Branches of Mathematics

Pure mathematics

• Algebra
• Calculus
• Geometry
• Topology
• Trignometry
• Combinatorics
• Logic
• Number theory

Applied mathematics

• Dynamical systems and differential equations
• Mathematical physics
• Computing
• Information theory and signal processing
• Probability and statistics
• Game theory
• Operations research

Related Topics

• Electromagnetic Spectrum
• Linear Equations
• Applied Physics
• Nano Technology
• Engineering Sciences
• Mathematical Medicine
• Fluid dynamics
• Computational Mathematics
• Gamma Ray Optics
• Onfrared Optics
• Relative Velocity
• Iciam
• Intelligent Imaging Neuroscience
• Biomedical Engineering
• Neuroscience Research
• Quantum Cosmology
• Brain Research

• Abstract algebra
• Ada Lovelace
• Alan Turing
• Alfred W. Adler
• Alfréd Rényi
• Algebraic geometry
• Alicia Boole Stott
• Alonzo Church
• Analysis
• Andrey Kolmogorov
• Applied mathematics
• Archimedes
• Aryabhatta
• Balzan Prize
• Bernhard Riemann
• Bhaskara II
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• C. P. Snow
• Calculus
• Carl Friedrich Gauss
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• Category theory
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• Conjecture
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• Data
• David Hilbert
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• Euclid of Alexandria
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• Game theory
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• Generalization
• Geometry
• Georg Cantor
• Gottfried Leibniz
• Henri Poincaré
• Information theory
• Integer
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• Jacob Bernoulli
• Johann Bernoulli
• Joseph Fourier
• Jules Henri Poincaré
• Julia Robinson
• Knowledge
• Kurt Gödel
• Leonhard Euler
• Logic
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• Maria Gaetana Agnesi
• Mary Cartwright
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• Mathematical science
• Mathematician
• Mathematics
• MathWorld
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• Nevanlinna Prize
• Nikolay Bogolyubov
• Nikolay Lobachevsky
• Nilakantha Somayaji
• Number
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• Numerical analysis
• Olga Taussky-Todd
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• Person
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• Pierre de Fermat
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• Portal Mathematics
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• Rózsa Péter
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• Set theory
• Shaw Prize
• Sofia Kovalevskaya
• Sophie Germain
• Space
• Srinivasa Ramanujan
• Statistics
• String theory
• Structure
• Tom Lehrer
• Topology
• Truth claim
• Von Neumann
• Wolf Prize
• World War II
• Émilie du Châtelet
• Évariste Galois
• 
  

• 
  Ada Lovelace
  Augusta Ada King, Countess of Lovelace (10 December 1815 - 27 November 1852), born Augusta Ada Byron, was an English mathematician and writer chiefly known for her work on Charles Babbage's early mechanical general-purpose computer, the analytical engine. Her notes on the engine include what is recognised as the first algorithm intended to be processed by a machine; thanks to this, she is sometimes considered the world's first computer programmer.
  She was the only legitimate child of the poet Lord Byron (with Anne Isabella Milbanke, 11th Baroness Wentworth). She had no relationship with her father, who died when she was nine. As a young adult, she took an interest in mathematics, and in particular Babbage's work on the analytical engine. Between 1842 and 1843, she translated an article by Italian mathematician Luigi Menabrea on the engine, which she supplemented with a set of notes of her own. These notes contain what is considered the first computer programme — that is, an algorithm encoded for processing by a machine. Though Babbage's engine has never been built, Lovelace's notes are important in the early history of computers. She also foresaw the capability of computers to go beyond mere calculating or number-crunching while others, including Babbage himself, focused only on these capabilities.
  
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  Alan Turing
  Alan Mathison Turing, OBE, FRS ( /ˈtjʊərɪŋ/ TEWR-ing; 23 June 1912 – 7 June 1954), was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a significant role in the creation of the modern computer. Turing is widely considered to be the father of computer science and artificial intelligence.
  During the Second World War, Turing worked for the Government Code and Cypher School (GCCS) at Bletchley Park, Britain's codebreaking centre. For a time he was head of Hut 8, the section responsible for German naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine.
  After the war he worked at the National Physical Laboratory, where he created one of the first designs for a stored-program computer, the ACE. In 1948 Turing joined Max Newman's Computing Laboratory at Manchester University, where he assisted in the development of the Manchester computers and became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis, and he predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, which were first observed in the 1960s.
  
