List of amateur mathematicians
Encyclopedia
This is a list of amateur mathematicians—people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics. In general, they are not listed in the Mathematics Genealogy Project
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And the man widely regarded as "The King of Amateurs",
Mathematics Genealogy Project
The Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...
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- Maria Gaetana Agnesi (primary school teacher)
- AhmesAhmesAhmes was an ancient Egyptian scribe who lived during the Second Intermediate Period and the beginning of the Eighteenth Dynasty . He wrote the Rhind Mathematical Papyrus, a work of Ancient Egyptian mathematics that dates to approximately 1650 BC; he is the earliest contributor to mathematics...
(scribe) - Robert AmmannRobert AmmannRobert Ammann was an amateur mathematician who made several significant and groundbreaking contributions to the theory of quasicrystals and aperiodic tilings....
(programmer and postal worker) - John ArbuthnotJohn ArbuthnotJohn Arbuthnot, often known simply as Dr. Arbuthnot, , was a physician, satirist and polymath in London...
(surgeon and author) - Jean-Robert ArgandJean-Robert ArgandJean-Robert Argand was a gifted amateur mathematician. In 1806, while managing a bookstore in Paris, he published the idea of geometrical interpretation of complex numbers known as the Argand diagram.-Life:...
(bookkeeper) - Leon BankoffLeon BankoffLeon Bankoff , born in New York City, New York, was an American dentist and mathematician.- Life :...
(Beverly Hills Dentist) - Rev. Thomas BayesThomas BayesThomas Bayes was an English mathematician and Presbyterian minister, known for having formulated a specific case of the theorem that bears his name: Bayes' theorem...
(Presbyterian minister) - Andrew BealAndrew BealD. Andrew "Andy" Beal is a Dallas, Texas-based billionaire businessman who was born and raised in Lansing, Michigan. He made his fortune in banking and real estate and is the founder and chairman of Beal Bank and Beal Aerospace Technologies. Beal is also known for his high-stakes poker games and...
(businessman) - Friedrich BesselFriedrich Bessel-References:* John Frederick William Herschel, A brief notice of the life, researches, and discoveries of Friedrich Wilhelm Bessel, London: Barclay, 1847 -External links:...
(accountant) - Bernard Frénicle de BessyBernard Frénicle de BessyBernard Frénicle de Bessy , was a French mathematician born in Paris, who wrote numerous mathematical papers, mainly in number theory and combinatorics. He is best remembered for Des quarrez ou tables magiques, a treatise on magic squares published posthumously in 1693, in which he described all...
(Counsellor, Cour des monnaies) - Chester Ittner BlissChester Ittner BlissChester Ittner Bliss was primarily a biologist, who is best known for his contributions to statistics. He was born in Springfield, Ohio in 1899 and died in 1979.-Academic qualifications:*Bachelor of Arts in Entomology from Ohio State University, 1921...
(biologist) - Napoléon Bonaparte (general)
- George BooleGeorge BooleGeorge Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...
(primary school teacher) - Mary Everest BooleMary Everest BooleMary Everest Boole was a self-taught mathematician who is best known as an author of didactic works on mathematics, such as Philosophy and Fun of Algebra, and as the wife of fellow mathematician George Boole...
(homemaker, librarian) - William BourneWilliam Bourne (mathematician)William Bourne was an English mathematician, innkeeper and former Royal Navy gunner who invented the first navigable submarine and wrote important navigational manuals...
(innkeeper) - Nathaniel BowditchNathaniel BowditchNathaniel Bowditch was an early American mathematician remembered for his work on ocean navigation. He is often credited as the founder of modern maritime navigation; his book The New American Practical Navigator, first published in 1802, is still carried on board every commissioned U.S...
(indentured bookkeeper) - Achille BrocotAchille BrocotAchille Brocot was a French clockmaker and amateur mathematician. He is known for his discovery of the Stern–Brocot tree, a mathematical structure useful in approximating real numbers by rational numbers; this sort of approximation is an important part of the design of gear ratios for clocks...
