>> In 2019, he and Carl Pomerance, his adviser at Dartmouth — who, according to Lola Thompson, a mathematician at Utrecht University and a former student of Pomerance, essentially “came out of retirement to work with him”
Somehow that made this whole story a lot more human to me. Pomerance is a big name in modern number theory (to me anyway) but apparently at the end of the day he's just another guy with a particular set of interests who will pop up again when the right thing comes his way.
For those who don't know, Carl Pomerance was the guy who came up with/discovered the quadratic field sieve which for a time was the fastest factoring algorithm for large (100-ish digits) semiprimes. He has a beautiful write-up describing the algorithm and the story of its discovery:
Pomerance, Carl. “A Tale of Two Sieves.” In Biscuits of Number Theory, edited by Arthur Benjamin and Ezra Brown, 85–104. Providence, Rhode Island: American Mathematical Society, 2009. https://doi.org/10.1090/dol/034/15.
To this day the question I have about the Quadratic Seive is something like "what is being reduced in degrees of freedom by each relation added to the matrix?"
It seems like the sequence of primes in the factor base (which are quadratic residues) is very much related to the residues of the factors (they are) and somehow this it's doing in the abstract something like CRT to construct the factors. But I have never read a deeper explanation beyond the mechanics of implementation.
Somehow that made this whole story a lot more human to me. Pomerance is a big name in modern number theory (to me anyway) but apparently at the end of the day he's just another guy with a particular set of interests who will pop up again when the right thing comes his way.