Talk:Mathematical coincidence

Nonce word suggestion

I am here to propose that 'decimaleasemeta' be used, eventually, as synonymous and eventually clearer than what is meant by 'mathematical coincidences' collectively here. It is difficult to come up with a mathematical coincidence that is known to toddlers, for example, before the expression '2.718281828' -- the 10-digit calculator's unhidden value of exp(1) -- is seen. I have no use in mind; this would be new. It just forms an abbrevatory single word out of 'decimal e's meta', 'meta' not really being a proper word generally other than in informal ways.

Nanocentury

(I'm putting this in a new section because the comment I'm replying to is years old and my reply will be a leaf in the forest if posted inline.)

>$\pi$ seconds is a nanocentury (ie $10^{-7}$ years); correct to within about 0.5%

>* Yes, or 3, or 3.1, or... basically, nothing special about pi here.

You conveniently forget to mention that although a nanocentury is 1.004π s, it's 1.018·3.1 s and 1.052·3 s.

Insofar as it's a coincidence there is in some sense nothing special about π here, but that's basically just an argument for deleting this entire article. But if you compare it to π, it's remarkable how much closer it is than compared to even 3.1 and that's kind of the point of a coincidence. So I don't understand why it was removed.

The "Feynman point" and WP:Original research

@Quack5quack: Thanks for your edit about the "Feynman point". You are correct that Six nines in pi calls the attribution to Feynman into question. There is one problem with the reference for that article though: The reference is this blog by Wikipedia user DavidWBrooks; compare the discussion at Talk:Six nines in pi#Did he do it? that preceded that blog entry. To quote the blog:

But there’s a problem: As was discovered by several Wikipedia editors, Feynman probably didn’t say it. These editors, including me, stumbled across the issue while improving the Wikipedia article titled “Feynman point.” [...] Turns out that Wikipedia can generate new knowledge, not just disseminate existing knowledge. Pretty cool!

That's some impressive research, but right now it is also a textbook example of WP:Original research. Or has this information since been covered by a reliable source, so we can replace the reference? Renerpho (talk) 18:55, 4 January 2025 (UTC)

I wrote about it in a published article in a daily newspaper, not just a blog post - the blog is owned by the paper, and this is a reprint of the column - and that's usually accepted as a "reliable source" - DavidWBrooks (talk) 00:28, 6 January 2025 (UTC)

I've made the requisite change to that article per your note. If nobody can cite the exact lecture or paper where Feynman claimed knowledge of it, it really should be called a misattribution or a ghost attribution. As Abraham Lincoln said, anyone can make up anything on the internet without proper citations. -- Quack5quack (talk) 19:46, 4 January 2025 (UTC)

@Quack5quack: The attribution to Arndt & Haenel (2001) is strange, considering that Eric Weisstein's MathWorld called it the Feynman Point by May 1999;[1] compare Weisstein's CRC concise encyclopedia of mathematics published that same year.[2] The March 1998 edition of Concise Encyclopedia of Mathematics already does so as well.[3] That's the earliest mention of it that I can find with a quick search of the Internet Archive. Whether or not the attribution is a mistake, we cannot blame it on Arndt and Haenel's 2001 book (as the 2016 blog post doesn't do so)! We probably shouldn't blame it on Weisstein either. I still think that the blog post is original research, and is not fit as a reference on Wikipedia. And neither is the rest of the talk page discussion that is currently used (if only implicitly). Renerpho (talk) 00:34, 5 January 2025 (UTC)

Although it's interesting that Weisstein (1999) cites a 1998 book by Arndt and Haenel...[4] That edition is not available online, but the 2013 edition of that book mentions the Feynman point three times.[5] Renerpho (talk) 00:50, 5 January 2025 (UTC)

@DavidWBrooks and XOR'easter: About the blog vs. WP:OR thing, that may be okay, although I'm not feeling good about the author of a reliable source also being the Wikipedia editor they are writing about. It's just a bit hard to untangle. How do we take a WP:NPOV if the source is so close to Wikipedia itself?

There have been a few edits to Six nines in pi over the past few days (with Quack5quack's edit largely being reverted), which is why I am tagging XOR'easter. And I'm still not sure if citing Arndt and Haenel's 2001 book is a good idea, given that we can find citations from the late 1990s that may or may not lead back to the first edition of that book (depending largely on the exact timing of Weisstein's publication vs. theirs). See my previous comments.

