about the
Analytical Engine (asshowninhernotes) examininghow individualsand society relate to technology as
a collaborative tool.
She died of uterine cancer in 1852 at the age of 36.

2. Fibonacci
Fibonacci (c. 1175 – c. 1250) was an Italian mathematician, considered to be "the most talented
Western mathematician of the Middle Ages". The name he is commonly called, "Fibonacci"
(Italian:[fibona'tʃ:i]),isshortfor"figlio di Bonacci" ("son of Bonacci") and he is also known as Leonardo
Bonacci, Leonardo of Pisa, Leonardo Pisano Bigollo, or Leonardo Fibonacci.
Fibonacci popularized the Hindu–Arabic numeral system in the Western World[5]
primarily through his
composition in 1202 of Liber Abaci (Book of Calculation). He also introduced Europe to the sequence
of Fibonacci numbers, which he used as an example in Liber Abaci.
Biography
Fibonacci was born around 1175 to Guglielmo Bonacci, a wealthy Italian merchant and, by some
accounts,the consul for Pisa.Guglielmodirectedatradingpostin Bugia,a port inthe Almohaddynasty's
sultanate in North Africa. Fibonacci travelled with him as a young boy, and it was in Bugia
(now Béjaïa, Algeria) that he learned about the Hindu–Arabic numeral system.
Fibonacci travelled extensively around the Mediterranean coast, meeting with many merchants and
learningabouttheir systems of doing arithmetic. He soon realised the many advantages of the Hindu-
Arabic system. In 1202, he completed the Liber Abaci (Book of Abacus or Book of Calculation) which
popularized Hindu–Arabic numerals in Europe.
Fibonacci became a guest of Emperor Frederick II, who enjoyed mathematics and science. In 1240,
the Republic of Pisa honored Fibonacci (referred to as Leonardo Bigollo)[8]
by granting him a salary in a
decree that recognized him for the services that he had given to the city as an advisor on matters of
accounting and instruction to citizens.
The date of Fibonacci's death is not known, but it has been estimated to be between 1240 and 1250,
most likely in Pisa.

3. GEORG CANTOR
Georg Ferdinand Ludwig Philipp Cantor (/ˈkæntɔːr/ kan-tor; German: [ˈɡeɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfɪlɪp
ˈkantɔʁ]; March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician. He
invented set theory, which has become a fundamental theory in mathematics. Cantor established the
importance of one-to-one correspondence betweenthe membersof twosets,defined infiniteand well-
orderedsets,and proved that the real numbers are more numerous than the natural numbers. In fact,
Cantor's methodof proof of thistheoremimpliesthe existence of an "infinity of infinities". He defined
the cardinal and ordinal numbersandtheirarithmetic.Cantor'sworkisof greatphilosophical interest, a
fact of which he was well aware.
Cantor's theoryof transfinite numbers wasoriginallyregardedassocounter-intuitive – even shocking –
that itencounteredresistance frommathematical contemporariessuchas LeopoldKronecker and Henri
Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig
Wittgenstein raisedphilosophical objections.Cantor, a devout Lutheran, believed the theory had been
communicated to him by God. Some Christian theologians (particularly neo-Scholastics) saw Cantor's
workas a challenge tothe uniquenessof the absolute infinity in the nature of God[6]
– on one occasion
equating the theory of transfinite numbers with pantheism – a proposition that Cantor vigorously
rejected.
The objectionstoCantor'swork were occasionallyfierce: Henri Poincaré referredtohisideasasa "grave
disease" infecting the discipline of mathematics, and Leopold Kronecker's public opposition and
personal attacksincludeddescribingCantorasa "scientific charlatan", a "renegade" and a "corrupter of
youth." Kronecker objected to Cantor's proofs that the algebraic numbers are countable, and that the
transcendental numbersare uncountable, results now included in a standard mathematics curriculum.
WritingdecadesafterCantor'sdeath, Wittgenstein lamented that mathematics is "ridden through and
through with the pernicious idioms of set theory," which he dismissed as "utter nonsense" that is
"laughable"and"wrong".[10]
Cantor'srecurringboutsof depressionfrom1884 to the end of his life have
beenblamedonthe hostile attitudeof manyof hiscontemporaries, thoughsome have explained these
episodes as probable manifestations of a bipolar disorder.

