Wiles proved the Taniyama-Shimura conjecture using proof by
induction.. which is:
(1) Prove that the statement is true for the first case
(2) Prove that if the statement is true for one case, it must be
true for the next. (e.g. n+1)
A good analogy to this method would be the domino effect. First,
you would have to get it rolling by knocking down the first domino.
Then, you would have to make sure that the dominos are spaced such
that any given domino would definitely hit the next one, causing a
rippling domino effect, and thus proving all cases of a
statement.
For this to happen, Wiles depended on Galoiss concept of group
theory Galois in the 19th century had attempted to find a general
solution to quintic equations using this method of group
theory
i still don't understand group theory...
anyway..Wiles employed this method of group theory and was then
able to prove that the first element of each E-series did indeed
match the first element of each M-series. (E and M series derived
from 5 clock arithmatic)
Wiles then ran into some problems trying to topple the rest of the
dominoes. Eventually, he employed the Kolyvagin-Fach method,
combind with the Iwaswa method to achieve this, and thus by proof
of induction, solved the Taniyama-Shimura conjecture and thus
Fermats Last Theorem.
i think fermat just anyhow say one la..then somehow got correct
