Talk:Number theory

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Numbers

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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.

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Image in lead paragraph (Ulam spiral)

The image in the lead paragraph has been replaced by one of the Ulam spiral.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]

adding a picture of sir andrew

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]

Wiki Education Foundation-supported course assignment

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]

NT

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. AD vs. CE 2. More important issues

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]

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]