(clockmaker) - Harlan J. BrothersHarlan J. BrothersHarlan J. Brothers is an inventor, mathematician, and musician based in Branford, Connecticut.- Life and work :In 1997, while examining the sequence of counting numbers raised to their own power , Brothers discovered some simple algebraic formulas that yielded the number 2.71828..., the universal...
(teacher, inventor, and musician) - Jost Bürgi (clockmaker)
- Marvin Ray Burns (veteran)
- Gerolamo CardanoGerolamo CardanoGerolamo Cardano was an Italian Renaissance mathematician, physician, astrologer and gambler...
(medical doctor) - D. G. ChampernowneD. G. ChampernowneDavid Gawen Champernowne was an English economist and mathematician.After academic work at Cambridge and the London School of Economics, he worked at the London School of Economics and Cambridge University...
, (college student) - Thomas ClausenThomas Clausen (mathematician)Thomas Clausen was a Danish mathematician and astronomer....
(technical assistant) - Sir James Cockle (judge)
- Federico CommandinoFederico CommandinoFederico Commandino was an Italian humanist and mathematician.Born in Urbino, he studied at Padua and at Ferrara, where he received his doctorate in medicine. He translated the works of ancient mathematicians and was responsible for the publication of the works of Archimedes...
(medical doctor) - William CrabtreeWilliam CrabtreeWilliam Crabtree was an astronomer, mathematician, and merchant from Broughton, then a township near Manchester, which is now part of Salford, Greater Manchester, England...
(merchant) - Nathan DabollNathan DabollNathan Daboll was an American teacher who wrote the mathematics textbook most commonly used in American schools in the first half of the 19th century...
(cooper) - Felix DelastelleFelix DelastelleFélix Marie Delastelle was a Frenchman most famous for his invention of several systems of polygraphic substitution ciphers including the bifid, trifid, and the four-square ciphers....
(bonded warehouseman) - Martin DemaineMartin DemaineMartin L. Demaine is an artist and mathematician, the Angelika and Barton Weller artist in residence at the Massachusetts Institute of Technology....
(goldsmith and glass artist) - Humphry DittonHumphry DittonHumphry Ditton was an English mathematician.-Life:Ditton was born at Salisbury. He studied theology, and was for some years a dissenting minister at Tonbridge, but on the death of his father he devoted himself to the congenial study of mathematics...
(minister) - Harvey DubnerHarvey DubnerHarvey Dubner is a semi-retired engineer living in New Jersey, noted for his contributions to finding large prime numbers. In 1984, he and his son Robert collaborated in developing the 'Dubner cruncher', a board which used a commercial finite impulse response filter chip to speed up dramatically...
(engineer) - Henry DudeneyHenry DudeneyHenry Ernest Dudeney was an English author and mathematician who specialised in logic puzzles and mathematical games. He is known as one of the country's foremost creators of puzzles...
(civil servant) - M. C. EscherM. C. EscherMaurits Cornelis Escher , usually referred to as M. C. Escher , was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints...
(graphic artist) - Sarah FlannerySarah FlannerySarah Flannery was, at sixteen years old, the winner of the 1999 Esat Young Scientist Exhibition for development of the Cayley–Purser algorithm, based on work she had done with researchers at Baltimore Technologies during a brief internship there...
(high school student) - Reo FortuneReo FortuneReo Franklin Fortune was a New Zealand social anthropologist. Originally trained as a psychologist, Fortune was a lecturer in social anthropology at the Cambridge University, and a specialist in Melanesian language and culture. He was married to Margaret Mead, with whom he undertook field studies...
(anthropologist) - John G.F. FrancisJohn G.F. FrancisJohn G.F. Francis is an English computer scientist, who in 1961 published the QR algorithm for computing the eigenvalues and eigenvectors of matrices, which has been named as one of the ten most important algorithms of the twentieth century. The algorithm was also proposed independently by Vera N...
