Andrew Wiles on the struggle and beauty of mathematics

[warent]

Some of my favorite quotes related:

    "As Wiles began his lectures, there was more and more speculation 
    about what it was going to be," Dr. Ribet said.
    ... Finally, at the end of his third lecture, Dr. Wiles concluded
    that he had proved a general case of the Taniyama conjecture.
    Then, seemingly as an afterthought,
    he noted that that meant that Fermat's last theorem was true. Q.E.D. [1]

And

    "I had to give the next lecture," Dr. Ribet said.
    "It was something incredibly mundane."
    Since mathematicians are "a pretty well-behaved
    bunch," they listened politely.
    But, he said, it was hard to concentrate.
    "Most people in the room, including me, were incredibly shell-shocked," [1]

Very funny, but also gives me goosebumps. That would have been some lecture!

[1] http://www.nytimes.com/1993/06/24/us/at-last-shout-of-eureka...

[throwaway3123]

I think true happiness often can really only come from developing a skill; to be an old school artisan is the way forth.

This is an idea I'd dismissed at first, 'work is worship' and all that jazz, as some propaganda by the classes incl. and above the bourgeoisie.

I then the same illustrated by Alan Watts, and illustrated beautifully some months back in Oatmeal.

http://theoatmeal.com/comics/unhappy

... and then I realized both were true. Words are both the instruments of the savior and the devil.

[lodi]

I think there are two concepts being conflated here, but I'm not sure what to call them. Let's call them X and Y.

---

1) Saving whatever% off your car insurance makes you X.

2) Having sex makes you X.

3) Scoring the winning point in a close game makes you X.

A) Laying the last brick on a house you built with your bare hands makes you Y.

B) Watching your daughter get her doctorate makes you Y.

C) Solving a non-trivial theorem for the first time in history makes you Y.

---

I'm just not sure what to call X and Y; perhaps "happiness" vs "fulfillment", or "joy" vs "happiness", or "happiness" vs "true happiness"...

[10-6]

I've never seen that comic on the oatmeal, it's amazing, thanks for sharing

[utopcell]

what a wonderful link -- thank you for sharing.

[ggm]

The night Wiles did the fermat reveal I took a call from a Canadian mathematician friend working the (internet, phone) tree to get the word out. I found myself, no mathematican, ringing the ABC australia science desk, asking for, and getting connected to Robin Williams (one of our formost science journalists) to try and encourage him to go with the story on the national news. Quite an engaging moment for me: in my domain of computer science we'd call what I did almost a social engineering attack: "I have important scienting news, put me through to your chief scienting reporter..." and it worked!

[heinrichf]

A beautiful and touching documentary about Fermat's last theorem, Wiles, and the other mathematicians involved in its proof: http://www.dailymotion.com/video/x223gx8

[h43k3r]

I watched this documentary during a summer afternoon and I was left with tears in my eyes. It was touching and inspiring. A lot of hard work went into proving this. It made me appreciate mathematics in a much more deep sense.

[copperx]

That was beautiful. It makes you wonder whether Fermat really had a proof, and if he did, why no one has replicated it using more rudimentary mathematics? If a mathematician could explain that I would be thankful.

[osrec]

I remember trying to "prove" Fermat's last theorem while at school (I was around 16 at the time and obviously somewhat naive). The equation itself looked so simple that I was convinced a proof would be equally as concise. After a few failed attempts, I googled for solutions and stumbled up on Andrew Wiles' proof. I was dumbfounded at its complexity! There is still a part of me that hopes/believes that there exists some undiscovered crafty little mathematical trick that can distill this monster proof into something simple!

[amelius]

If that crafty little trick is really that little, perhaps we could try to find it by brute forcing it on a computer (symbolically, using a proof system) (?)

[eli_gottlieb]

Number theory often involves theorems that are simple to state and extraordinarily difficult to prove. It's one of the branches of maths that comes closest to hard problems in computational complexity and proof theory (at least, as I understand the matter).

[mhomde]

I'm still intrigued by the possibility of a more "elegant" solution to Fermat being out there. Wiles approach seems like brute forcing it by stitching together different proofs. It seems very implausible that Fermat actually had an actual solution, but it should be possible that one exists.

I guess the incentive to find it is much less now though when the theorem has been proved.

[jlarcombe]

"Brute forcing it by stitching together different proofs"? Seems a bit of a harsh assessment! My (limited) understanding is that Wiles' proof introduced some hugely powerful new techniques related to modular forms and opened up a lot of new areas of study.