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Mathematics Top‑priority 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 articles Top This article has been rated as Top-priority on the project's priority 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.

The image in the lead paragraph has been replaced by one of the Ulam spiral. The legend reads "The prime factorisation of the integers is a central point of study in number theory and can be visualised with this Ulam spiral variant. Number theory seeks to understand the properties of integer systems like this, in spite of their apparent complexity." Unfortunately, several things here seem to be a ltitle off. An Ulam spiral depicts primality, not factorization. It's unclear what is meant by "integer system" here, or even "apparent complexity".

The Ulam spiral may not be a very good choice for an image in the lead: it gives the reader the illusion of some imperfect patterns (due to small-number effects), whereas it is a standard conjecture that the statistical tendency towards such patterns is zero, once trivial local effects are set aside. Garald ( talk) 16:04, 8 August 2019 (UTC) reply

PS. Some of those initial patterns do have number-theoretical significance, but discussing that involves algebraic number theory and would probably take us too far afield. Garald ( talk) 11:59, 30 January 2021 (UTC) reply

The number theory navbox has a link to "Combinatorial number theory" but that just links to a non-existent section on the number theory article. Should the link be removed or should the number theory article have a section for "Combinatorial number theory"? I notice there is a section called "arithmetic combinatorics" - is that just a modern name for "Combinatorial number theory"? Fdfexoex ( talk) 03:07, 21 November 2019 (UTC) reply

In the Number theory navbox, I have replaced Combinatorial number theory with Arithmetic combinatorics. Combinatorial number theory was a link to a section of Number theory that was deleted 02:50, 10 October 2011. Arithmetic combinatorics is the closest replacement. Thank you for pointing this out. — Anita5192 ( talk) 04:51, 21 November 2019 (UTC) reply

(related to reference 2 on the term takiltum being problematic - btw, one would expect to be able to click on the term takiltum to see some article on what it means) "But the author of Plimpton 322 did not have a modern viewpoint. According to Robson, the p/q theory fails to account for many of the features of the tablet, including that fact that it records values of (c/a)2 instead of a. The reciprocal pair explanation, she says, makes more sense in light of what’s been learned about Old Babylonian tablets in the last half century. One key is the label for the first column. Neugebauer and Sachs rendered it as “The takiltum of the diagonal which has been subtracted such that the width...,” leaving takiltum untranslated and the label unfinished, because part of it near the end is unreadable. (“Diagonal” means “hypotenuse,” since right triangles arise by cutting a rectangle diagonally in half. “Width” and “short side” are also synonymous.) Subsequent scholars, observing the use of takiltum in other mathematical tablets, determined that it refers to a “helping” or “holding” number. With that meaning and an educated guess for what makes grammatical sense (and also fits physically) in the unreadable and damaged portions, Robson offers a new translation: “The holding-square of the diagonal from which 1 is torn out, so that the short side comes up.” That reading, she says, aligns well with the Old Babylonian approach to solving reciprocal-pair-type problems and with other mathematical tablets of the time. So it seems that the author of Plimpton 322 was no lone genius—but he was probably a very good teacher." https://www.ams.org/publicoutreach/happ5-history.pdf — Preceding unsigned comment added by 46.246.247.51 ( talk) 04:14, 17 February 2020 (UTC) reply

is it fair to include a portrait of sir andrew wiles on the Number Theory page, considering there is a picture of erdos and terry?

i mean, he did prove The Last Theorem, right?

it seems there is a bit of text dedicated to this theorem on the page, right?

from what i can see, it's mentioned under Early modern number theory, subsections fermat, euler, and 'lagrange, legendre and gauss'.

i know some would say he's not any of the people on this page, the 'lowest' probably being Erdos or terry. i respect all these guys.

but my view is if Erdos gets a spot, so does sir andrew. he did prove it. and he deserves some recognition outside of the fermat's last theorem page.

just my 2c

before i forget, just for redrose74: " 198.53.108.48 ( talk) 23:10, 23 June 2021 (UTC)" reply

Adding his pictures seems okay, given the other portraits. -- A D Monroe III^{( talk)} 14:37, 25 June 2021 (UTC) reply

This article was the subject of a Wiki Education Foundation-supported course assignment, between 7 September 2020 and 18 December 2020. Further details are available on the course page. Student editor(s): Adam Ghannam.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT ( talk) 05:29, 17 January 2022 (UTC) reply

User:Anita5192 https://www.numbertheoryonline.org/ . I don't mind either way, as I came here shoring up NT, so if no, this entry should be removed there. Widefox; talk 22:42, 19 March 2022 (UTC) reply

I see the abbreviation, "NT", used twice at that website. I don't believe that constitutes regular usage. If you know of any reputable sources indicating that "NT" is a common abbreviation for "Number Theory", please discuss them here. Until then, "NT" should not be mentioned in this article.— Anita5192 ( talk) 23:00, 19 March 2022 (UTC) reply

( edit conflict):To editor Widefox: The entry in the disambiguation page must not be removed, because readers may search for it, even if the acronym is rarely used (in your source, NT is not really an acronym for the mathematical area, it is a part of the acronym of a conference). On the other hand, adding it in the first line of the article suggest wrongly that the abbreviation is common (see WP:UNDUE). So Anita5192 revert is perfectly correct, and, definitively, does not imply any edit of the disambiguation page. D.Lazard ( talk) 23:15, 19 March 2022 (UTC) reply

User:D.Lazard no, please see MOS:DABACRO When considering articles to include in the list, it is important that each individual entry is referred to by its respective abbreviation within its article, and see the worked example that I put there. So no, if it should not be in this article, it should not be in the dab. I have no opinion on if inclusion or not is desirable, but from briefly looking for usage it seems it's mainly at a technical level rather than a normal acronym https://mathoverflow.net/questions/tagged/nt.number-theory https://arxiv.org/list/math.NT/recent ) . So User:Anita5192 is correct to remove it [1] from the dab. Widefox; talk 10:43, 20 March 2022 (UTC) reply

MOS:DABACRO is clearly motivated by WP:LEAST. When the acronym is clearly an abbreviation of the article title, WP:LEAST does not applies, and MOS:DABACRO deserves to be further discussed in this case. D.Lazard ( talk) 12:23, 20 March 2022 (UTC) reply

1. Someone went systematically through the text and changed all occurrences of "CE" and "BCE" to "ÁD" and "BC". This is odd. Both usages are accepted, but surely we should revert to what was the default?

2. Shouldn't we make a list of what changes (minor one, one would hope) are needed before the article can be nominated to B-class? The current C rating (inherited from an ancient version of the page) is a shame. Garald ( talk) 16:28, 17 August 2022 (UTC) reply

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

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

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