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  Alfréd Rényi
  Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory.
  Rényi was born in Budapest to Artur Rényi and Barbara Alexander; his father was a mechanical engineer while his mother was the daughter of a philosopher and literary critic, Bernát Alexander. He was prevented from enrolling in university in 1939 due to the anti-Jewish laws then in force, but enrolled at the University of Budapest in 1940 and finished his studies in 1944. At this point he was drafted to forced labour service, escaped, and completed his Ph.D. in 1947 at the University of Szeged, under the advisement of Frigyes Riesz. He married Katalin Schulhof (who used Kató Rényi as her married name), herself a mathematician, in 1946; their daughter Zsuzsanna was born in 1948. After a brief assistant professorship at Budapest, he was appointed Professor Extraordinary at the University of Debrecen in 1949. In 1950, he founded the Mathematics Research Institute of the Hungarian Academy of Sciences, now bearing his name, and directed it until his early death. He also headed the Department of Probability and Mathematical Statistics of the Eötvös Loránd University, from 1952. He was elected a corresponding member(1949), full member (1956) of the Hungarian Academy of Sciences
  
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• Alicia Boole Stott
  Alicia Boole Stott (June 8, 1860, Cork, Ireland – December 17, 1940, England) was the third daughter of George Boole and Mary Everest Boole. Before marrying Walter Stott, an actuary, in 1890, she was known as Alicia Boole. She is best known for coining the term "polytope" for a convex solid in four dimensions, and having an impressive grasp of four-dimensional geometry from a very early age.
  She found that there were exactly six regular polytopes in four dimensions and that they are bounded by 5, 16 or 600 tetrahedra, 8 cubes, 24 octahedra or 120 dodecahedra. She then produced three-dimensional central cross-sections of all the six regular polytopes by purely Euclidean constructions and synthetic methods for the simple reason that she had never learned any analytic geometry. She made beautiful cardboard models of all these sections.
  After taking up secretarial work near Liverpool in 1889 she met and married Walter Stott in 1890. Stott learned of Pieter Schoute's work on central sections of the regular polytopes in 1895. Schoute came to England and worked with Alicia Stott, persuading her to publish her results which she did in two papers published in Amsterdam in 1900 and 1910.
  
  wn.com/Alicia_Boole_Stott
• Alonzo Church
  Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, solving the Entscheidungsproblem, Frege–Church ontology, and the Church–Rosser theorem.
  Alonzo Church was born on June 14, 1903 in Washington, D.C. where his father, Samuel Robbins Church, was the judge of the Municipal Court for the District of Columbia. The family later moved to Virginia after his father lost this position because of failing eyesight. With help from his uncle, also named Alonzo Church, he was able to attend the Ridgefield School for Boys in Ridgefield, Connecticut. After graduating from Ridgefield in 1920, Church attended Princeton University where he was an exceptional student, publishing his first paper, on Lorentz transformations, and graduating in 1924 with a degree in mathematics. He stayed at Princeton, earning a Ph.D. in mathematics in three years under Oswald Veblen.
  
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  Andrey Kolmogorov
  Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров) (25 April 1903 – 20 October 1987) was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.
  Kolmogorov was born at Tambov in 1903. His unwed mother died in childbirth and he was raised by his aunts in Tunoshna near Yaroslavl at the estate of his grandfather, a wealthy nobleman. His father, an agronomist by trade, was deported from Saint-Petersburg for participation in the revolutionary movement. He disappeared and was presumed to have been killed in the Russian Civil War.
  Kolmogorov was educated in his aunt's village school, and his earliest literary efforts and mathematical papers were printed in the school newspaper. As an adolescent he designed perpetual motion machines, concealing their (necessary) defects so cleverly that his secondary-school teachers could not discover them. In 1910, his aunt adopted him and then they moved to Moscow, where he went to a gymnasium, graduating from it in 1920.
  
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  Archimedes
  Archimedes of Syracuse (Ancient Greek: Ἀρχιμήδης; c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.
  Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.
  