4. Emmy Noether
Amalie Emmy Noether (German: [ˈnøːtɐ]; 23 March 1882 – 14 April 1935) was a
German mathematician known for her landmark contributions to abstract algebra and theoretical
physics.
She was describedby Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert
Wiener as the most important woman in the history of mathematics. As one of the leading
mathematicians of her time, she developed the theories of rings, fields, and algebras. In
physics, Noether's theorem explains the connection between symmetry and conservation laws
Noether was born to a Jewish family in the Franconian town of Erlangen; her father was a
mathematician, Max Noether. She originally planned to teach French and English after passing the
requiredexaminations,butinsteadstudiedmathematicsatthe Universityof Erlangen,where her father
lectured.Aftercompletingherdissertationin1907 underthe supervisionof Paul Gordan, she worked at
the Mathematical Institute of Erlangen without pay for seven years. At the time, women were largely
excludedfromacademicpositions. In 1915, she was invited by David Hilbert and Felix Klein to join the
mathematics department at the University of Göttingen, a world-renowned center of mathematical
research.The philosophical facultyobjected,however,andshe spentfouryearslecturingunderHilbert's
name. Her habilitation was approved in 1919, allowing her to obtain the rank of Privatdozent.
Noether remained a leading member of the Göttingen mathematics department until 1933; her
students were sometimes called the "Noether boys". In 1924, Dutch mathematician B. L. van der
Waerdenjoinedhercircle andsoonbecame the leadingexpositor of Noether's ideas: her work was the
foundationforthe secondvolume of hisinfluential 1931 textbook,Moderne Algebra.By the time of her
plenary address at the 1932 International Congress of Mathematicians in Zürich, her algebraic acumen
was recognizedaroundthe world.The followingyear,Germany'sNazi governmentdismissed Jews from
universitypositions,andNoethermovedtothe UnitedStatestotake up a positionat Bryn Mawr College
inPennsylvania.In1935 she underwentsurgeryforanovariancyst and,despite signsof arecovery,died
four days later at the age of 53.

5. Noether's mathematical work has been divided into three "epochs". In the first (1908–19), she made
contributions to the theories of algebraic invariants and number fields.
John Forbes Nash Jr.
John Forbes Nash Jr. (June 13, 1928 – May 23, 2015) was an American mathematician who made
fundamental contributionsto game theory, differential geometry, and the study of partial differential
equations.[2][3] Nash's work has provided insight into the factors that govern chance and decision-
making inside complex systems found in everyday life.
His theories are widely used in economics. Serving as a Senior Research Mathematician at Princeton
University during the latter part of his life, he shared the 1994 Nobel Memorial Prize in Economic
Scienceswithgame theoristsReinhardSelten and John Harsanyi. In 2015, he also shared the Abel Prize
with Louis Nirenberg for his work on nonlinear partial differential equations.
In 1959, Nash began showing clear signs of mental illness, and spent several years at psychiatric
hospitalsbeingtreatedforparanoidschizophrenia.After1970, his condition slowly improved, allowing
himto returnto academicworkby the mid-1980s. His struggleswithhisillnessandhisrecoverybecame
the basis for Sylvia Nasar's biography, A Beautiful Mind, as well as a film of the same name starring
Russell Crowe. OnMay23, 2015, Nashand hiswife,AliciaNash,were killed in a car crash while riding in
a taxi on the New Jersey Turnpike.
Nash was born on June 13, 1928, in Bluefield, West Virginia. His father, John Forbes Nash, was an
electrical engineer for the Appalachian Electric Power Company. His mother, Margaret Virginia (née
Martin) Nash,had beena schoolteacherbefore she married.He wasbaptizedinthe Episcopal Church.[8]
He had a younger sister, Martha (born November 16, 1930).
Nashattendedkindergartenand publicschool,and he learned from books provided by his parents and
grandparents.[9] Nash's parents pursued opportunities to supplement their son's education, and
arranged for him to take advanced mathematics courses at a local community college during his final
yearof highschool.He attended Carnegie Institute of Technology through a full benefit of the George

