Sophie Germain: mathématicienne extraordinaire - Scripps College

Conclusion 69
the Frey curve must not exist. The Frey curve, however, is constructed
by starting with any non-trivial rational solution (A, B, C) of the equation
x p + y p = z p . Since the Frey curve cannot exist, it follows that no non-trivial
integer solutions to the equation x n + y n = z n can exist. [12]
6.2 Conclusion
Few believe that Fermat actually had a correct general proof and none
imagine that he could have had Wiles’ proof in mind. Andrew Wiles’ proof
of over 120 pages incorporates many highly nuanced and extremely specialized
mathematical techniques which were unavailable a century ago,
much less in the early 1600’s. For many, this is the end; the unsolved intrigue
which drew so many mathematicians has now been solved. Others
are still left unsatisfied, feeling intuitively that there should be a much more
accessible proof for such a seemingly simple theorem. John Conway, a colleague
of Wiles, sums it up, “I’m sad in some ways. Fermat’s Last Theorem
has been responsible for so much. What will we find to take its place”[12]
6.2.1 Synthesis
Sophie Germain is considered the first woman to contribute to “the advancement
of mathematical knowledge” by conducting research. [4] In addition,
her findings set in motion further exploration of fields which had
previously been ignored–or perhaps more accurately, were untouched due
to the daunting nature of such materiel. [1; 3] Her lack of formal education
was likely they key factor leading to her original approaches and conse-