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  Bernhard Riemann
  Georg Friedrich Bernhard Riemann [ˈʁiːman] ( listen) (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting contributions to analysis, number theory and differential geometry, some of them enabling the later development of general relativity.
  Riemann was born in Breselenz, a village near Dannenberg in the Kingdom of Hanover in what is the Federal Republic of Germany today. His father, Friedrich Bernhard Riemann, was a poor Lutheran pastor in Breselenz who fought in the Napoleonic Wars. His mother, Charlotte Ebell, died before her children had reached adulthood. Riemann was the second of six children, shy, and suffered from numerous nervous breakdowns. Riemann exhibited exceptional mathematical skills, such as fantastic calculation abilities, from an early age but suffered from timidity and a fear of speaking in public.
  During 1840, Riemann went to Hanover to live with his grandmother and attend lyceum (middle school). After the death of his grandmother in 1842, he attended high school at the Johanneum Lüneburg. In high school, Riemann studied the Bible intensively, but he was often distracted by mathematics. His teachers were amazed by his adept ability to solve complicated mathematical operations, in which he often outstripped his instructor's knowledge. In 1846, at the age of 19, he started studying philology and theology in order to become a priest and help with his family's finances.
  
  wn.com/Bernhard_Riemann
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  Brahmagupta
  Brahmagupta (Sanskrit: ब्रह्मगुप्त;  listen (help·info)) (598–668 CE) was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta (Correctly Established Doctrine of Brahma), written in 628 in Bhinmal. Its 25 chapters contain several unprecedented mathematical results.
  Brahmagupta is believed to have been born in 598 AD in Bhinmal city in the state of Rajasthan of Northwest India. In ancient times Bhillamala was the seat of power of the Gurjars. His father was Jisnugupta. He likely lived most of his life in Bhillamala (modern Bhinmal in Rajasthan) during the reign (and possibly under the patronage) of King Vyaghramukha. As a result, Brahmagupta is often referred to as Bhillamalacarya, that is, the teacher from Bhillamala. He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote four texts on mathematics and astronomy: the Cadamekela in 624, the Brahmasphutasiddhanta in 628, the Khandakhadyaka in 665, and the Durkeamynarda in 672. The Brahmasphutasiddhanta (Corrected Treatise of Brahma) is arguably his most famous work. The historian al-Biruni (c. 1050) in his book Tariq al-Hind states that the Abbasid caliph al-Ma'mun had an embassy in India and from India a book was brought to Baghdad which was translated into Arabic as Sindhind. It is generally presumed that Sindhind is none other than Brahmagupta's Brahmasphuta-siddhanta.
  
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  Carl Friedrich Gauss
  Johann Carl Friedrich Gauss ( /ˈɡaʊs/; German: Gauß  listen (help·info), Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and physical scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.
  Sometimes referred to as the Princeps mathematicorum (Latin, "the Prince of Mathematicians" or "the foremost of mathematicians") and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians. He referred to mathematics as "the queen of sciences".
  Carl Friedrich Gauss was born on 30 April 1777 in Braunschweig, in the duchy of Braunschweig-Wolfenbüttel, now part of Lower Saxony, Germany, as the son of poor working-class parents. Indeed, his mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension, which itself occurs 40 days after Easter. Gauss would later solve this puzzle for his birthdate in the context of finding the date of Easter, deriving methods to compute the date in both past and future years. He was christened and confirmed in a church near the school he attended as a child.
  
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  David Hilbert
  David Hilbert, FRS (German pronunciation: [ˈdaːvɪt ˈhɪlbɐt]; January 23, 1862 – February 14, 1943) was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
  Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century.
  Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.
  
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  Edgar Allan Poe
  Edgar Allan Poe (born Edgar Poe; January 19, 1809 – October 7, 1849) was an American author, poet, editor and literary critic, considered part of the American Romantic Movement. Best known for his tales of mystery and the macabre, Poe was one of the earliest American practitioners of the short story and is considered the inventor of the detective fiction genre. He is further credited with contributing to the emerging genre of science fiction. He was the first well-known American writer to try to earn a living through writing alone, resulting in a financially difficult life and career.
  He was born as Edgar Poe in Boston, Massachusetts; he was orphaned young when his mother died shortly after his father abandoned the family. Poe was taken in by John and Frances Allan, of Richmond, Virginia, but they never formally adopted him. He attended the University of Virginia for one semester but left due to lack of money. After enlisting in the Army and later failing as an officer's cadet at West Point, Poe parted ways with the Allans. His publishing career began humbly, with an anonymous collection of poems, Tamerlane and Other Poems (1827), credited only to "a Bostonian".
  
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  Emmy Noether
  Amalie Emmy Noether (German: [ˈnøːtɐ]; 23 March 1882 – 14 April 1935), sometimes referred to as Emily or Emmy, was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, Norbert Wiener and others as the most important woman in the history of mathematics, she revolutionized the theories of rings, fields, and algebras. In physics, Noether's theorem explains the fundamental connection between symmetry and conservation laws.
  She was born to a Jewish family in the Bavarian town of Erlangen; her father was mathematician Max Noether. Emmy 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.
  
  wn.com/Emmy_Noether
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  Georg Cantor
  Georg Ferdinand Ludwig Philipp Cantor ( /ˈkæntɔr/ KAN-tor; German: [ɡeˈɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfiːlɪp ˈkantɔʁ]; March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician, best known as the inventor of 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.
  