(research assistant) - Benjamin FranklinBenjamin FranklinDr. Benjamin Franklin was one of the Founding Fathers of the United States. A noted polymath, Franklin was a leading author, printer, political theorist, politician, postmaster, scientist, musician, inventor, satirist, civic activist, statesman, and diplomat...
(founding father) - Bernard Frénicle de BessyBernard Frénicle de BessyBernard Frénicle de Bessy , was a French mathematician born in Paris, who wrote numerous mathematical papers, mainly in number theory and combinatorics. He is best remembered for Des quarrez ou tables magiques, a treatise on magic squares published posthumously in 1693, in which he described all...
(counsellor) - Gemma FrisiusGemma FrisiusGemma Frisius , was a physician, mathematician, cartographer, philosopher, and instrument maker...
(medical doctor) - Britney GallivanBritney GallivanBritney Crystal Gallivan of Pomona, California, is best known for determining the maximum number of times which paper or other materials can be folded.-Biography:...
(high school student)
- James GarfieldJames GarfieldJames Abram Garfield served as the 20th President of the United States, after completing nine consecutive terms in the U.S. House of Representatives. Garfield's accomplishments as President included a controversial resurgence of Presidential authority above Senatorial courtesy in executive...
(United States President) - Thorold GossetThorold GossetThorold Gosset was an English lawyer and an amateur mathematician. In mathematics, he is noted for discovering and classifying the semiregular polytopes in dimensions four and higher.According to H. S. M...
(lawyer) - Jørgen Pedersen GramJørgen Pedersen GramJørgen Pedersen Gram was a Danish actuary and mathematician who was born in Nustrup, Duchy of Schleswig, Denmark and died in Copenhagen, Denmark....
(actuary) - Hermann GrassmannHermann GrassmannHermann Günther Grassmann was a German polymath, renowned in his day as a linguist and now also admired as a mathematician. He was also a physicist, neohumanist, general scholar, and publisher...
(school teacher) - John GrauntJohn GrauntJohn Graunt was one of the first demographers, though by profession he was a haberdasher. Born in London, the eldest of seven or eight children of Henry and Mary Graunt. His father was a draper who had moved to London from Hampshire...
(haberdasher) - George GreenGeorge GreenGeorge Green was a British mathematical physicist who wrote An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism...
(miller) - André-Michel GuerryAndré-Michel GuerryAndré-Michel Guerry was a French lawyer and amateur statistician. Together with Adolphe Quetelet he may be regarded as the founder of moral statistics which led to the development of criminology, sociology and ultimately, modern social science.- Early life and education :Guerry was born in Tours,...
(lawyer)
- Charles James HargreaveCharles James HargreaveCharles James Hargreave was an English judge and mathematician.-Life:The eldest son of James Hargreave, woollen manufacturer, he was born at Wortley, Leeds, Yorkshire, in December 1820. He was educated at Bramham, near Leeds, and at University College, London, and took the degree of LL.B. with...
(judge) - Oliver HeavisideOliver HeavisideOliver Heaviside was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's field equations in terms of electric and...
(telegraph operator) - Kurt HeegnerKurt HeegnerKurt Heegner was a German private scholar from Berlin, who specialized inradio engineering and mathematics...
(private scholar) - Alfred Bray KempeAlfred KempeSir Alfred Bray Kempe D.C.L. F.R.S. was a mathematician best known for his work on linkages and the four color theorem....
(lawyer) - Thomas Kirkman (church rector)
- Emanuel LaskerEmanuel LaskerEmanuel Lasker was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years...
(chess player) - Harry LindgrenHarry LindgrenHarry Lindgren was a British/Australian engineer, linguist and amateur mathematician. He was born in Newcastle-on-Tyne in England.In 1935 he emigrated to Australia...
(civil servant) - Ada LovelaceAda LovelaceAugusta Ada King, Countess of Lovelace , born Augusta Ada Byron, was an English writer chiefly known for her work on Charles Babbage's early mechanical general-purpose computer, the analytical engine...
