Ada LovelaceA gifted mathematician, Ada Lovelace is considered to have written instructions for the first computer program in the 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 algorithm intended to be carried out by such a machine. As a result, she is often regarded 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"), Lady Wentworth. All Byron's other 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 months later, eventually dying of disease in the 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 remained interested in him despite this (and was, upon her eventual death, buried next to him at her request). Often ill, she spent most of her childhood sick. Ada married William 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 David Brewster, Charles Wheatstone, Michael Faraday and the author Charles Dickens, which she used to further her education. Ada described her approach as "poetical science" and herself as an "Analyst (& Metaphysician)".

When she was a teenager, her mathematical talents led her to a long working relationship and friendship with fellow British mathematician Charles Babbage, also known as 'the father of computers', and in particular, Babbage's work on the Analytical Engine. Lovelace first met him in June 1833, through their mutual 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 computer program—that is, an algorithm designed to be carried out by a machine. Lovelace's notes are important in the early history of 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, focused only on those capabilities. Her mindset of "poetical science" led her to ask questions about the Analytical Engine (as shown in her notes) examining how individuals and society relate to technology as a collaborative tool.

She died of uterine cancer in 1852 at the age of 36.

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]), is short for "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.

BiographyFibonacci was born around 1175 to Guglielmo Bonacci, a wealthy Italian merchant and, by some accounts, the consul for Pisa. Guglielmo directed a trading post in Bugia, a port in the Almohad dynasty'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 learning about their 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.

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 between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.

Cantor's theory of transfinite numbers was originally regarded as so counter-intuitive – even shocking – that it encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections. Cantor, a devout Lutheran, believed the theory had been communicated to him by God. Some Christian theologians (particularly neo-Scholastics) saw Cantor's work as a challenge to the uniqueness of 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 objections to Cantor's work were occasionally fierce: Henri Poincaré referred to his ideas as a "grave disease" infecting the discipline of mathematics, and Leopold Kronecker's public opposition and personal attacks included describing Cantor as a "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 numbers are uncountable, results now included in a standard mathematics curriculum. Writing decades after Cantor's death, 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's recurring bouts of depression from 1884 to the end of his life have been blamed on the hostile attitude of many of his contemporaries, though some have explained these episodes as probable manifestations of a bipolar disorder.

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 described by 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 required examinations, but instead studied mathematics at the University of Erlangen, where her father lectured. After completing her dissertation in 1907 under the supervision of Paul Gordan, she worked at the Mathematical Institute of Erlangen without pay for seven years. At the time, women were largely excluded from academic positions. 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 faculty objected, however, and she spent four years lecturing under Hilbert'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 Waerden joined her circle and soon became the leading expositor of Noether's ideas: her work was the foundation for the second volume of his influential 1931 textbook, Moderne Algebra. By the time of her plenary address at the 1932 International Congress of Mathematicians in Zürich, her algebraic acumen was recognized around the world. The following year, Germany's Nazi government dismissed Jews from university positions, and Noether moved to the United States to take up a position at Bryn Mawr College in Pennsylvania. In 1935 she underwent surgery for an ovarian cyst and, despite signs of a recovery, died four days later at the age of 53.

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 contributions to 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 Sciences with game theorists Reinhard Selten 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 hospitals being treated for paranoid schizophrenia. After 1970, his condition slowly improved, allowing him to return to academic work by the mid-1980s. His struggles with his illness and his recovery became the basis for Sylvia Nasar's biography, A Beautiful Mind, as well as a film of the same name starring Russell Crowe. On May 23, 2015, Nash and his wife, Alicia Nash, 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 been a schoolteacher before she married. He was baptized in the Episcopal Church.[8] He had a younger sister, Martha (born November 16, 1930).

Nash attended kindergarten and public school, 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 year of high school. He attended Carnegie Institute of Technology through a full benefit of the George Westinghouse Scholarship, initially majoring in chemical 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 ʒɛʁm ]; 1 April 1776 – 27 June 1831) was a Frenchɛ̃ mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by society, she gained education from books in her father's library including ones by Leonhard Euler and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss. One of the pioneers of elasticity theory, she won the grand prize from the Paris Academy of Sciences for her essay on the subject. Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. 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. According to most sources, her father, Ambroise-Franҫois, was a wealthy silk 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, which he saw change into the Constitutional Assembly. It is therefore assumed that Sophie witnessed many discussions between her father and his friends 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 had one younger sister, named Angélique-Ambroise, and one older sister, named Marie-Madeline. Her mother was also named Marie-Madeline, and this plethora of "Maries" may have been the reason she 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 theoryCorrespondence with LegendreGermain first became interested in number theory in 1798 when Adrien-Marie Legendre published Essai sur la théorie des nombres. After studying the work, she opened correspondence with him on number theory, and later, elasticity. Legendre showed some of Germain's work in the Supplément to his second edition of the Théorie des Nombres, where he calls it très ingénieuse ["very ingenious"] (See Her work on Fermat's Last Theorem).

