Talk:Number theory

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Top	This article has been rated as Top-priority on the project's priority scale.

Numbers

	This article is within the scope of WikiProject Numbers, a collaborative effort to improve the coverage of Numbers on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.NumbersWikipedia:WikiProject NumbersTemplate:WikiProject NumbersNumbers
???	This article has not yet received a rating on the project's importance scale.

Number theory was nominated as a Mathematics good article, but it did not meet the good article criteria at the time (March 3, 2019). There are suggestions on the review page for improving the article. If you can improve it, please do; it may then be renominated.

Archives: 1

This page has archives. Sections older than 365 days may be automatically archived by when more than 10 sections are present.

Crypto currency as an application of number theory

We already list cryptography as used in computer science. Crypto currencies are an application of cryptography, not number theory. It feels duplicative to list cryptography a second time like this (or pointing to tls, etc) Very Average Editor (talk) 05:07, 27 April 2023 (UTC)[reply]

Done I agree. I removed it.—Anita5192 (talk) 13:26, 27 April 2023 (UTC)[reply]

Is Greek mathematics an indigenous tradition?

In the section Classical Greece and the early Hellenistic period, it states that "Greek mathematics is also an indigenous tradition." You would expect the quotation that follows to support this statement, when it instead supports the opposite. (It is a quotation from Eusebius, claiming that Pythagoras didn't learn any mathematics from the Greeks, and only learned from the countries he traveled to.) It seems that either a different support is needed, or the statement is in error. Rlitwin (talk) 23:00, 5 November 2023 (UTC)[reply]

Agreed, I'm a bit confused on the wording here as well. Sock-the-guy (talk) 22:48, 7 March 2024 (UTC)[reply]

1. AFAIK there's little or no direct evidence for the influence of Egypt or Babylon on Greek mathematics - emphasis on "AFAIK" and "direct"; that is, I would be extremely interested in learning about such evidence. What we have is Greek sources telling us that Pythagoras traveled to Egypt and to Babylon and "brought knowledge" from there. Eusebius is really not a great source because he is so late; there's a brief passage in Isocrates (http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0144%3Aspeech%3D11%3Asection%3D28), which is much earlier (though not contemporary with Pythagoras).

I don't know of any sort of close analysis that shows when and how Babylonian mathematics influenced the Greeks, in the way that, say, we can tell (apud Plofker) that Indians reverse-engineered trigonometry (having some contact with it in an astronomical/astrological context) but had no contact with Euclid's Elements. Again, the emphasis is on "I don't know".

2. Obviously Greek mathematics had a tremendous development far beyond what was going elsewhere at the time, regardless of its exact origins. Not sure that "indigenous tradition" is even a useful concept.

I'd be in favor of deleting the sentence "While Asian mathematics influenced Greek and Hellenistic learning, it seems to be the case that Greek mathematics is also an indigenous tradition." (the first half is only a possibility, and the second half is sort of wimpy). We can keep the paragraph from Eusebius for now and call it "the late source Eusebius". It would be best to get input from an actual historian of science specializing in the period. Garald (talk) 13:10, 23 October 2024 (UTC)[reply]

Possible Mistranslation/Erroneous Inclusion of Quote

I'll preface this by saying I know only basic German, so take this with a grain of salt. The quote attributed to Gauss at the beginning of the article uses the word Arithmetik in the original German, per the note, but the translation gives this as "number theory". From what I can tell (see here: https://www.dict.cc/?s=number+theory), the common term for "number theory" in German is "Zahlentheorie" (which is also the word used for the title of the German-language version of this article), and "Arithmetik" simply translates to "arithmetic" (https://www.dict.cc/?s=arithmetik). The translated quote therefore seems to incorrectly attribute to Gauss a belief that he may not have actually held and should be removed.

I recognize that there may be historical changes in terminology that I'm not taking into account, and that there may be some nuances of that translation of which I'm not aware, so please chime in if you're more knowledgeable there.

On a more aesthetic note, the quote feels like a partial non-sequitur at its location in the introduction and not wholly relevant. Chollasequoia (talk) 00:23, 4 January 2024 (UTC)[reply]

Per WP:BOLD, I've just gone ahead and removed it. Chollasequoia (talk) 01:09, 4 January 2024 (UTC)[reply]

The tern number theory did not exist in the 18th century, the field of studying the properties of integers was called arithmetic (etc.) in both German and English. The modern term number theory basically functions to distinguish advanced arithmetic from the elementary arithmetic one learns in primary school. Remsense诉 23:07, 7 March 2024 (UTC)[reply]

In this context, "number theory" is definitely the right translation. But if the quote's gone, it doesn't really matter. - CRGreathouse (t | c) 12:27, 20 September 2024 (UTC)[reply]

The lede says itself that "arithmetic" is an older term for "number theory" (and that's the case also in German, not just in English). Garald (talk) 13:12, 23 October 2024 (UTC)[reply]

Excessive use of quotes?

I feel that the use of quotes such as Gauss' in the first paragraph detracts from the encyclopedic tone. However, this would be my first actual edit to a Wikipedia article and I wanted to pass it by some other people just to make sure that it actually makes sense. Thanks! Gracen! (yell at me here) 17:59, 19 September 2024 (UTC)[reply]

Gauss's quotation is famous and appropriate here. However, some terms were in quotation marks instead of italics. I have updated them.—Anita5192 (talk) 18:56, 19 September 2024 (UTC)[reply]

Thanks, I appreciate the advice! Gracen! (yell at me here) 19:04, 19 September 2024 (UTC)[reply]

Revert of 5-years-old edits

It is uncommon to revert 5-years-old edits, as I did recently. The reason is as follows: coming back recently to this article I found it worse than I remembered. So, I searched in the history and found that an editor removed explanation of the sort of problems that a subarea is aimed to solve (in two case) or removed a sentence without which the next paragraph becomes non-sequitur. So, I reverted these edits, with small style improvements.

I have not checked whether some other disimprovements occured durring these five years without being reverted. D.Lazard (talk) 14:51, 22 September 2024 (UTC)[reply]

Corrections to gross mistakes get reverted

A look at the page was enough to spot some glaring mistakes that seem to have been recently introduced:

an assertion that any curve of genus 1 with at least one rational point has infinitely many rational points [sic]

some truly terrible grammar ("While evidence of Babylonian number theory is only survived by the Plimpton 322 tablet": this does not mean what whoever wrote that seems to think it means!)

paragraphs that stopped making sense or flowing at all because a crucial bit was hidden in a footnote.

I took the trouble to fix these rather obvious instances - and then some editor went undid my changes (which had been fully explained). Not much of a point in trying to keep this page in some sort of reasonable shape if one's work goes to waste in this fashion!

This page could still bear much improvement, particularly in the latter sections (which could use more sources) - but that is not happening. Garald (talk) 00:37, 29 March 2025 (UTC)[reply]

I appreciate your engaging in good faith on talk like I asked. I only have a response to your second point, as the present sentence I think is better tweaked as you've done. I've gone ahead and restored your changes otherwise, and sorry for getting in your way. Thanks for helping to improve this article. Remsense ‥ 论 00:50, 29 March 2025 (UTC)[reply]

OK, this looks reasonable. Garald (talk) 00:53, 29 March 2025 (UTC)[reply]

Aristotle

"In the case of number theory, this means largely Plato and Euclid." got changed to "Plato, Aristotle and Euclid" at some point. Please educate me - what does Aristotle have to say about number theory? Garald (talk) 09:51, 22 April 2025 (UTC)[reply]

Road to GA

Hello. I see this article as one of the closest vital maths article to GA. I am looking at the algebra and arithmetic article as comparison (because there very similar very broad articles). Number theory was reviewed in 2019 and has improved since back then. Id like to open this thread to get suggestions on improvements. Right now I see that the other subdivisions section is still too large and think it should be condensed to 1 subsection. I am also contenplating moving main subdivisions before history and trim history (one idea is to say what concepts/new disciplines they developed instead of listing theorems). For now I am expanding elementary number theory to something like elementary algebra. Toukouyori Mimoto (talk) 17:46, 9 May 2025 (UTC)[reply]

Should this article define units?

The distiction is made between prime and composite numbers. Should we also specify that 1 and –1 are units; that is, that they are the only integers that have multiplicative inverses within the set of integers? This is why 1 is neither prime nor composite.—Anita5192 (talk) 18:14, 9 May 2025 (UTC)[reply]

I think not in the main text but maybe in a footnote. This article isnt about primes themselves so I think the reader can just accept the definition. But curious readers can check the footnote. Toukouyori Mimoto (talk) 10:58, 10 May 2025 (UTC)[reply]

Othering

Hello again. Im thinking of condensing everything in the other subfields section down to 3 comprehensive paras. Something like Philosophy#Other traditions. Probabilistic, combinatorial, and computational number theory are minor subfields in the grand scheme of number theory. Im open to objections or other proposals. Toukouyori Mimoto (talk) 14:14, 18 May 2025 (UTC)[reply]