the theory of curves and a conjecture put forward by two Japanese
mathematicians Yutaka Taniyama and Goro Shimura. In 1993 Andrew Wiles
gave a lecture on this theory at Cambridge and included his proof of Fermat’s
theorem. Unhappily this proof was wrong.
The similarly named French mathematician André Weil dismissed such
attempts. He likened proving the theorem with climbing Everest and added that if
a man falls short by 100 yards he has not climbed Everest. The pressure was on.
Wiles cut himself off and worked on the problem incessantly. Many thought Wiles
would join that throng of the nearly people.
With the help of colleagues, however, Wiles was able to excise the error and
substitute a correct argument. This time he convinced the experts and proved the
theorem. His proof was published in 1995 and he claimed the Wolfskehl prize
just inside the qualifying period to become a mathematical celebrity. The ten-
year-old boy sitting in a Cambridge public library reading about the problem
years before had come a long way.

the condensed idea

Proving a marginal point