Albert  Einstein 

Albert Einstein was unquestionably one of the two greatest physicists in all of history. The atomic theory achieved general acceptance only after Einstein's 1905 paper which showed that atoms' discreteness explained Brownian motion. Another 1905 paper introduced the famous equation E = mc2; yet Einstein published other papers that same year, two of which were more important and influential than either of 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, and held minor jobs including patent examiner.) 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 a very famous and 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 is more precious than its possession." Einstein is most famous for his Special and General 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 quantum principle in a 1905 paper which has been called "the most revolutionary sentence written by a physicist of the twentieth century." Einstein's discovery of the photon in that paper led to his only Nobel Prize; years later, he was first to call attention to the "spooky" nature of quantum entanglement. Einstein was 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 had developed a flat 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. Einstein certainly has the breadth, depth, and historical importance to qualify for this list; but his genius and significance were not in the field of pure mathematics. (He acknowledged his limitation, writing "I admire the elegance of your [Levi-Civita's] method of computation; it must be nice to ride through these 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 physics and invented the Einstein summation notation. That Einstein's equation explained a 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.

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."

GEORGE BOOLE

George Boole (/ˈbuːl/; 2 November 1815 – 8 December 1864) was an English mathematician, educator, philosopher and logician. He worked in the fields of differential equations and algebraic logic, and is best 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 method for the solution of questions in the theory of 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 was born in Lincoln, 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 helped him with Latin, which he may also have learned at the school of Thomas Bainbridge. He was self-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 InstituteBoole 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 Stevens Dickson of St Swithin's, Lincoln.[10] Without a teacher, it took him many years 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 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."

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."

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."

Baron Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (French: [oɡyst lwi koʃi]; 21 August 1789 – 23 May 1857) was aɛ̃ French mathematician who made pioneering contributions to analysis. He was one of the first to state and prove theorems of calculus rigorously, rejecting the heuristic principle of the generality of algebra of 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 educationCauchy was the son of Louis François Cauchy (1760–1848) and Marie-Madeleine Desestre. Cauchy had two brothers, Alexandre Laurent Cauchy (1792–1857), who became a president of a division of 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's father (Louis François Cauchy) was a high official 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-Louis was born.[2] The Cauchy family survived the revolution and the following Reign 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-François Cauchy was further promoted, and became Secretary-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 proving Fermat's Last Theorem, for which he received the 2016 Abel Prize Wiles has received numerous other honours.

Education and early lifeWiles was born in 1953 in Cambridge, England, the son of Maurice Frank Wiles (1923–2005), the Regius Professor of Divinity at the University of Oxford,and Patricia Wiles (née Mowll). His father worked as the Chaplain at Ridley Hall, Cambridge, for the years 1952–55. Wiles attended King's College School, Cambridge, and The Leys School, Cambridge.

Wiles states 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 nobody had proven it, 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 researchWiles earned his bachelor's degree in mathematics in 1974 at Merton College, Oxford, and a PhD in 1980 at Clare College, Cambridge. After a stay at the Institute for Advanced Study in New Jersey in 1981, Wiles became a professor at Princeton University. In 1985–86, Wiles was a Guggenheim Fellow at the Institut des Hautes Études Scientifiques near Paris and at the École Normale Supérieure. From 1988 to 1990, Wiles was a Royal Society Research Professor at the University of Oxford, and then he returned to Princeton. He rejoined Oxford in 2011 as Royal Society Research Professor. Wiles's graduate research was guided by John Coates beginning in the summer of 1975. Together these colleagues worked on the arithmetic of elliptic curves with complex 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."

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."

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.")

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."

Grigori Yakovlevich Perelman

Grigori Yakovlevich Perelman (Russian: Григ рий ковлевич Перельм н; IPA: [ɡrʲɪˈɡorʲɪjо́ Я́ а́ 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.

UNIVERISITY OF NORTHEASTERN PHILIPPINESIriga City

S/Y 2017-2018

Submitted by:

ROXANNE CHEE I. BESADA V- CARIÑOSA

Submitted to:

MRS. RICHELLE M. SERGIO

Teacher

UNIVERISITY OF NORTHEASTERN PHILIPPINESIriga City

S/Y 2017-2018

Submitted by:

ROXANNE CHEE I. BESADA V- CARIÑOSA

Submitted to: