Talk:Number theory

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Mathematics grading: B Class Top Importance  Field: Number theory
Needs more information about modern advances in number theory and a more comprehensive timeline of significant milestones in number theory. Also has some awkward spots. shotwell 06:18, 6 October 2006 (UTC) A vital article.
Many questions in elementary number theory are exceptionally deep and require completely new approaches. Examples are

What's that supposed to mean? Of the four conjectures, three haven't yet been proven. Mihailesca's proof of Catalan's conjecture has been said to use only elementary methods (and it has been said that the newer versions of the proof use no mathematical theory beyond what was available to Catalan himself).

As for the other three, I wouldn't rule out elementary proofs of any of them, and it is possible some of them cannot be proved at all. It's still not clear any of them would require completely new approaches.

Prumpf 15:26, 23 Nov 2003 (UTC)

I agree with the above. It doesn't make any sense to say they are exceptionally deep when they are very simple concepts, and it doesn't make any sense to claim that they require completely new approaches when we simply don't know.

Mysteronald 18:49, 5 Sep 2004 (UTC)

It does make some sense to say that they may lie deep or require new methods (which is not quite the same, but something closely related). Obviously simple assertion falls down on the test of being POV.

Charles Matthews 21:27, 5 Sep 2004 (UTC)

Sure. That does make some sense. This is a mathematical topic, and I think there's value in being precise in this instance. I've changed it, then.

Mysteronald 12:41, 6 Sep 2004 (UTC)

Combinatorial number theory should not be omitted! I hope someone could write description of this important branch of number theory.

Larry Hammick 07:44, 4 Apr 2005 (UTC)

Maybe the article should mention Diophantine approximation as a branch of number theory.

But it does, under analytic number theory. I would regard combinatorial number theory as growing out of ANT, also, but I can see that not everyone would agree. Charles Matthews 10:57, 4 Apr 2005 (UTC)

Contents

[edit] Elementary?

In the section of "Elementary Number Theory", it mentioned four difficult problem, three of which is still open. I won't agree that these problem should put into this section, just because they're appear to be simple. When people're talking about elementary number theory, Goldbach problem will never come into their mind. I hope someone could make a better arrangement for these topics.

[edit] Jargon as opposed to development of thought

Guys (and gals), this "article" is a fine, bulletized shopping list of topics within number theory, but it completely lacks any sort of thought development...it is something of a technicolor yawn of topics, with nothing connecting the jargon.

In has no character of lucid explanation. There is no development of thought, and it merely reads like a jargon-laden index (only), not an article. It's something of a number theory "jargon router," and needs to be either entirely re-written to show a flow of thought, or to have someone make the considerable effort to connect the many, many jargon "dots" that have been thrown down on the floor.

As it exists, it is an excellent list, but a poor explanation. No offense intended.

It might be salvageable if someone were to take the time to (1) slow down, rather than skipping merrily from one jargon-label to another, and (2) exhibit some sense of both connectedness and branches of thought. --AustinKnight 12:15, 11 December 2005 (UTC)

Well, number theory doesn't really exist in the kind of unified way that supposes. Various branches do hang together. Therefore something of the kind can be considered inevitable. The only way to mollify the bittiness is to write more of the history, but that assumes much of the reader. Charles Matthews 12:25, 11 December 2005 (UTC)
That doesn't get past the problem of "shopping-list-ness." The article is virtually opaque in terms of thought-development. It would help to provide some basis (brief definition?) as to why "(jargon-label-of-choice here)" has something to do with number theory. If there is no connectedness, how can there be an overall label (number theory) for the topic? --AustinKnight 12:29, 11 December 2005 (UTC)
Number theory is notoriously the hardest part of mathematics. The article is called 'number theory' because that is what the topic is called. The lack of 'connectedness' is characteristic of all so-called combinatorial mathematics; in other words areas driven by the type of problems to solve, rather than the methods used to solve them. What I see is that the history section is badly incomplete. Charles Matthews 12:36, 11 December 2005 (UTC)
The fundamental problems that I'm seeing with the article are that it is too terse and cryptic...something that a mathematics undergrad or grad student might find useful for routing-of-interest purposes, but there's not much use beyond that. It certainly isn't encyclopedic. --AustinKnight 12:37, 11 December 2005 (UTC)
I do agree that fixing the history section would help fill-in-the-blanks when it comes to development of thought. That'd be a fine approach for fixing the article, which needs to be a tree with branches, rather than a pile of leaves on the ground. --AustinKnight 22:49, 11 December 2005 (UTC)

What about application of number theory to computer science? Maybe to put some links to other relevant articles of application to CS.--Čikić Dragan 14:45, 1 February 2006 (UTC)

[edit] Picture?

Isn't that picture a little off-topic? Elliott C. Bäck 02:25, 10 March 2006 (UTC)

An attractive picture displaying numbers would be unnecessary. This is worse. Nor do other wiki branches of mathematics have a representational illustration (thankfully) MotherFunctor 23:53, 16 April 2006 (UTC)

I was horrified to see such an 'illustration'. It does not belong to a serious article. I am going to cut it immediately.


a pkture tells more then a 1000 words. bring the pictur back NOW. you silly woman eliot--194.237.142.10 09:12, 20 June 2006 (UTC).

[edit] Cleanup tag

I asked Stevertigo to explain why he placed the cleanup tag on this article. Here is his explanation, copied from my talk page ... Gandalf61 08:08, 7 April 2006 (UTC)

The second paragraph on the etymology is out of place - get into the general areas what number theory is about instead. Is it limited to integers? Is there no number theory about complex numbers, etc? They way the intro is stated it makes it seem as if NT is a misnomer for integer theory. Its just not clear on the generalities ... Its an editorial issue, not a math issue - be explanatory. -Ste|vertigo 01:06, 7 April 2006 (UTC)
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