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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](https://xenaproject.wordpress.com/2019/09/27/does-anyone-know-a-proof-of-fermats-last-theorem/)). 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](https://mathoverflow.net/questions/361714/recent-developments-in-the-proof-of-fermats-last-theorem) on mathoverflow. – user779120 May 30 '20 at 13:07

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