# Influential Mathematicians

## 41 terms · Cauchy to Riemann to Gauss

### Riemann

19th German; Zeta function; ___ surfaces; ___ hypothesis; Theory of quadriatic functions,

### Gauss

18th 19th German; proved the fundamental theorem of algebra; FTA(arithmetic)

### Gauss

18th 19th German; proved the law of quadratic reciprocity; and the prime number theorem.

### Cauchy

18th 19th French; established when ∞ series converge; est first rigorous def. of an integral

### Cauchy

18th 19th French. Proved Fermat's 3 triangle thm. Extended polyhedral formula.

### LaGrange

18th Italian; est metric standard; buried in Pantheon; created calculus of variations.

### LaGrange

18th Italian; worked on 3 body problem and came up with ____ pts.;

### Cramer

18th Swiss; ___ paradox which clarifies Mcclaurin series regarding points and cubic curves; ___ rule

### Euler

18th Swiss; tutored by Johann Bernulli; 7 bridges; intro a lot of symbols; went blind; Introducio in analysin infinitorum (1748) provided the foundations of analysis

### Euler

18th Swiss; showed that any complex number to a complex power can be written as a complex number; divergence of the harmonic series implied an infinite number of Primes;

### Euler

18th Swiss; factored the fifth Fermat number (thus disproving Fermat's conjecture), proved Fermat's lesser theorem, and showed that e was irrational

### Hamilton

19th Irish; extended complex #s to 4 dimentions by inventing quaternions: non commutative field with 6 square roots of -1, ___ path

### DeMorgan

19th English; "on the studies and difficulties of mathematics": math history book; creates inventories with math laws; "Formal Logic"; ___ law

### Cayley

19th English; "on the theory of linear transformations"; theory of invariants

### Cayley

19th English; showed that two 0's intersect at 4pts: two imaginary; unified metric and projectile geometry

### Weierstrass

19th German; father of modern analysis; ___ and Riemann put the finishing touches on Abelian function theory(generalization of elliptic functions); developed the definition of the limit; developed a technique of analytic continuation

### Weierstrass

19th German; suffered from a nervous breakdown in 1859, and was plagued by dizzy spells for the rest of his life

### Cantor

18th 19th German; ___ set, built a hierarchy of ∞ sets according to their cardinal number, originated set theory

### Venn

18th 19th English; logic and probability theory; Keynes praised his "symbolic logic", book on Cambridge history; Cricket bowling machine

### Ramanujan

19th 20th Indian; his notebooks; taxi cab #s; intimate familiarity with numbers, and excelled especially in number theory and modular function theory

### Chebyshev

19th Russian; put limits on the asymptotic limit of the totient function which allowed him to prove Bertrand's postulate. ___ parallel notion

### Thales of Miletus

600s B.C. pre-Socratic Greek; Invented deductive math. ___ thm.

### Pythagoras of Samos

500s B.C. Ionian Greek; root 2= ___ constant; music of the spheres (planets); ___thm; had a cult

### Archimedes of Syracuse

200s B.C. Greek; ratios between SA and V of a sphere and circumscribed cyclinder; estimated pi,∞ series with method of exhauston

### Archimedes of Syracuse

200s B.C. Greek; "on the Eq. of planes":levers; "on the measurement of a circle": pi; "the sand reckoner": # grains of sand in the universe; area between parabola and line shortcut

### Plutarch

not a mathematician. Roman biographer. "Parallel Lives"

### Euclid of Alexandria

300s B.C. Greek; 5 postulates that define normal space; fifth (parallel postulate) can be broken to create spherical and hyperbolic geometries;

### Euclid of Alexandria

300s B.C. Greek; "Elements", proved infinitude of prime #s, tutored Archimedes; ___ algorithm: finds GCD(divisor)

### Brahmagupta

600s Indian; Hindu mathematician who asserted that 0/0=1; introduced negative numbers; Brâhma-sphuta-siddhânta concepts, most indispensable mathematician

### Brahmagupta

600s Indian; Hindu mathematician; ___ formula gives the area of a cyclic quadrilateral, ___ identity, also called Fibonacci's identity, implies that the product of two sums each of two squares is itself a sum of two squares

### Fibonacci AKA Pisano

12th 13th Italian; Rabbit problem (144 rabbits after a year); ___ spiral approximates the golden spiral; ___ identitiy; ___ seq. Brahmagupta's identity, also called ___ identity, implies that the product of two sums each of two squares is itself a sum of two squares

### Fermat

17th French; "little theorem" that a^p will be divisible by p if p is prime; ___ primes: 2^2n +1; He and Pascal founded probability theory; discovered methods for finding the maxima and minima of functions and the areas under polynomials that anticipated calculus and inspired Isaac Newton

### Fermat

17th French; lawyer who pursued mathematics in his spare time; discovered the least time principle which states that light will travel through an optical system in such a way as to pass from starting to ending point in the least amount of time

### Descartes

16th 17th French; 'La Géométrie', introduced the ideas of coordinate geometry and in particular the use of Cartesian coordinates; the first to publish a detailed account of how to use coordinates for locating points in space, called analytic geometry, although Fermat developed the concept slightly earlier.

### Descartes

16th 17th French; In an appendix to his book "Discours de la méthode"; gave analytic geometry to the world and used the new technique to solve problems in geometry. Analytic geometry made calculus and many other advances in mathematics possible.

### Pascal

17th French; ___ principle: hydrostatic pressure; mechanical adding machines called "firstname lastname"ine; spent most of his final years writing on religious philosophy

### Simpson

18th British; ___ rule to approx. integrals; his trapezoidal approx. can find exact answers

### MacLaurin

17th 18th Scottish; disciple of Newton's; published the first systematic formulation of Newton's methods in A Treatise of Fluxions (1742); in the same work he developed ___ series

### Goldbach

17th 18th German; ___ partition: when you put a # as a sum of two primes; showed that the sum of 1/(p−1) over the set of perfect powers p is 1; Russian, tutored czar and died in Moscow

### DeMoivre

17th 18th French; discovered the "Central Limit Theorem" of probability which LaPlace expanded; His Philosophical Transactions (1711) was expanded into the important Doctrine of Chances (1718). It included Stirling's formula and the Gaussian integral; ___ identity/formula: links complex #s and trig

### Goldbach

17th 18th German; ___ conjecture: any even integer greater than two can be expressed as the sum of two prime numbers,appears to be true but aint been proven