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  Henri Poincaré
  Jules Henri Poincaré (29 April 1854 – 17 July 1912) (French pronunciation: [ˈʒyl ɑ̃ˈʁi pwɛ̃nkaˈʁe]) was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.
  As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, which was one of the most famous unsolved problems in mathematics until it was solved in 2002–2003. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology.
  Poincaré made clear importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Dutch physicist Hendrik Lorentz (1853–1928) in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity.
  
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  Isaac Newton
  Sir Isaac Newton PRS MP (25 December 1642 – 20 March 1727 [NS: 4 January 1643 – 31 March 1727]) was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived." His monograph Philosophiæ Naturalis Principia Mathematica, published in 1687, lays the foundations for most of classical mechanics. In this work, Newton described universal gravitation and the three laws of motion, which dominated the scientific view of the physical universe for the next three centuries. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws, by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the Scientific Revolution.
  
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  Jacob Bernoulli
  Jacob Bernoulli (also known as James or Jacques) (27 December 1654 – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.
  Jacob Bernoulli was born in Basel, Switzerland. Following his father's wish, he studied theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy. He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences. This included the work of Robert Boyle and Robert Hooke.
  He became familiar with calculus through a correspondence with Gottfried Leibniz, then collaborated with his brother Johann on various applications, notably publishing papers on transcendental curves (1696) and isoperimetry (1700, 1701). In 1690, Jacob Bernoulli became the first person to develop the technique for solving separable differential equations.
  Upon returning to Basel in 1682, he founded a school for mathematics and the sciences. He was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life.
  
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  Johann Bernoulli
  Johann Bernoulli (27 July 1667 – 1 January 1748; also known as Jean or John) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educated Leonhard Euler in his youth.
  Johann was born in Basel, the son of Nikolaus Bernoulli, an apothecary, and his wife, Margaretha Schonauer and began studying medicine at Basel University. His father desired that he study business so that he might take over the family spice trade, but Johann Bernoulli disliked business and convinced his father to allow him to study medicine instead. However, Johann Bernoulli did not enjoy medicine either and began studying mathematics on the side with his older brother Jacob. Throughout Johann Bernoulli’s education at Basel University the Bernoulli brothers worked together spending much of their time studying the newly discovered infinitesimal calculus. They were among the first mathematicians to not only study and understand calculus but to apply it to various problems.
  
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  Joseph Fourier
  Jean Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French mathematician and physicist best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's Law are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect.
  Fourier was born at Auxerre (now in the Yonne département of France), the son of a tailor. He was orphaned at age eight. Fourier was recommended to the Bishop of Auxerre, and through this introduction, he was educated by the Benvenistes of the Convent of St. Mark. The commissions in the scientific corps of the army were reserved for those of good birth, and being thus ineligible, he accepted a military lectureship on mathematics. He took a prominent part in his own district in promoting the French Revolution, serving on the local Revolutionary Committee. He was imprisoned briefly during the Terror but in 1795 was appointed to the École Normale Supérieure, and subsequently succeeded Joseph-Louis Lagrange at the École Polytechnique.
  
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  Julia Robinson
  Julia Hall Bowman Robinson (December 8, 1919 – July 30, 1985) was an American mathematician best known for her work on decision problems and Hilbert's Tenth Problem.
  Robinson was born in St. Louis, Missouri, the daughter of Ralph Bowers Bowman and Helen (Hall) Bowman. Her older sister was the mathematical popularizer and biographer Constance Reid. The family moved to Arizona and then to San Diego when the girls were a few years old. Julia attended San Diego High.
  She entered San Diego State University in 1936 and transferred as a senior to University of California, Berkeley in 1939. She received her BA degree in 1940 and continued in graduate studies. She received the Ph.D. degree in 1948 under Alfred Tarski with a dissertation on "Definability and Decision Problems in Arithmetic".
  In 1975 she became a full professor at Berkeley, teaching quarter-time because she still did not feel strong enough for a full-time job.
  Hilbert's tenth problem asks for an algorithm to determine whether a Diophantine equation has any solutions in integers. A series of results developed in the 1940s through 1970 by Robinson, Martin Davis, Hilary Putnam, and Yuri Matiyasevich resolved this problem in the negative; that is, they showed that no such algorithm can exist.
  