6. Westinghouse Scholarship,initiallymajoringinchemical engineering. He switched to a chemistry major
and eventually, at the advice of his teacher John Lighton Synge, to mathematics. After graduating in
1948 (at age 19) with both a B.S. and M.S. in mathematics, Nash accepted a scholarship to Princeton
University, where he pursued further graduate studies in mathematics.
John Forbes Nash Jr.
Marie-Sophie Germain (French: [maʁi sɔfi ʒɛʁmɛ̃]; 1 April 1776 – 27 June 1831) was a French
mathematician,physicist,andphilosopher. Despite initial opposition from her parents and difficulties
presentedbysociety,she gainededucationfrombooks inherfather'slibraryincludingonesbyLeonhard
Euler and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss.
One of the pioneersof elasticitytheory,she wonthe grandprize fromthe ParisAcademyof Sciences for
heressayon the subject.Herwork onFermat'sLast Theoremprovidedafoundationformathematicians
exploringthe subject forhundredsof yearsafter. Because of prejudice against her sex, she was unable
to make a career out of mathematics, but she worked independently throughout her life.[2] At the
centenary of her life, a street and a girls' school were named after her. The Academy of Sciences
established The Sophie Germain Prize in her honor.
Marie-Sophie Germain was born on 1 April 1776, in Paris, France, in a house on Rue Saint-Denis.
Accordingto mostsources,herfather,Ambroise-Franҫois,wasawealthysilk merchant,[3][4][5] though
some believe he was a goldsmith.[6] In 1789, he was elected as a representative of the bourgeoisie to
the États-Généraux,whichhe sawchange intothe Constitutional Assembly.Itistherefore assumed that
Sophie witnessedmanydiscussionsbetweenherfatherandhisfriends on politics and philosophy. Gray
proposes that after his political career, Ambroise-Franҫois became the director of a bank; at least, the
family remained well-off enough to support Germain throughout her adult life.
Marie-Sophie hadone youngersister,namedAngélique-Ambroise, and one older sister, named Marie-
Madeline. Her mother was also named Marie-Madeline, and this plethora of "Maries" may have been
the reasonshe went by Sophie. Germain's nephew Armand-Jacques Lherbette, Marie-Madeline's son,
published some of Germain's work after she died (see Work in Philosophy).
Early work in number theory
Correspondence with Legendre
Germainfirstbecame interestedinnumbertheoryin1798 whenAdrien-Marie LegendrepublishedEssai
sur la théorie desnombres. Afterstudying the work, she opened correspondence with him on number

7. theory,andlater,elasticity.Legendre showedsomeof Germain'sworkin the Supplément to his second
editionof the Théorie desNombres,wherehe calls it très ingénieuse ["very ingenious"] (See Her work
on Fermat's Last Theorem).
Albert Einstein
AlbertEinstein wasunquestionablyone of the twogreatestphysicistsinall of history.The atomictheory
achieved general acceptance only after Einstein's 1905 paper which showed that atoms' discreteness
explainedBrownianmotion.Another 1905 paper introduced the famous equation E = mc2
; yet Einstein
publishedotherpapersthatsame year,twoof whichwere more importantandinfluential thaneitherof
the two just mentioned. No wonder that physicists speak of the Miracle Year without bothering to
qualify it as Einstein's Miracle Year! (Before his Miracle Year, Einstein had been a mediocre
undergraduate,andheldminorjobsincludingpatentexaminer.) Altogether Einstein published at least
300 books or papers on physics. For example, in a 1917 paper he anticipated the principle of the laser.
Also, sometimes in collaboration with Leo Szilard, he was co-inventor of several devices, including a
gyroscopic compass, hearing aid, automatic camera and, most famously, the Einstein-Szilard
refrigerator.He became averyfamousand influential public figure. (For example, it was his letter that
led Roosevelt to start the Manhattan Project.) Among his many famous quotations is: "The search for
truth ismore preciousthanits possession."EinsteinismostfamousforhisSpecial andGeneral Theories
of Relativity, but he should be considered the key pioneer of Quantum Theory as well, drawing
inferences from Planck's work that no one else dared to draw. Indeed it was his articulation of the
quantumprinciple ina1905 paperwhichhas been called"the mostrevolutionarysentence written by a
physicistof the twentiethcentury."Einstein'sdiscoveryof the photoninthatpaperledto hisonlyNobel
Prize; years later, he was first to call attention to the "spooky" nature of quantum entanglement.
Einsteinwas also first to call attention to a flaw in Weyl's earliest unified field theory. But despite the
importance of his other contributions it is Einstein's General Theory which is his most profound
contribution.Minkowski haddevelopedaflat 4-dimensional space-time to cope with Einstein's Special
Theory; but it was Einstein who had the vision to add curvature to that space to describe acceleration.

8. Einsteincertainlyhasthe breadth,depth,andhistorical importance toqualifyforthislist; but his genius
and significancewere notinthe fieldof pure mathematics. (He acknowledged his limitation, writing "I
admire the elegance of your[Levi-Civita's] methodof computation;itmustbe nice to ride throughthese
fields upon the horse of true mathematics while the like of us have to make our way laboriously on
foot.") Einstein was a mathematician, however; he pioneered the application of tensor calculus to
physicsandinventedthe Einstein summation notation.ThatEinstein'sequationexplaineda discrepancy.
Oswald Veblen
Oswald Veblen's first mathematical achievement was a novel system of axioms for geometry.
He also worked in topology; projective geometry; differential geometry (where he was first to
introduce the concept of differentiable manifold); ordinal theory (where he introduced the
Veblen hierarchy); and mathematical physics where he worked with spinors and relativity. He
developed a new theory of ballistics during World War I and helped plan the first American
computer during World War II. His famous theorems include the Veblen-Young Theorem (an
important algebraic fact about projective spaces); a proof of the Jordan Curve Theorem more
rigorous than Jordan's; and Veblen's Theorem itself (a generalization of Euler's result about
cycles in graphs). Veblen, a nephew of the famous economist Thorstein Veblen, was an
important teacher; his famous students included Alonzo Church, John W. Alexander, Robert L.
Moore, and J.H.C. Whitehead. He was also a key figure in establishing Princeton's Institute of
Advanced Study; the first five mathematicians he hired for the Institute were Einstein, von
Neumann, Weyl, J.W. Alexander and Marston Morse.

9. Luitzen Egbertus Jan Brouwer
Brouwer is often considered the "Father of Topology;" among his important theorems were the
Fixed Point Theorem, the "Hairy Ball" Theorem, the Jordan-Brouwer Separation Theorem, and
the Invariance of Dimension. He developed the method of simplicial approximations, important
to algebraic topology; he also did work in geometry, set theory, measure theory, complex
analysis and the foundations of mathematics. He was first to anticipate forms like the Lakes of
Wada, leading eventually to other measure-theory "paradoxes." Several great mathematicians,
including Weyl, were inspired by Brouwer's work in topology.
Brouwer is most famous as the founder of Intuitionism, a philosophy of mathematics in sharp
contrast to Hilbert's Formalism, but Brouwer's philosophy also involved ethics and aesthetics
and has been compared with those of Schopenhauer and Nietzsche. Part of his mathematics
thesis was rejected as "... interwoven with some kind of pessimism and mystical attitude to life
which is not mathematics ..." As a young man, Brouwer spent a few years to develop topology,
but once his great talent was demonstrated and he was offered prestigious professorships, he
devoted himself to Intuitionism, and acquired a reputation as eccentric and self-righteous.
Intuitionism has had a significant influence, although few strict adherents. Since only
constructive proofs are permitted, strict adherence would slow mathematical work. This didn't
worry Brouwer who once wrote: "The construction itself is an art, its application to the world
an evil parasite."

10. GEORGE BOOLE
George Boole (/ˈbuːl/; 2 November 1815 – 8 December 1864) was an English mathematician, educator,
philosopherandlogician.He workedinthe fieldsof differential equationsandalgebraiclogic,andisbest
known as the author of The Laws of Thought (1854) which contains Boolean algebra. Boolean logic is
credited with laying the foundations for the information age.[3] Boole maintained that:
No general methodforthe solutionof questionsinthe theoryof probabilities can be established which
does not explicitly recognise, not only the special numerical bases of the science, but also those
universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to
their essence, are at least mathematical as to their form
Boole wasborn inLincoln,Lincolnshire, England, the son of John Boole Sr (1779–1848), a shoemaker[5]
and Mary Ann Joyce.[6] He had a primary school education, and received lessons from his father, but
had little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have
helpedhimwithLatin,whichhe mayalsohave learnedatthe school of Thomas Bainbridge.He was sel f-
taught in modern languages. At age 16 Boole became the breadwinner for his parents and three
younger siblings, taking up a junior teaching position in Doncaster at Heigham's School.[7] He taught
briefly in Liverpool.
Greyfriars, Lincoln, which housed the Mechanic's Institute
Boole participated in the Mechanics Institute, in the Greyfriars, Lincoln, which was founded in 1833.
Edward Bromhead, who knew John Boole through the institution, helped George Boole with
mathematics books[9] and he was given the calculus text of Sylvestre François Lacroix by the Rev.
George StevensDicksonof StSwithin's,Lincoln.[10] Withoutateacher,ittookhimmanyyears to master
calculus. At age 19, Boole successfully established his own school in Lincoln. Four years later he took
over Hall's Academy in Waddington, outside Lincoln, following the death of Robert Hall. In 1840 he
moved back to Lincoln, where he ran a boarding school. Boole immediately became involved in the
Lincoln Topographical Society, on which he served as a member of the committee. On 30 November

11. 1841 he read a paper on On the origin, progress and tendencies Polytheism, especially amongst the
ancient Egyptians, and Persians, and in modern India.
Waclaw Sierpinski
Sierpinski won a gold medal as an undergraduate by making a major improvement to a famous
theorem by Gauss about lattice points inside a circle. He went on to do important research in
set theory, number theory, point set topology, the theory of functions, and fractals. He was
extremely prolific, producing 50 books and over 700 papers. He was a Polish patriot: he
contributed to the development of Polish mathematics despite that his land was controlled by
Russians or Nazis for most of his life. He worked as a code-breaker during the Polish-Soviet War,
helping to break Soviet ciphers.
Sierpinski was first to prove Tarski's remarkable conjecture that the Generalized Continuum
Hypothesis implies the Axiom of Choice. He developed three famous fractals: a space-filling
curve; the Sierpinski gasket; and the Sierpinski carpet, which covers the plane but has area zero
and has found application in antennae design. Borel had proved that almost all real numbers
are "normal" but Sierpinski was the first to actually display a number which is normal in every
base. He proved the existence of infinitely many Sierpinski numbers having the property that,
e.g. (78557·2n+1) is composite number for every natural number n. It remains an unsolved
problem (likely to be defeated soon with high-speed computers) whether 78557 is the smallest
such "Sierpinski number."

12. Solomon Lefschetz
Lefschetz was born in Russia, educated as an engineer in France, moved to U.S.A., was severely
handicapped in an accident, and then switched to pure mathematics. He was a key founder of
algebraic topology, even coining the word topology, and pioneered the application of topology
to algebraic geometry. Starting from Poincaré's work, he developed Lefschetz duality and used
it to derive conclusions about fixed points in topological mappings. The Lefschetz Fixed-point
Theorem left Brouwer's famous result as just a special case. His Picard-Lefschetz theory
eventually led to the proof of the Weil conjectures. Lefschetz also did important work in
algebraic geometry, non-linear differential equations, and control theory. As a teacher he was
noted for a combative style. Preferring intuition over rigor, he once told a student who had
improved on one of Lefschetz's proofs: "Don't come to me with your pretty proofs. We don't
bother with that baby stuff around here."

13. George David Birkhoff
Birkhoff is one of the greatest native-born American mathematicians ever, and did important
work in many fields. There are several significant theorems named after him: the Birkhoff-
Grothendieck Theorem is an important result about vector bundles; Birkhoff's Theorem is an
important result in algebra; and Birkhoff's Ergodic Theorem is a key result in statistical
mechanics which has since been applied to many other fields. His Poincaré-Birkhoff Fixed Point
Theorem is especially important in celestial mechanics, and led to instant worldwide fame: the
great Poincaré had described it as most important, but had been unable to complete the proof.
In algebraic graph theory, he invented Birkhoff's chromatic polynomial (while trying to prove
the four-color map theorem); he proved a significant result in general relativity which implied
the existence of black holes; he also worked in differential equations and number theory; he
authored an important text on dynamical systems. Like several of the great mathematicians of
that era, Birkhoff developed his own set of axioms for geometry; it is his axioms that are often
found in today's high school texts. Birkhoff's intellectual interests went beyond mathematics;
he once wrote "The transcendent importance of love and goodwill in all human relations is
shown by their mighty beneficent effect upon the individual and society."

14. Baron Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy FRS FRSE (French: [oɡystɛ̃ lwi koʃi]; 21 August 1789 – 23 May 1857) was a
Frenchmathematicianwhomade pioneering contributions to analysis. He was one of the first to state
and prove theoremsof calculusrigorously,rejectingthe heuristicprinciple of the generalityof algebraof
earlier authors. He almost singlehandedly founded complex analysis and the study of permutation
groups in abstract algebra. A profound mathematician, Cauchy had a great influence over his
contemporaries and successors. His writings range widely in mathematics and mathematical physics.
"More concepts and theorems have been named for Cauchy than for any other mathematician (in
elasticity alone there are sixteen concepts and theorems named for Cauchy)." Cauchy was a prolific
writer; he wrote approximately eight hundred research articles and five complete textbooks.
Youth and education
Cauchy was the son of Louis François Cauchy (1760–1848) and Marie-Madeleine Desestre. Cauchy had
twobrothers,AlexandreLaurentCauchy(1792–1857), whobecame a presidentof adivisionof the court
of appeal in 1847, and a judge of the court of cassation in 1849; and Eugene François Cauchy (1802–
1877), a publicist who also wrote several mathematical works. Cauchy married Aloise de Bure in 1818.
She was a close relative of the publisher who published most of Cauchy's works. By her he had two
daughters, Marie Françoise Alicia (1819) and Marie Mathilde (1823).
Cauchy'sfather(LouisFrançoisCauchy) wasa highofficial in the Parisian Police of the New Régime. He
lost his position because of the French Revolution (July 14, 1789) that broke out one month before
Augustin-Louiswasborn.[2] The Cauchyfamilysurvivedthe revolutionandthe followingReign of Terror
(1794) by escaping to Arcueil, where Cauchy received his first education, from his father. After the
execution of Robespierre (1794), it was safe for the family to return to Paris. There Louis-François
Cauchy found himself a new bureaucratic job, and quickly moved up the ranks. When Napoleon
Bonaparte came to power(1799), Louis-FrançoisCauchywasfurther promoted, and became Secretary-

