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    • CommentAuthorEugene
    • CommentTimeMay 23rd 2012
     
    I was inspired to undertake math as a career after watching a documentary on the proof of Fermat's Last Theorem. As such it's been a small goal of mine to understand Wiles et al's proof. I had noticed that there were a few "roadmap posts" (http://mathoverflow.net/search?q=roadmap) on MO but these were from a long time ago. I was hoping to check if it was alright to ask for such a roadmap on mathoverflow for FLT, as a community wiki. I am currently a first year graduate student with the usual algebra, analysis, and topology prerequisites. I also have a course in algebraic number theory and algebraic curves under my belt.
  2.  

    It's worth thinking about discussing a roadmap with a local expert at your graduate school instead of on MO. They'll be able to better assess what papers you're ready to understand.

    • CommentAuthorEugene
    • CommentTimeMay 23rd 2012
     
    Good point. Thanks for the suggestion!
  4.  

    Well, FLT may just follow from the Peano Axioms by current work of Macintyre and McLarty, so if you're prepared to read a very looong proof... :-)

    More seriously, there is also the more recent proof by way of Serre's conjecture. Experts would be able to say which of the proofs is easier, and which is more profitable to spend the time tackling.

  5.  

    If you do ask your roadmap question, you may want to take into account what Joel D. Hamkins wrote in a comment on my roadmap question:

    I don't think this question should be community wiki, because to answer well, as Andres has, is a demanding task.

    It's not necessarily applicable to every roadmap, but it's something to take into account. (On the other hand, no one on MO cares about reputation... :-))

    • CommentAuthorEmerton
    • CommentTimeMay 24th 2012
     

    Dear Eugene,

    Get a copy of the book "Modular forms and Fermat's Last Theorem" and read it. It remains the best introduction to this part of mathematics (unless you are in the situation of having an expert at hand to teach you directly). You will want to read a lot of other things for background as well, unless you know a lot of number theory already. My guide to learning Galois representations (should be easy to find on the main site) gives one possible approach.

    Regards,

    Matthew

    P.S. There is also the excellent paper of Darmon, Diamond, and Taylor. You could read that in conjunction with the BU volume. I don't think there is any advantage to going via the Serre's conjecture literature. Many of the key ingredients are the same, but the proof of Serre's conjecture (since it is proving a more general result) is harder going at various points, and requires more input from the theory of automorphic forms.

    • CommentAuthorEugene
    • CommentTimeMay 24th 2012
     
    Dear Professor Emerton,

    Thank you for your insightful reply. I greatly appreciate the advice you have dispensed to me on mathoverflow and mathstackexchange.

    I have since posted my question (linked here http://mathoverflow.net/questions/97820/a-recommended-roadmap-to-fermats-last-theorem).

    Professor Emerton, could you post your reply as a formal answer in case I choose to accept it to close the question down? Sorry for any inconveniences I may have caused.

    Thanks
    Eugene
    • CommentAuthorvoloch
    • CommentTimeMay 24th 2012
     
    Matt's answer is the same as the three other answers already given to the question (read Cornell, Silverman and Stevens). Why would you have him post that and accept it?
    • CommentAuthorEugene
    • CommentTimeMay 24th 2012 edited
     
    I wasn't sure how to proceed since I forgot to post a link here. He did (somewhat) address the Galois representation portion of my question.

    I am sorry if it was unseemly of me to suggest this.
    • CommentAuthorEmerton
    • CommentTimeMay 24th 2012
     

    Dear Eugene,

    Sorry, I didn't see that the question had already been asked on the main site. As Felipe says, my reply above doesn't really add anything, so I don't see any need to post it there. (But I don't think you did anything unseemly!)

    Best wishes,

    Matt

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