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  Kurt Gödel
  Kurt Friedrich Gödel (/ˈkɜrt ɡɜrdəl/; German pronunciation: [ˈkʊʁt ˈɡøːdəl] ( listen); April 28, 1906 – January 14, 1978) was an Austrian/American logician, mathematician, and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.
  Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.
  
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  Leonhard Euler
  Leonhard Euler (German pronunciation: [ˈɔʏlɐ], ( Swiss German pronunciation (help·info)) ( Standard German pronunciation (help·info)) English approximation, "Oiler"; 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy.
  Euler spent most of his adult life in St. Petersburg, Russia, and in Berlin, Prussia. He is considered to be the preeminent mathematician of the 18th century, and one of the greatest of all time. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all."
  
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  Maria Gaetana Agnesi
  Maria Gaetana Agnesi (May 16, 1718 – January 9, 1799) was an Italian linguist, mathematician, and philosopher. Agnesi is credited with writing the first book discussing both differential and integral calculus. She was an honorary member of the faculty at the University of Bologna. According to Dirk Jan Struik, Agnesi is "the first important woman mathematician since Hypatia (fifth century A.D.)".
  Her sister was Maria Teresa Agnesi Pinottini, a pianist and composer.
  Maria Gaetana Agnesi was born in Milan on May 16, 1718, to a wealthy and literate family. Her father wanted to elevate his family into the Milanese nobility. In order to achieve his goal, he had married in 1717 Anna Fortunata Brivio. Her mother's death provided her the excuse to retire from public life. She took over management of the household.
  
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• Mary Cartwright
  Dame Mary Lucy Cartwright DBE FRS (17 December 1900 – 3 April 1998) was a leading 20th-century British mathematician. She was born in Aynho, Northamptonshire where her father was the vicar and died in Cambridge, England. Through her Grandmother Jane Holbech she was descended from the poet John Donne and William Mompesson the Vicar of Eyam.
  She then taught at Alice Ottley School in Worcester and Wycombe Abbey School in Buckinghamshire before returning to Oxford in 1928 to read for her D.Phil.
  She was supervised by G. H. Hardy in her doctoral studies. During the academic year 1928–9 Hardy was at Princeton, so it was E. C. Titchmarsh who took over the duties as a supervisor. Her thesis on zeros of entire functions was examined by J. E. Littlewood whom she met for the first time as an external examiner in her oral examination for the D.Phil. She would later become a major collaborator with Littlewood, over many years.
  In 1930 Cartwright was awarded a Yarrow Research Fellowship and she went to Girton College, Cambridge, to continue working on the topic of her doctoral thesis. Attending Littlewood's lectures, she solved one of the open problems which he posed. Her theorem, now known as Cartwright's theorem, gives an estimate for the maximum modulus of an analytic function that takes the same value no more than p times in the unit disc. To prove the theorem she used a new approach, applying a technique introduced by Lars Ahlfors for conformal mappings.
  
  wn.com/Mary_Cartwright
• Nikolay Bogolyubov
  Nikolay Nikolayevich Bogolyubov (Russian: Никола́й Никола́евич Боголю́бов; 21 August 1909, Nizhny Novgorod – 13 February 1992, Moscow), also transliterated as Bogoliubov, was a Soviet mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and to the theory of dynamical systems; a recipient of the Dirac Prize (1992).
  Nikolay Bogolyubov was born on 21 August 1909 in Nizhny Novgorod, Russian Empire to Russian Orthodox Church priest and seminary teacher of theology, psychology and philosophy Nikolay Mikhaylovich Bogolyubov, and Olga Nikolayevna Bogolyubova, a teacher of music. The Bogolyubovs relocated to the village of Velikaya Krucha in the Poltava Governorate (now in Poltava Oblast, Ukraine) in 1919, where the young Nikolay Bogolyubov began to study physics and mathematics. The family soon moved to Kiev in 1921, where they continued to live in poverty as the elder Nikolay Bogolyubov only found a position as a priest in 1923.
  
