Transcript Document

MATHEMATICAL
INNOVATIONS
“While pursuing a single
problem through the centuries “
Balakumar R
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 - 500 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 (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
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
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 (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
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
THANK YOU