# YGK: Mathematicians

## Terms

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(Pierre) de Fermat
French, best known for creating the "little theorem". He also studied primes that were named after him, and he and Blaise Pascal founded the probability theory. He also discovered methods for finding the maxima and minima of functions and the areas under polynomials that anticipated calculus and inspired Issac Newton.
(William Rowan) Hamilton
Irish, best known for extending the notion of complex numbers to four dimensions by inventing the quatemions.
Euclid
This Alexandrian Greek is principally known for five postulates that we commonly use in Geometry, including the 'Parallel Postulate' which can be broken to create spherical and hyperbolic geometries. He also proved the infinitude of prime numbers.
(Kurt) Godel
Austrian best known for his two incompleteness theorems.
(Issac) Newton
Generalized the binomial theorem to non-integer exponents, manipulated the power series, and had a method for finding roots. Had a lengthy fued with Gottfried Leibniz over who invented calculus. He called the differential aspect of calculus the 'method of fluxions'.
(Leonhard) Euler
Swiss, best known for his prolific output and the fact that he continued to produce seminal results even after going blind. Richard Feynman called some of his work "the most beautiful equation in mathematics". He invented the graph theory with the Seven Bridges of Konigsberg problem and introduced the use of 'i' and trigonometric functions.
(Carl Friedrich) Gauss
German, considered the "Prince of Mathematicians". His work 'Disquisitones Arithmeticae' systemized number theory and stated the fundamental theorem of arithmetic. He proved the fundamental theorem of algebra, the law of quadratic reciprocity, and the prime number theorem. He also developed the formula for the summation of the arithmetic series.
(Andrew) Wiles
Brit who is best known for proving the Taniyama-Shimura conjectures that all rational semi-stable elliptic curves are modular. A corollary of that result established Fermat's Last Theorem.
(Gottfried) Leibniz
German known for developing calculus, over which he had a feud with Issac Newton. He used 'd' to indicate a differential, and also invented binary numbers, boolean algebra, and symbolic logic.
Archimedes
used density considerations to determine the purity of a gold crown. He found ratios between surface areas and volumes of a sphere and a circumscribed cylinder. He also accurately estimated pi, and created the "method of exhaustion". Eureka!

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