A nice email from Ro about how the proof of Fermat’s Last Theorem is an example of ‘ideas are made of other ideas‘:
Hi Scott, My name is Ro, I’m from Italy and currently a graduate student in computer science from the University of California Irvine. On a monthly base I catch up with your essays, that I found really sharp-serious-funny (plus, I try to learn something more about being a good writer). Recently – like last night, I had dinner with a friend, a quite well known name in math (cryptography), who, not surprisingly, likes to tell jokes and stories about math and other mathematicians.
During the dinner he explained the Proof of Fermat’s Last Theorem (a.k.a. the FLT) in a few steps involving theorems from other fields of math. Each of these theorems were developed in adjacent fields of number theory and never meant to proof the FLT. Nevertheless, a composition of these theorems inspired Andre Wiles and a few other contemporary mathematicians to first draft a proof of the FLT (the idea from other ideas) and subsequently proof that their draft proof was correct.
All of this happened from ~1997 to ~2005, after 350 years passed from the original claim by Fermat. When my friend was done talking, your claim “ideas are made of other ideas” came to my mind and I thought to tell the story and provide a reference to you. A summary of such a short but inspiring description about proof of FLT can be found here.
The author of the theorem died 350 years before the proof was provided and there has been a long wave of mathematicians obsessing on this problem, whose solution has been composed from other solutions from other fields. Hope the above can be helpful as an additional example about “ideas are made of other ideas” for your future inspiring essays and talks. Keep up with your dream – filling up your shelf with your books :) Cheers, – Ro