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It's been 20 years since fermat's last theorem was proved by Andrew Wiles.
Has there been any simplification in proof in the last 20 years?
What I do only know is that different proofs of faltings's theorem were given by Vojta and Bombieri.

Arctic Char
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user779120
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    The main readable text is 'Gary Cornell, Joseph H. Silverman, Glenn Stevens - Modular forms and Fermat's last theorem (1997, Springer).djvu' – reuns May 11 '20 at 13:02
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    @reuns I wouldn't put a book written in 1997 in the "recent development" category. – Sam May 11 '20 at 20:21
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    Darmon, Diamond and Taylor published in 2009 this well written paper "Fermat's Last Theorem" (that infact I haven't read completely) that seems to simplify some facts, but they say it serves as an "introduction" to the work of Wiles.http://www.math.mcgill.ca/darmon/pub/Articles/Expository/05.DDT/paper.pdf – Fraz May 22 '20 at 17:41
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    This question is probably better suited to MathOverflow. But two comments: 1) Khare-Wintenberger's proof of Serre's Conjecture gives a different proof of FLT. The proof uses many of Wiles' ideas, but is able to circumvent some of the black box inputs that Wiles used (see the first comment to this blog post). It's certainly not a simplification per se. 2) The abc conjecture would, if proven, give a completely different proof of FLT. – Mathmo123 May 25 '20 at 13:28
  • Thanks for your comments. I will look into Khare-Wintenberger's proof of Serre's Conjecture. Also, I'll post the same question on mathoverflow. I'll write the hyperlink in the comment after I post it. – user779120 May 26 '20 at 11:48
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    I posted it on mathoverflow. – user779120 May 30 '20 at 13:07

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