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MATHEMATICAL INNOVATIONS

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

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MATHEMATICAL INNOVATIONS

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

  2. Agenda • The theorem • Origins • Pierre De Fermat • The Pursuers • The Finding

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

  4. Origins • Pythagoras ( 580 BC - 500 BC ) • More a Philosopher than a mathematician • The Pythagorean Brotherhood • Belief - Numbers were the ultimate reality • Euclid and Diophantus

  5. 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

  6. 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

  7. 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

  8. Sophie Germain (1776-1831) • 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

  9. Evariste Galois (1811-1832 ) • Time of Cauchy, Jacobi, Poisson and Fourier, Papers refused by Cauchy and Poisson • Denied admission to Ecole Polytechnique • Tragic mysterious death • Contribution - Group theory

  10. 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

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

  12. Taniyama (1927-1958) • 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

  13. Andrew Wiles ( 1953 – still alive!) • Fascinated with the problem at 10 • 1986- connection established between TS conjecture and Fermat’s last theorem • Begins work in secret • Collaboration with Nick Klatz • The Cambridge conference

  14. THANK YOU

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