  wn.com/Nikolay_Bogolyubov
• Nilakantha Somayaji
  Kelallur Nilakantha Somayaji (Malayalam: നീലകണ്ഠ സോമയാജി, Hindi: नीलकण्ठ सोमयाजि) (1444–1544) (also referred to as Kelallur Comatiri) was a major mathematician and astronomer of the Kerala school of astronomy and mathematics. One of his most influential works was the comprehensive astronomical treatise Tantrasamgraha completed in 1501. He had also composed an elaborate commentary on Aryabhatiya called the Aryabhatiya Bhasya. In this Bhasya, Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra and spherical geometry. Grahapareeksakrama is a manual on making observations in astronomy based on instruments of the time.
  Nilakantha Somayaji was one of the very few authors of the scholarly traditions of India who had cared to record details about his own life and times. So fortunately a few accurate particulars about Nilakantha Somayaji are known.
  In one of his works titled Siddhanta-darpana and also in his own commentary on Siddhanta-darpana, Nilakantha Somayaji has stated that he was born on Kali-day 1,660,181 which works out to 14 th June 1444 CE. A contemporary reference to Nilakantha Somayaji in a Malayalam work on astrology implies that Somayaji lived to a ripe old age even to become a centenarian. Sankara Variar, a pupil of Nilakantha Somayaji, in his commentary on Tantrasamgraha titled Tantrasamgraha-vyakhya, points out that the first and last verses of Tantrasamgraha contain chronograms specifying the Kali-days of the commencement (1,680,548) and of completion (1,680,553) of Somayaji's magnum opus Tantrasamgraha. Both these days occur in 1500 CE.
  
  wn.com/Nilakantha_Somayaji
• 
  Omar Khayyám
  Omar Khayyám (1048–1131; Persian: ‏عمر خیام‎) was a Persian polymath: philosopher, mathematician, astronomer and poet. He also wrote treatises on mechanics, geography, mineralogy, music, climatology and Islamic theology.
  Born in Nishapur, at a young age he moved to Samarkand and obtained his education there, afterwards he moved to Bukhara and became established as one of the major mathematicians and astronomers of the medieval period. He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. He contributed to a calendar reform.
  His significance as a philosopher and teacher, and his few remaining philosophical works, have not received the same attention as his scientific and poetic writings. Al-Zamakhshari referred to him as “the philosopher of the world”. Many sources have testified that he taught for decades the philosophy of Avicenna in Nishapur where Khayyám was born and buried and where his mausoleum today remains a masterpiece of Iranian architecture visited by many people every year.
  
  wn.com/Omar_Khayyám
• 
  Paul Erdős
  Paul Erdős (occasionally spelled Erdos or Erdös; Hungarian: Erdős Pál, pronounced [ˈɛrdøːʃ ˈpaːl]; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory. He is also known for his "legendarily eccentric" personality.
  Paul Erdős was born in Budapest, Hungary on March 26, 1913. He was the only surviving child of Anna and Lajos Erdős (formerly Engländer); his siblings died before he was born, aged 3 and 5. His parents were both Jewish mathematicians from a vibrant intellectual community. His fascination with mathematics developed early—at the age of three, he could calculate how many seconds a person had lived.
  Both of Erdős's parents were high school mathematics teachers, and Erdős received much of his early education from them. Erdős always remembered his parents with great affection. At 16, his father introduced him to two of his lifetime favorite subjects—infinite series and set theory. During high school, Erdős became an ardent solver of the problems proposed each month in KöMaL, the Mathematical and Physical Monthly for Secondary Schools. Erdős later published several articles in it about problems in elementary plane geometry.
  
  wn.com/Paul_Erdős
• 
  Paul Halmos
  Paul Richard Halmos (March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.
  Halmos obtained his B.A. from the University of Illinois, majoring in philosophy and minoring in mathematics. He took only three years to obtain the degree, and was only 19 when he graduated. He then began a Ph.D. in philosophy, but after failing his masters' oral exams, shifted to mathematics, graduating in 1938. Joseph Doob supervised his dissertation, titled Invariants of Certain Stochastic Transformations: The Mathematical Theory of Gambling Systems. Shortly thereafter, Halmos left for the Institute for Advanced Study, lacking both job and grant money. Six months later, he was working under John von Neumann, which proved a decisive experience. While at the Institute, Halmos wrote his first book, Finite Dimensional Vector Spaces, which immediately established his reputation as a fine expositor of mathematics.
  
