h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

http://www.h2g2.com/A483446

This is a rather comprehensive survey of the history of Fermat's last theorem -- from Fermat himself and the note that started it all over to the proof of the theorem by Andrew Wiles in the early 1990's and what results he built upon.

Very interesting and I feel it would be even more interesting to me if I knew anything about maths. The stuff about the Germain primes is really tidy.

Since I don't know anything about maths (beyond the basics) and I'd like to say something helpful, I'll say this: there are a few typos such as spaces missing between words. Also, it would look nicer if changed from plain text to GuideML - then you could do proper underlines, bold, italic and so on.

Anyhow, nice entry. Makes me wish I knew more.

A good article - although I must admit I didn't understand a lot of it.

It's probably not possible to explain the concepts involved to a layman. One thing you might do, though, is define one or two of the terms involved. For example: I did not know what a Prime Exponent was (though I do know the convention it refers to) and it may be that some people will not even know what a prime number is. A footnote there, perhaps ? It might be worth using the phrase "whole number" too, instead of "integer", the first time around, for exactly the same reason.

What do other people think about that ? Is it necessary for the reader to understand absolutely everything here ?

The phrase "..unable to commit suicide over a tragic (for him) love story due to reading about FLT..." is a little clumsy. Taken literally, it implies he was going to commit suicide after merely READING a tragic love story.

"...started pouring in false proofs...and work on FLT was no longer appropriate in the mathematical community..." Again, a little clumsy. "False proofs" could be taken as meaning proof that is simply incorrect, rather than evidence to disprove one element of the puzzle, which I assume is the intended meaning.

Finally: the link to the other article will probably have to be removed. Edited entries can only be linked to other edited entries (or to external websites). If you had written the second article yourself I would have recommended incorporating it into your own piece, but perhaps you might like to include a small element of biography in any case. I don't think it would be out of place.



MDS

Argh! This was one of the topics 'to write on soon' in h2g2, now Exile was first.

OK, good entry! Since FLT is theoretical maths and (even worse) number theory, the topic is very hard to explain, even if one just tries to explain the *problem* rather than the solution (proof) to it. I recently read a popular book on Fermat's last theorem and had major difficulties understanding it from the point the Shimura-Taniyama conjecture came into play. I guess a lot of people have such a strong dislike for maths that they wouldn't voluntarily read such a book, even though it is quite thrilling. At the end, I asked myself if perhaps Fermat was joking when he wrote the margin note. After all, it took more than 300 years to prove the theorem.

I'd go with Shorn Canary and MDS with their comments on it. Perhaps the editors could combine the two articles into one.

Furthermore, the ending is rather short. Perhaps you could try to explain the _idea_ of elliptic curves and modular forms in order to show _why_ (*not* how) the Shimura-Taniyama conjecture is necessary to prove FLT. As I understood it, it is sort of a trick (sort of a diversion in theoretical maths) to prove FLT. It's just that I don't know whether that can be explained in short for ordinary people like me and you.

Oops, sorry - you and me...

It's a shame it's not possible to put in some examples. An example could sort of paint a thousand words (or whatever that phrase is). Is there the wherewithal to put in maths symbol? Probably not. Ah well.

The part about "false proofs" actually does mean "proofs that are simply incorrect", so if that is how one understands it, that's great. =)

This is a very important subject, and I personally feel that it could only be covered fully in all its aspects by something of the order of a UoL project.

However, this is a very good attempt, but I would mention the tessellation aspect of modular forms, and the "far too wierd" elliptical equation that a^3 + b^3 = c^3 would create.

Someone should write an article on T-S.

Grrmblthfff...

If only the ***** CRC Press wouldn't have ***** injucted Mathworld.... I'd write it in, and write up an article -- if only I could look up some details on 'tesselated aspect' and recall the actual mathematics involved with the Frey curve....

Oh well... I've updated according to most of the comments now... Hope it got better

// Mikael Johansson

(p.s. about <LINK href (URL removed by moderator)Eric Weisstein sold a snapshot of his glorious maths-encyclopedia to CRC Press; but due to some idiotic subtleities (mispeled, I know... I couldn't work out the correct spelling right now), they now claim to have full rights to the whole website, and have had the court shut down the whole site )

Readable & understandable to me (i.e. someone who has a fair (but not expert) understanding of maths).

An excellent entry!

Excellent! This is the best account I've read of FLT. You give an explanation of Elliptic functions that makes perfect sense, and I wonder why nobody's ever said something that straighforward to me before. Thank you for advancing my understanding of mathematics.

Wey Hey

Thanks for your recommendation. You'll be glad to know that we think this entry is great, and it has now gone into the Editorial Process for future inclusion in the Edited Guide. When it does get into the Edited Guide, we will email to let you know, but please bear in mind it can take a while for entries to go through the sub-editing system.

Well Done.

Well deserved!

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