Wikipedia:WikiProject Mathematics/A-class rating/Riemann hypothesis

The following discussion is preserved as an archive. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Riemann hypothesis

What problems do you see? The ideal solution would be to fix them and retain the rating. (Note: I am not defending the article; they aren't glaringly obvious at a glance, that's all.) Septentrionalis PMAnderson 18:23, 10 October 2008 (UTC)[reply]

Closed as it is not ready yet. Sadly, I and some others have gotten too busy to improve this page like planned, and the article is in clear need of work. If the comments below are addressed, the article should be worth nominating again. --C S (talk) 22:40, 7 February 2009 (UTC)[reply]

comment by Jakob.scholbach

It was me who came up with this idea, so I also have the duty to give some actionable criticism. Here are some points. A more in-depth analysis would certainly uncover more problems.

A real problem is the lack of precise references, indicated by some ^{[citation needed]} tags, but many other statements need a ref, too, IMO. For example the footnote 2 is nothing but an extension of the statement made in the lead. Every single phrase in the footnote deserves a reference, or else has to be scrapped.
The organization of the article is far from optimal: e.g.
- "The traditional formulation of the Riemann hypothesis obscures somewhat the true importance of the conjecture." leaves both unclear the traditional formulation (??) and the true importance. Neither of the two are touched in previous paragraphs.
- What is the specific intention of "The Riemann hypothesis and primes" compared to "Consequences and eq.formulations..." THe former section contains several equivalent formulations.
- THe "Weil's criterion, Li's criterion" section is short.
Most importantly, I feel the article is written in a way that just collects some facts, but does not give any connection. E.g. the equivalent formulations: why are they equivalent (at least indicating that is necessary), what is their importance etc.
The definition of zeta(s) is obviously a key asset in the whole story. This has to be in the article.
The article has to explain why the -2, -4 etc. are called trivial zeroes. This is easily done using the decomposition in the part stemming from the infinite place of Q, and the finite-places Euler factors. So not a big deal, but an example of how little meaningful content the article conveys.
The "Popular References" section is somehow crappy. I may have too puristic a taste, but if that many popular refs are included, at least somehow the public reception of the conjecture in The Simpsons or whereever has to be explained in the article as well (I personally don't need that, but some people seem to).
"Cited References"?? What does that mean?

OK, these are some points. As far as I understand it, A-class means better than GA. IMO, this article is not "good" (in its natural meaning), nor good (already by lack of citations, but more serious issue is article structure and content) in Wikispeak. The article, as present at the moment, deserves B-class rating, IMO. Jakob.scholbach (talk) 21:17, 10 October 2008 (UTC)[reply]

comment by C S

There is one problem that just leaps out when reading this article. It doesn't do a very good job of explaining the history and motivation behind the statement of the conjecture. The first section is "history" and it immediately jumps into work on resolving the conjecture instead of explaining why Riemann would make the conjecture. The next section is about RH and prime distribution, probably the section most laypeople are interested in. The very first mention of the prime numbers is in relation to a somewhat technical 1901 result. That's a tad ludicrous.

Even that might be ok, if it were not written in a somewhat opaque manner to non-mathematicians. It's something that can elegantly be described mostly in words, not in a "here is the equation" followed by "where blah blah denotes this, blah blah denotes that, etc." manner. This is not an isolated example. The writing really is not excellent and the lede is completely inadequate.

A crucial issue (as already pointed out) is how much we are supposed to explain about the defining of the zeta function. For an article on a very specific major problem like this, I would expect something, not nothing.

This is an article that is just way below par, in accessibility and readability, of any of the main references available (like the intro to Edwards' book or Bombieri's official Clay math problem description). Of course, this is true of many articles here, but this is supposed to be an A-class article. I believe it is nowhere as well-written or thought-out as the other articles that have passed the A class review process. --C S (talk) 02:32, 26 October 2008 (UTC)[reply]

The above discussion is preserved as an archive. Please do not modify it. Subsequent comments should be made on the appropriate discussion page, such as the current discussion page. No further edits should be made to this discussion.