  wn.com/Paul_Halmos
• 
  Person
  A person is a being, such as a human, that has certain capacities or attributes constituting personhood, the precise definition of which is the subject of much controversy.^{[vague language]} The common plural of "person", "people", is often used to refer to an entire nation or ethnic group (as in "a people"), so the plural "persons" is often used in contexts which require precision such as philosophical and legal writing.
  In ancient Rome, the word "persona" (Latin) or "prosopon" (πρόσωπον: Greek) originally referred to the masks worn by actors on stage. The various masks represented the various "personae" in the stage play, while the masks themselves helped the actor's voice resonate and made it easier for the audience to hear.
  In Roman law, the word "persona" became used to refer to a role played in court, and it became established that it was the role rather than the actor that could have rights, powers, and duties, because different individuals could assume the same roles, the rights, powers, and duties followed the role rather than the actor, and each individual could act in more than one role, each a different "person" in law.^{[tortured english][citation needed]}
  
  wn.com/Person
• 
  Pierre de Fermat
  Pierre de Fermat (French pronunciation: [pjɛːʁ dəfɛʁˈma]; 17 August 1601 or 1607/8 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and an amateur mathematician who is given credit for early developments that led to infinitesimal calculus, including his adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the then unknown differential calculus, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for Fermat's Last Theorem, which he described in a note at the margin of a copy of Diophantus' Arithmetica.
  Fermat was born in Beaumont-de-Lomagne, Tarn-et-Garonne, France; the late 15th century mansion where Fermat was born is now a museum. He was of Basque origin. Fermat's father was a wealthy leather merchant and second consul of Beaumont-de-Lomagne. Pierre had a brother and two sisters and was almost certainly brought up in the town of his birth. There is little evidence concerning his school education, but it may have been at the local Franciscan monastery.
  
  wn.com/Pierre_de_Fermat
• 
  Raoul Bott
  Raoul Bott, FRS (September 24, 1923 – December 20, 2005) was a Hungarian mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.
  Bott was born in Budapest, Hungary, grew up in Slovakia and spent his working life in the United States. His family emigrated to Canada in 1938, and subsequently he served in the Canadian Army in Europe during World War II. He later went to college at McGill University in Montreal, where he studied electrical engineering. He then earned a Ph.D. in mathematics from Carnegie Mellon University in Pittsburgh in 1949. His thesis, titled Electrical Network Theory, was written under the direction of Richard Duffin. Afterward, he began teaching at the University of Michigan in Ann Arbor. He was a professor at Harvard University from 1959 to 1999. He died 2005 in San Diego after a battle with cancer.
  Initially he worked on the theory of electrical circuits (Bott-Duffin theorem from 1949), then switched to pure mathematics.
  
  wn.com/Raoul_Bott
• 
  Rózsa Péter
  Rózsa Péter (orig.: Politzer), Hungarian name Péter Rózsa, (17 February 1905–16 February 1977) was a Hungarian mathematician. She is best known for her work with recursion theory.
  Péter was born in Budapest, Hungary, as Rózsa Politzer (Hungarian: Politzer Rózsa). She attended Eötvös Loránd University, where she received her PhD in 1935. After the passage of the Jewish Laws of 1939 in Hungary, she was forbidden to teach because of her Jewish origin. After the war she published her key work, Recursive Functions.
  She taught at Eötvös Loránd University from 1955 until her retirement in 1975. She was a corresponding member of the Hungarian Academy of Sciences (1973).
  
  
  
  wn.com/Rózsa_Péter
• 
  Sofia Kovalevskaya
  Sofia Vasilyevna Kovalevskaya (Russian: Со́фья Васи́льевна Ковале́вская) (15 January [O.S. 3 January] 1850 – 10 February [O.S. 29 January] 1891), was the first major Russian female mathematician, responsible for important original contributions to analysis, differential equations and mechanics, and the first woman appointed to a full professorship in Northern Europe. She was also one of the first females to work for a scientific journal as an editor.
  There are some alternative transliterations of her name. She herself used Sophie Kowalevski (or occasionally Kowalevsky), for her academic publications. After moving to Sweden, she called herself Sonya.
  Sofia Kovalevskaya (née Korvin-Krukovskaya), was born in Moscow, the second of three children. Her father, Vasily Vasilyevich Korvin-Krukovsky, was Lieutenant-General of Artillery who served in the Imperial Russian Army. Her mother, Yelizaveta Fedorovna Schubert, was a scholarly woman of German ancestry and Sofia's grandmother was Romani. When she was 11 years old, the wall paper in her room had differential and integral analysis, which was her early preparation for calculus.
  
  wn.com/Sofia_Kovalevskaya
• 
  Sophie Germain
  Marie-Sophie Germain (April 1, 1776 – June 27, 1831) was a French mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by a gender-biased society, she gained education from books in her father's library 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 gender, she was unable to make a career out of mathematics, but she worked independently throughout her life.
  Marie-Sophie Germain was born on April 1, 1776, in Paris, France, in a house on Rue Saint-Denis. According to most sources, her father, Ambroise-Franҫois, was a wealthy silk merchant. However, Dr. Mary Gray, the chairman of the Department of Mathematics and Statistics at American University in Washington, D.C., has said that he was a goldsmith. 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.
  
