Comment by QuesnayJr
9 hours ago
Holy shit. The proof of FLT is a giant detour through several different areas of mathematics, so formalizing it is a lot of work.
An interesting next target would be formalizing the classification of finite simple groups. The original proof scattered over thousands of pages of journal articles, plus Aschbacher and Smith's 1300 page 2 volume monograph. It's so long it's hard to know if there are any gaps. Researchers have been working on a streamlined new proof, but it's already many volumes long.
New proof: The Classification of the Finite Simple Groups (American Mathematical Society Mathematical Surveys and Monographs vol. 40).
https://www.ams.org/publications/authors/books/postpub/surv-...
Number 1 (1994), Number 2 (1995), Number 3 (1997), Number 4 (1999), Number 5 (2002), Number 6 (2004), Number 7 (2018), Number 8 (2018), Number 9 (2021), Number 10 (2023). 10 volumes and >4000 pages so far, number 11 is in progress, and end is in sight, probably two more volumes or so.
https://www.ams.org/journals/notices/201806/rnoti-p646.pdf
People were curious what is going on during 2004-2018. A progress report was published in 2018 right before publication of number 7 and 8. In a sense it was the peak, number 8 completes the proof of so-called "generic case". The rest is "special case". It doesn't mean things get easier, but in some specific sense number 8 completed proof for almost all groups.
Now new proof's end is in sight, people are planning new new proof.