15. General of the Senate, working directly under Laplace (who is now better known for his work on
mathematical physics). The famous mathematician Lagrange was also a friend of the Cauchy family.
Sir Andrew John Wiles
Sir Andrew John Wiles KBE FRS (born 11 April 1953) is a British mathematician and a Royal Society
Research Professor at the University of Oxford, specialising in number theory. He is most notable for
provingFermat'sLast Theorem,forwhichhe receivedthe 2016 Abel Prize Wileshasreceived numerous
other honours.
Education and early life
Wileswasborn in 1953 inCambridge, England, the son of Maurice Frank Wiles (1923–2005), the Regius
Professorof Divinity atthe Universityof Oxford,andPatriciaWiles(née Mowll).His fatherworkedas the
Chaplain at Ridley Hall, Cambridge, for the years 1952–55. Wiles attended King's College School,
Cambridge, and The Leys School, Cambridge.
Wilesstates that he came across Fermat's Last Theorem on his way home from school when he was 10
years old. He stopped by his local library where he found a book about the theorem.[8] Fascinated by
the existence of a theorem that was so easy to state that he, a ten-year-old, could understand it, but
nobodyhadprovenit,he decided to be the first person to prove it. However, he soon realised that his
knowledge was too limited, so he abandoned his childhood dream, until it was brought back to his
attention at the age of 33 by Ken Ribet's 1986 proof of the epsilon conjecture, which Gerhard Frey had
previously linked to Fermat's famous equation.
Career and research
Wiles earned his bachelor's degree in mathematics in 1974 at Merton College, Oxford, and a PhD in
1980 at Clare College,Cambridge.Afterastayat the Institute forAdvancedStudyinNew Jersey in 1981,
Wiles became a professor at Princeton University. In 1985–86, Wiles was a Guggenheim Fellow at the
Institutdes Hautes Études Scientifiques near Paris and at the École Normale Supérieure. From 1988 to
1990, Wileswasa Royal SocietyResearchProfessoratthe Universityof Oxford,andthen he returned to
Princeton. He rejoined Oxford in 2011 as Royal Society Research Professor. Wiles's graduate research
was guidedbyJohnCoatesbeginninginthe summerof 1975. Together these colleagues worked on the

16. arithmeticof ellipticcurveswithcomplex multiplication by the methods of Iwasawa theory. He further
worked with Barry Mazur on the main conjecture of Iwasawa theory over the rational numbers, and
soon afterward, he generalised this result to totally real fields
Hermann Klaus Hugo (Peter) Weyl
Weyl studied under Hilbert and became one of the premier mathematicians of the 20th
century. His discovery of gauge invariance and notion of Riemann surfaces form the basis of
modern physics. He excelled at many fields including integral equations, harmonic analysis,
analytic number theory, Diophantine approximations, and the foundations of mathematics, but
he is most respected for his revolutionary advances in geometric function theory (e.g.,
differentiable manifolds), the theory of compact groups (incl. representation theory), and
theoretical physics (e.g., Weyl tensor, gauge field theory and invariance). For a while, Weyl was
a disciple of Brouwer's Intuitionism and helped advance that doctrine, but he eventually found
it too restrictive. Weyl was also a very influential figure in all three major fields of 20th-century
physics: relativity, unified field theory and quantum mechanics. Because of his contributions to
Schrödinger, many think the latter's famous result should be named Schrödinger-Weyl Wave
Equation.
Vladimir Vizgin wrote "To this day, Weyl's [unified field] theory astounds all in the depth of its
ideas, its mathematical simplicity, and the elegance of its realization." Weyl once wrote: "My
work always tried to unite the Truth with the Beautiful, but when I had to choose one or the
other, I usually chose the Beautiful."

18. John Edensor Littlewood
John Littlewood was a very prolific researcher. (This fact is obscured somewhat in that many
papers were co-authored with Hardy, and their names were always given in alphabetic order.)
The tremendous span of his career is suggested by the fact that he won Smith's Prize (and
Senior Wrangler) in 1905 and the Copley Medal in 1958. He specialized in analysis and analytic
number theory but also did important work in combinatorics, Fourier theory, Diophantine
approximations, differential equations, and other fields. He also did important work in practical
engineering, creating a method for accurate artillery fire during the First World War, and
developing equations for radio and radar in preparation for the Second War. He worked with
the Prime Number Theorem and Riemann's Hypothesis; and proved the unexpected fact that
Chebyshev's bias, and Li(x)>π(x), while true for most, and all but very large, numbers, are
violated infinitely often. Some of his work was elementary, e.g. his elegant proof that a cube
cannot be dissected into unequal cubes; but most of his results were too specialized to state
here, e.g. his widely-applied 4/3 Inequality which guarantees that certain bimeasures are finite,
and which inspired one of Grothendieck's most famous results. Hardy once said that his friend
was "the man most likely to storm and smash a really deep and formidable problem; there was
no one else who could command such a combination of insight, technique and power."
Littlewood's response was that it was possible to be too strong of a mathematician, "forcing
through, where another might be driven to a different, and possibly more fruitful, approach."