(countess) - Kenneth McIntyreKenneth McIntyreKenneth Gordon McIntyre OBE was an Australian lawyer, historian and mathematician who is perhaps best known for his controversial book The Secret Discovery of Australia - Portuguese ventures 200 years before Captain Cook....
(lawyer) - Danica McKellarDanica McKellarDanica Mae McKellar is an American actress, academic, and education advocate. She is best known for her role as Winnie Cooper in the television show The Wonder Years, and later as author of the three The New York Times bestsellers, Math Doesn't Suck, Kiss My Math, and Hot X: Algebra Exposed, which...
(actress) - Anderson Gray McKendrickAnderson Gray McKendrickAnderson Gray McKendrick was a Scottish physician and epidemiologist pioneered the use of mathematical methods in epidemiology...
(medical doctor) - Marin MersenneMarin MersenneMarin Mersenne, Marin Mersennus or le Père Mersenne was a French theologian, philosopher, mathematician and music theorist, often referred to as the "father of acoustics"...
(theologian) - Abraham de MoivreAbraham de MoivreAbraham de Moivre was a French mathematician famous for de Moivre's formula, which links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He was a friend of Isaac Newton, Edmund Halley, and James Stirling...
(bon vivant) - Florence NightingaleFlorence NightingaleFlorence Nightingale OM, RRC was a celebrated English nurse, writer and statistician. She came to prominence for her pioneering work in nursing during the Crimean War, where she tended to wounded soldiers. She was dubbed "The Lady with the Lamp" after her habit of making rounds at night...
(nurse) - Rudolf Ondrejka (veterinarian)
- Jacques OzanamJacques OzanamJacques Ozanam was a French mathematician.-Biography:Jacques Ozanam was born in Sainte-Olive, Ain, France....
(tutor) - Nicolò Paganini (schoolboy)
- Pāṇini (linguist)
- Blaise PascalBlaise PascalBlaise Pascal , was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen...
(heir, private scholar) - Henry PerigalHenry PerigalHenry Perigal, Jr. FRAS MRI was a British stockbroker and amateur mathematician, known for his dissection-based proof of the Pythagorean theorem and for his unorthodox belief that the moon does not rotate.-Biography:...
(stockbroker) - Kenneth Perko (lawyer)
- PingalaPingalaPingala is the traditional name of the author of the ' , the earliest known Sanskrit treatise on prosody.Nothing is known about Piṅgala himself...
(musician) - William PlayfairWilliam PlayfairWilliam Playfair was a Scottish engineer and political economist, the founder of graphical methods of statistics....
(draftsman) - Henry Cabourn PocklingtonHenry Cabourn PocklingtonHenry Cabourn Pocklington was an English physicist and mathematician. His primary profession was as a schoolmaster, but he has made important contributions to number theory with the discovery of Pocklington's primality test in 1914.-References:...
(schoolmaster) - François ProthFrançois ProthFrançois Proth was a French self-taught mathematician farmer who lived in Vaux-devant-Damloup near Verdun, France. He stated four primality-related theorems, the most famous of which is Proth's theorem, published around 1878...
(farmer) - Srinivasa RamanujanSrinivasa RamanujanSrīnivāsa Aiyangār Rāmānujan FRS, better known as Srinivasa Iyengar Ramanujan was a 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...
(clerk) - RamchundraRamchundraRamchundra was British India's first major mathematician. His book, Treatise on Problems of Maxima and Minima, was promoted by the prominent mathematician Augustus De Morgan....
(head master) - Marjorie RiceMarjorie RiceMarjorie Rice is an American homemaker most famous for her discoveries in geometry. She lives in San Diego....
(homemaker) - Olinde RodriguesOlinde RodriguesBenjamin Olinde Rodrigues , more commonly known as Olinde Rodrigues, was a French banker, mathematician, and social reformer.Rodrigues was born into a well-to-do Sephardi Jewish family in Bordeaux....
(banker, social reformer) - Robert SchlaiferRobert SchlaiferRobert O. Schlaifer was a pioneer of Bayesian decision theory. At the time of his death he was William Ziegler Professor of Business Administration Emeritus of the Harvard Business School....