  wn.com/Sophie_Germain
• 
  Srinivasa Ramanujan
  Srīnivāsa Rāmānujan FRS  pronunciation (help·info) (Tamil: ஸ்ரீநிவாச ராமானுஜன்) (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions. Ramanujan was said to be a natural genius by the English mathematician G.H. Hardy, in the same league as mathematicians like Euler and Gauss.
  Born in a poor Brahmin family, Ramanujan's introduction to formal mathematics began at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney that he mastered them by age 12, and even discovered theorems of his own, including independently re-discovering Euler's identity. He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant. Ramanujan received a scholarship to study at Government College in Kumbakonam, but lost it when he failed his non-mathematical coursework. He joined another college to pursue independent mathematical research, working as a clerk in the Accountant-General's office at the Madras Port Trust Office to support himself. In 1912–1913, he sent samples of his theorems to three academics at the University of Cambridge. G. H. Hardy, recognizing the brilliance of his work, invited Ramanujan to visit and work with him at Cambridge. He became a Fellow of the Royal Society and a Fellow of Trinity College, Cambridge, dying of illness, malnutrition and possibly liver infection in 1920 at the age of 32.
  
  wn.com/Srinivasa_Ramanujan
• 
  Tom Lehrer
  Thomas Andrew Lehrer (born April 9, 1928) is an American singer-songwriter, satirist, pianist, and mathematician. He has lectured on mathematics and musical theater. Lehrer is best known for the pithy, humorous songs he recorded in the 1950s and 1960s.
  His work often parodies popular song forms, though Lehrer usually creates original melodies when doing so. A notable exception is his song "The Elements", where he sets the names of the chemical elements to the tune of the "Major-General's Song" from Gilbert and Sullivan's Pirates of Penzance. Lehrer's earlier work typically dealt with non-topical subject matter and was noted for its black humor, seen in songs such as "Poisoning Pigeons in the Park". In the 1960s, he produced a number of songs dealing with social and political issues of the day, particularly when he wrote for the U.S. version of the television show That Was The Week That Was.
  In the early 1970s, he retired from public performances to devote his time to teaching mathematics and music theatre at the University of California, Santa Cruz. He did two additional performances in 1998 at a London gala show celebrating the career of impresario Cameron Mackintosh.
  
  wn.com/Tom_Lehrer
• 
  Émilie du Châtelet
  Gabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet (17 December 1706, Paris – 10 September 1749, Lunéville) was a French mathematician, physicist, and author during the Age of Enlightenment. Her crowning achievement is considered to be her translation and commentary on Isaac Newton's work Principia Mathematica. The translation, published ten years after her death in 1759, is still considered the standard French translation.
  Voltaire, one of her lovers, declared in a letter to his friend King Frederick II of Prussia that du Châtelet was "a great man whose only fault was being a woman".
  Du Châtelet was born on 17 December 1706 in Paris, the only daughter of six children. Three brothers lived to adulthood: René-Alexandre (b. 1698), Charles-Auguste (b. 1701), and Elisabeth-Théodore (b. 1710). Her eldest brother, René-Alexandre, died in 1720, and the next brother, Charles-Auguste, died in 1731. However, her younger brother, Elisabeth-Théodore, lived to a successful old age, becoming an abbé and eventually a bishop. Two other brothers died very young. Du Châtelet also had an illegitimate half-sister, Michelle, who was born of her father and Anne Bellinzani, an intelligent woman who was interested in astronomy and married to an important Parisian official.
  
  wn.com/Émilie_du_Châtelet
• 
  Évariste Galois
  Évariste Galois (French pronunciation: [evaʁist ɡalwa]) (25 October 1811 – 31 May 1832) was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a long-standing problem. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. He was the first to use the word "group" (French: groupe) as a technical term in mathematics to represent a group of permutations. A radical Republican during the monarchy of Louis Philippe in France, he died from wounds suffered in a duel under questionable circumstances at the age of twenty.
  Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie (born Demante). His father was a Republican and was head of Bourg-la-Reine's liberal party. He became mayor of the village after Louis XVIII returned to the throne in 1814. His mother, the daughter of a jurist, was a fluent reader of Latin and classical literature and was responsible for her son's education for his first twelve years. At the age of 10, Galois was offered a place at the college of Reims, but his mother preferred to keep him at home.
  
  wn.com/Évariste_Galois

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