19. Thoralf Albert Skolem
Thoralf Skolem proved fundamental theorems of lattice theory, proved the Skolem-Noether
Theorem of algebra, also worked with set theory and Diophantine equations; but is best known
for his work in logic, metalogic, and non-standard models. Some of his work preceded similar
results by Gödel. He developed a theory of recursive functions which anticipated some
computer science. He worked on the famous Löwenheim-Skolem Theorem which has the
"paradoxical" consequence that systems with uncountable sets can have countable models.
("Legend has it that Thoralf Skolem, up until the end of his life, was scandalized by the
association of his name to a result of this type, which he considered an absurdity,
nondenumerable sets being, for him, fictions without real existence.")

20. George Pólya
George Pólya (Pólya György) did significant work in several fields: complex analysis, probability,
geometry, algebraic number theory, and combinatorics, but is most noted for his teaching How
to Solve It, the craft of problem posing and proof. He is also famous for the Pólya Enumeration
Theorem. Several other important theorems he proved include the Pólya-Vinogradov Inequality
of number theory, the Pólya-Szego Inequality of functional analysis, and the Pólya Inequality of
measure theory. He introduced the Hilbert-Pólya Conjecture that the Riemann Hypothesis
might be a consequence of spectral theory; he introduced the famous "All horses are the same
color" example of inductive fallacy; he named the Central Limit Theorem of statistics. Pólya was
the "teacher par excellence": he wrote top books on multiple subjects; his successful students
included John von Neumann. His work on plane symmetry groups directly inspired Escher's
drawings. Having huge breadth and influence, Pólya has been called "the most influential
mathematician of the 20th century."

21. Grigori Yakovlevich Perelman
Grigori Yakovlevich Perelman (Russian: Григо́рий Я́ковлевич Перельма́н; IPA: [ɡrʲɪˈɡorʲɪj
ˈjakəvlʲɪvʲɪtɕ pʲɪrʲɪlʲˈman] ( listen) /pɛrᵻlˈmɑːn/ perr-il-mahn; born 13 June 1966) is a Russian
mathematician. He was the winner of the all-Russian mathematical olympiad. He made a
landmark contribution to Riemannian geometry and geometric topology.
In 1994, Perelman proved the soul conjecture. In 2003, he proved (confirmed in 2006)
Thurston's geometrization conjecture. This consequently solved in the affirmative the Poincaré
conjecture.
In August 2006, Perelman was offered to be awarded the Fields Medal for "his contributions to
geometry and his revolutionary insights into the analytical and geometric structure of the Ricci
flow", but he declined to accept the award, stating: "I'm not interested in money or fame; I
don't want to be on display like an animal in a zoo."[2] On 22 December 2006, the scientific
journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific
"Breakthrough of the Year", the first such recognition in the area of mathematics.
On 18 March 2010, it was announced that he had met the criteria to receive the first Clay
Millennium Prize[4] for resolution of the Poincaré conjecture. On 1 July 2010, he turned down
the prize of one million dollars, saying that he considered the decision of the board of CMI and
the award very unfair and that his contribution to solving the Poincaré conjecture was no
greater than that of Richard S. Hamilton, the mathematician who pioneered the Ricci flow with
the aim of attacking the conjecture. He also turned down the prestigious prize of the European
Mathematical Society.

22. UNIVERISITY OF NORTHEASTERN PHILIPPINES
Iriga City
S/Y 2017-2018
Submitted by:
ROXANNE CHEE I. BESADA
V- CARIÑOSA
Submitted to:
MRS. RICHELLE M. SERGIO
Teacher

23. UNIVERISITY OF NORTHEASTERN PHILIPPINES
Iriga City
S/Y 2017-2018
Submitted by:
ROXANNE CHEE I. BESADA
V- CARIÑOSA
Submitted to: