MATHEMATICAL INNOVATIONS Balakumar R “While pursuing a single problem through the centuries “

Agenda The theorem Origins Pierre De Fermat The Pursuers The Finding

The Theorem n > 2 Where a,b and c are non-zero integers The theorem with the largest number of false proofs !!!!

Origins Pythagoras ( 580 BC BC ) More a Philosopher than a mathematician The Pythagorean Brotherhood Belief - Numbers were the ultimate reality Euclid and Diophantus

Pierre De Fermat (1601 – 1665) Profession – Lawyer Pioneer of calculus Not a professional mathematician Reclusive – only correspondence with Blaise Pascal Contributions in probability and analytical geometry

Pierre De Fermat “I have discovered a truly marvelous proof of this, which however the margin is not large enough to contain “ Proved it for n = 4 Majority of his theorems – no proofs existed at his time

Leonhard Euler (1707 – 1783) Swiss mathematician from Basle Most prolific mathematician of all times Blind at middle age Famous for solving 7 bridges of Koninsberg Solved fermat’s theorem for n = 3 Advent of complex numbers

Sophie Germain ( ) Fought against prejudice all her life Mentorship under Lagrange and correspondence with Gauss Contribution – sophie germain’s prime numbers Prime number = 2p + 1, where p is also a prime number

Evariste Galois ( ) Time of Cauchy, Jacobi, Poisson and Fourier, Papers refused by Cauchy and Poisson Denied admission to Ecole Polytechnique Tragic mysterious death Contribution - Group theory

Lame and Cauchy (April 1847) French academy of science offers prize Both mathmaticians in race Complete proof not published by either Kummer finds flaw with Unique factorization, not applicable to prime numbers

Paul Wolfskehl ( 1908 ) Research on the problem halted Rich German industrialist Amateur interest in mathematics The advantage of being overtly meticulous

Taniyama ( ) The Taniyama-Shimura conjecture L- series of an elliptic curve can be mapped into an M-series of a modular form Both - same mathematical object Very important as now old problems can be tackled using modern tools

Andrew Wiles ( 1953 – still alive!) Fascinated with the problem at connection established between TS conjecture and Fermat’s last theorem Begins work in secret Collaboration with Nick Klatz The Cambridge conference

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