, (classics scholar) - William ShanksWilliam ShanksWilliam Shanks was a British amateur mathematician.Shanks is famous for his calculation of π to 707 places, accomplished in 1873, which, however, was only correct up to the first 527 places. This error was highlighted in 1944 by D. F...
(landlord) - Abraham SharpAbraham SharpAbraham Sharp was an English mathematician and astronomer.-Biography:Sharp was born in Horton Hall in Little Horton, Bradford, the son of well-to-do merchant John Sharp and Mary Sharp and was educated at Bradford Grammar School.In 1669 he became a merchant's apprentice before becoming a...
, (schoolmaster) - Simon StevinSimon StevinSimon Stevin was a Flemish mathematician and military engineer. He was active in a great many areas of science and engineering, both theoretical and practical...
(merchants clerk) - Alicia Boole StottAlicia Boole StottAlicia Boole Stott was the third daughter of George Boole and Mary Everest Boole, born in Cork, Ireland. Before marrying Walter Stott, an actuary, in 1890, she was known as Alicia Boole...
(Secretary) - Gaston TarryGaston TarryGaston Tarry was a French mathematician. Born in Villefranche de Rouergue, Aveyron, he studied mathematics at high school before joining the civil service in Algeria....
(civil servant) - Niccolò Fontana TartagliaNiccolò Fontana TartagliaNiccolò Fontana Tartaglia was a mathematician, an engineer , a surveyor and a bookkeeper from the then-Republic of Venice...
(bookkeeper) - Sebastien TruchetSebastien TruchetSébastien Truchet was an eclectic Dominican Father born in Lyon and lived in Louis XIV times. He is known for being active in areas such as mathematics, hydraulics, graphics, typography, and for many inventions....
(monk) - Franciscus Vieta (lawyer)
- Giordano Vitale (soldier)
- William Wallace William Wallace (mathematician)William Wallace was a Scottish mathematician and astronomer who invented the eidograph.-Biography:Wallace was born at Dysart in Fife, where he received his school education...
(bookbinder) - Walter Frank Raphael WeldonWalter Frank Raphael WeldonWalter Frank Raphael Weldon DSc FRS generally called Raphael Weldon, was an English evolutionary biologist and a founder of biometry...
(evolutionary biologist) - Johannes WernerJohannes WernerJohann Werner was a German parish priest in Nuremberg and a mathematician...
(parish priest) - Magnus WenningerMagnus WenningerFather Magnus J. Wenninger OSB is a mathematician who works on constructing polyhedron models, and wrote the first book on their construction.-Early life and education:...
(monk) - Caspar WesselCaspar WesselCaspar Wessel was a Norwegian-Danish mathematician and cartographer. In 1799, Wessel was the first person to describe the complex numbers. He was the younger brother of poet and playwright Johan Herman Wessel....
(lawyer) - Leo WienerLeo WienerLeo Wiener was an Americanhistorian, linguist, author and translator of Polish-Jewish origin. Wiener was born in Russia and spent the early part of his childhood there, before coming to the United States alone, with the purpose of creating a vegetarian commune in Belize...
(linguist) - Frank WilcoxonFrank WilcoxonFrank Wilcoxon was a chemist and statistician, known for the development of several statistical tests....
(chemist) - Edouard ZeckendorfEdouard ZeckendorfEdouard Zeckendorf was a Belgian doctor, army officer and mathematician. In mathematics, he is best known for his work on Fibonacci numbers and in particular for proving Zeckendorf's theorem....
(medical doctor)
And the man widely regarded as "The King of Amateurs",
- Pierre de FermatPierre de FermatPierre de Fermat 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...
(lawyer)
See also
- Stefan BanachStefan BanachStefan Banach was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. He is generally considered to have been one of the 20th century's most important and influential mathematicians....
- Jean-Charles de BordaJean-Charles de BordaJean-Charles, chevalier de Borda was a French mathematician, physicist, political scientist, and sailor.-Life history:...
