As we consider the Great Theorem of this chapter in our first reading, we’ll also talk a bit more about one of the mathematicians we have mentioned a few times this semester: Pierre de Fermat. Dunham discusses a little of Fermat’s life story as well as Fermat’s famous “Last Theorem” in the first part of Chapter 7. Dunham’s text, however, is outdated on this subject: Fermat’s Last Theorem has in fact been proven! Our second reading does a good job of explaining the basic ideas of the theorem and the history of its proof.
The article in the second reading is still a little older than I’d like, however! Here is a bit more information to bring our story into the present.
- Since the article was published pretty close to the publication of Wiles’ proof, it ends with some uncertainty about the proof. That uncertainty has been removed - the proof has been reviewed and accepted.
- Wiles has since won a number of awards for his proof. For example, in 2016 he received the Abel Prize in Mathematics.
- Wiles originally gave the proof in about three lectures; now there are instances of entire courses being devoted to the matter. If you’re interested in seeing more details for the proof, you can find online anything from a very short summary, to an entire textbook! You will likely need to have had a significant abstract algebra course to understand much of the proof.
- The Wikipedia page for Fermat’s Last Theorem is heavily referenced and also not a bad place to get general information about the theorem. (But as always with Wikipedia, it’s good to confirm the information in a place that can’t be publicly edited.)
Finally, the optional third reading (from “Math with Bad Drawings”) offers us a more human perspective on this problem – and perhaps other difficult problems as well.
Readings
First reading: Dunham, Chapter 7, pages 174 - 183
Second reading: Fermat’s Last Theorem
Third reading: The State of Being Stuck