Wikipedia:Peer review/Andrew Wiles/archive3

Andrew Wiles

Previous peer review

I've listed this article for peer review because 1) the last one was carried out in 2006, 2) the article seems to have good enough sourcing to be fleshed out; the only macro-level issue is that the early life section is a bit thin; and 3) this article would be excellent to use as TFA on the 19th of September 2024, the 30th anniversary of his grand insight.

Thanks, Jarrod Baniqued (he/him) (talk) 02:21, 20 July 2024 (UTC)

Hi, thanks for submitting this for peer review.

1. Is there a reason why this sentence:

Wiles was born in Cambridge to theologian Maurice Frank Wiles and his wife Patricia.

Refers to his mother as "his wife Patricia" and not "Patricia Wiles"?

2.

After moving to Oxford and graduating from there in 1974, he worked on unifying Galois representations, elliptic curves and modular forms, starting with Barry Mazur's generalizations of Iwasawa theory. In the early 1980s, Wiles moved to Princeton University from Cambridge and worked on...

Could we mention more clearly that he was at Cambridge for a few years? The career and research section also might mention that John H. Coates was his doctoral advisor.

3. The phrasing "He trusts the letters" is a bit odd to me.

4. This sentence is run-on and should be split into 2-3 separate sentences:

Starting by assuming that the theorem was incorrect, Wiles then contradicted the Taniyama–Shimura–Weil conjecture as formulated under that assumption, with Ribet's theorem (which stated that if n were a prime number, no such elliptic curve could have a modular form, so no odd prime counterexample to Fermat's equation could exist), and Wiles also proved that the conjecture applied to the special case known as the semistable elliptic curves to which Fermat's equation was tied; in other words, Wiles had found that the Taniyama–Shimura–Weil conjecture was true in the case of Fermat's equation, and Ribet's finding, that the conjecture holding for semistable elliptic curves could mean Fermat's Last Theorem is true, prevailed, thus proving Fermat's Last Theorem.

5. The Awards and honours section has inconsistent punctuation.

6. Perhaps the section about Wiles' legacy might include some mention of his doctoral students? I'm not sure about this though, just a suggestion.

7. This needs better sourcing:

In August 1993, it was discovered that the proof contained a flaw in several areas, related to properties of the Selmer group and use of a tool called an Euler system.<FOOTNOTE> Wiles tried and failed for over a year to repair his proof. According to Wiles, the crucial idea for circumventing—rather than closing—this area came to him on 19 September 1994, when he was on the verge of giving up. According to Eric W. Weisstein, the circumvention involved "replacing elliptic curves with Galois representations, reducing the problem to a class number formula, solving that problem, and tying up loose ends", all using Iwasawa theory to fix "results from Matthias Flach based on ideas from Victor Kolyvagin", and letting Iwasawa's and Flach's approaches strengthen each other.<THREE FOOTNOTES>

More citations needed: there are not enough footnotes here and of the four that are, three are to Wolfram MathWorld, which is tertiary and not that reliable, and one is to TV tropes for some reason that escapes me.

8. I've added a few citation neededs elsewhere.

Good luck with this article! I hope you can get it to be TFA on Sep 19th. Mathwriter2718 (talk) 14:25, 26 July 2024 (UTC)

Much appreciated, thanks for the detail. I have no quibbles with your review. Jarrod Baniqued (he/him) (talk) 18:25, 31 July 2024 (UTC)

Also, unfortunately, I was unable to get it in the TFA queue for 19 September 2024. However, I will try for spring 2025, the 30th anniversary of the papers’ publication Jarrod Baniqued (he/him) (talk) 18:57, 31 July 2024 (UTC)

@Mathwriter2718 I’ve implemented all of these recommendations. How does it look now? Jarrod Baniqued (he/him) (talk) 20:29, 31 July 2024 (UTC)

Thank you, the page looks excellent. Mathwriter2718 (talk) 21:42, 31 July 2024 (UTC)

Sgubaldo

Lead and Infobox

• Infobox seems a bit too long, especially the list of prizes, so I would either keep only the most important ones in the infobox or use Template:Collapsed infobox section begin.

Early Career

• 'Wiles was born on 11 April 1953 in Cambridge, England, the son of....' - As this is the first time you're referring to Wiles in the body, you should use his full name (Andrew John Wiles)
• The sentences all start with 'In xxx', which is WP:PROSELINE.

Later Career

• Same WP:PROSELINE issues as in his early career, and you could probably even merge the two sentences. Also, is that really everything else he's done in his career after FLT that's worthy of mention?

Sourcing
I see the unreliable sources have been removed, which is good. I looked it up and I'm surprised to see that there have been no biographical books written about Wiles that I could find, but I digress.

• The source formatting needs a bit of work. For example, just for Ref. 44:

  Title doesn't need the –CNN

  Date is actually 17 March 2016, not 16 March

  CNN should be wikilinked and should be |website= not |publisher=

  It's missing both an archive link and a retrieval date.

i.e. try to add archive links where possible and wikilink the websites/publishers consistently (to be fair the latter point is more of a nitpick that doesn't always get picked up on).

Some further sources that could be of use (you don't need to add them, I just tried to find some stuff that might be useful):

• Book on Fermat's Last Theorem by Amir Aczel
• This post by Simon Singh; it's his self-published blog which is a little frowned upon, but the guy writing it is reliable
• This post by Oxford.

These comments are pretty general as I won't have much time to delve deep into the article this week. If this peer review is still open next week, I'll have some more specific comments. Sgubaldo (talk) 19:08, 5 August 2024 (UTC)