- André-Louis CholeskyAndré-Louis CholeskyAndré-Louis Cholesky was a French military officer and mathematician, born in Montguyon, France....
- Ada DietzAda DietzAda K. Dietz was an American weaver best known for her 1949 monograph Algebraic Expressions in Handwoven Textiles, which defines a novel method for generating weaving patterns based on algebraic patterns. Her method employs the expansion of multivariate polynomials to devise a weaving scheme...
- Charles Lutwidge DodgsonLewis CarrollCharles Lutwidge Dodgson , better known by the pseudonym Lewis Carroll , was an English author, mathematician, logician, Anglican deacon and photographer. His most famous writings are Alice's Adventures in Wonderland and its sequel Through the Looking-Glass, as well as the poems "The Hunting of the...
- Robert Leslie EllisRobert Leslie EllisRobert Leslie Ellis was an English polymath, remembered principally as a mathematician and editor of the works of Francis Bacon....
- Buckminster FullerBuckminster FullerRichard Buckminster “Bucky” Fuller was an American systems theorist, author, designer, inventor, futurist and second president of Mensa International, the high IQ society....
- Angelo GenocchiAngelo GenocchiAngelo Genocchi was an Italian mathematician who specialized in number theory. He worked with Giuseppe Peano. The Genocchi numbers are named after him.-References:...
- Sophie GermainSophie GermainMarie-Sophie Germain 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...
- Thomas HobbesThomas HobbesThomas Hobbes of Malmesbury , in some older texts Thomas Hobbs of Malmsbury, was an English philosopher, best known today for his work on political philosophy...
- Émile LemoineÉmile LemoineÉmile Michel Hyacinthe Lemoine was a French civil engineer and a mathematician, a geometer in particular. He was educated at a variety of institutions, including the Prytanée National Militaire and, most notably, the École Polytechnique...
- Ludwig Immanuel MagnusLudwig Immanuel MagnusLudwig Immanuel Magnus was a German Jewish mathematician who, in 1831, published a paper about the inversion transformation, which leads to inversive geometry....
- Henry MannHenry MannHenry Berthold Mann was a professor of mathematics and statistics at Ohio State University. Mann proved the Schnirelmann-Landau conjecture in number theory, and as a result earned the 1946 Cole Prize. He and his student developed the U-statistic of nonparametric statistics...
- Simon NewcombSimon NewcombSimon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...
- Paul PainlevéPaul PainlevéPaul Painlevé was a French mathematician and politician. He served twice as Prime Minister of the Third Republic: 12 September – 13 November 1917 and 17 April – 22 November 1925.-Early life:Painlevé was born in Paris....
- Richard A. ParkerRichard A. ParkerRichard A. Parker is a mathematician and freelance computer programmer in Cambridge, England. He invented many of the algorithms for computing the modular character tables of finite simple groups...
- Ludwig SchläfliLudwig SchläfliLudwig Schläfli was a Swiss geometer and complex analyst who was one of the key figures in developing the notion of higher dimensional spaces. The concept of multidimensionality has since come to play a pivotal role in physics, and is a common element in science fiction...
- Marcel-Paul SchützenbergerMarcel-Paul SchützenbergerMarcel-Paul "Marco" Schützenberger was a French mathematician and Doctor of Medicine. His work had impact across the fields of formal language, combinatorics, and information theory...
- William James SidisWilliam James SidisWilliam James Sidis was an American child prodigy with exceptional mathematical and linguistic abilities. His IQ was estimated to be between 250 and 300 - one of the highest ever recorded - he entered Harvard early at age 11, and as an adult was conversant in over 40 languages and dialects...
- Alfred YoungAlfred YoungAlfred Young, FRS was a British mathematician.He was born in Widnes, Lancashire, England and educated at Monkton Combe School in Somerset and Clare College, Cambridge, graduating BA as 10th Wrangler in 1895. He is known for his work in the area of group theory...
- H. C. von Warnsdorf
- MathematicianMathematicianA mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....