To speculate a bit: Assuming that the claim originates with Arndt and Haenel (which we don't know for sure), I think it was Weisstein's inclusion in MathWorld that popularized it. Renerpho (talk) 03:13, 8 January 2025 (UTC)

To clarify, I have no problem with doing research into this kind of stuff on-wiki. I've done this myself.[6][7] In my opinion, this only becomes a problem when we use talk page discussions as sources, by proxy of a secondary source -- like a newspaper article by a Wikipedia editor who writes about themselves. Citogenesis happens so easily! Renerpho (talk) 03:29, 8 January 2025 (UTC)

I agree that the newspaper item being cited as a source was written by the wikipedia editor doing some of the editing (that's me) looks weird, at the very least. Certainly feels OR-ish. But I contacted Gleick, who responded, and published the result in a creditable public source where it could be seen and, if necessary, refuted. That's the sort of work that is done all the time by sources that we cite. So I think it's legit, even if a bit self-referential! - DavidWBrooks (talk) 14:41, 8 January 2025 (UTC)

The point of citing Arndt and Haenel isn't to say that they originated the claim. It's to substantiate that the claim has been made. I removed the MathWorld citation because MathWorld is sloppy, particularly on matters of terminology (see previous discussions about them).

I don't see a problem with citing the Brooks column as a source in this context. It's a mildly unusual situation, but so what? The problem with citogenesis is if somebody makes up a claim in a Wikipedia article, that story gets repeated elsewhere, and those repetitions are then used to cycle the claim back with a spurious respectability. This isn't that. XOR'easter (talk) 04:11, 8 January 2025 (UTC)

About the number 13532385396179

Has it been verified to be the smallest example being equal to the concatenation of the primes and exponents in its prime factorization in decimal? I have the impression that it hasn't. 129.104.244.86 (talk) 07:01, 2 June 2025 (UTC)

Your impression is correct. It isn't know if this is the smallest example. Compare the note in A080670 (the situation hasn't changed since 2017). Renerpho (talk) 01:31, 3 June 2025 (UTC)

Thanks! 129.104.244.86 (talk) 09:13, 3 June 2025 (UTC)

We need a proper source and credit for this formula

We have an WP:Original Research issue with one of the formulas involving π. There has been extensive discussion and animosity at Talk:Mathematical_coincidence/Archive_2#Explaining_e^π_−_π_≈_20 in 2023 about the proof presented by Adomanmath, and communicated by me to Eric Weisstein. Today, an IP user has edited the article, writing about a comment by Noam D. Elkies on Math Overflow from 25 March 2013, more than a decade earlier, containing an outline of the same proof. Obviously the proof was known much earlier than I thought, and earlier than is currently said in Eric's MathWorld article, which credits it to "A. Doman, Sep. 18, 2023; communicated by D. Bamberger, Nov. 26, 2023".

I reported this to Eric so we have a proper source that can be cited on Wikipedia, rather than having to cite the original YouTube comment by A. Doman. But we're now back to citing a comment made on Math Overflow, completely without context, once again. In addition, I no longer believe that the credit for this belongs to A. Doman (at least not originally; they may well have found it independently). I don't know if credit should go to Elkies instead. Unlike Doman, Elkies makes no claim that the proof is his own, rather presenting it as an obscure but known fact. Renerpho (talk) 22:41, 19 September 2025 (UTC)

I have contacted Elkies. Here is his reply:

Yes, that was me.  For example, I mentioned the same thing in these lecture notes in 2015:
https://abel.math.harvard.edu/~elkies/M229.15/index.html
(search for the string "19.99"; the hyperlink goes to the same XKCD comic). It does not appear in the 2009 iteration of the class https://abel.math.harvard.edu/~elkies/M229.09/index.html, although the approximation $exp(\pi )\approx 8\pi -2$ does, see https://abel.math.harvard.edu/~elkies/M229.09/zeta1.pdf, problem 10. This much (i.e. deriving $exp(\pi )\approx 8\pi -2$ from the functional equation for theta) goes back to the 1998 notes; I noticed that application long before that, though I doubt that I was the first one.  I was probably not aware of the "coincidence" $exp(\pi )-\pi \approx 20$ until seeing it in XKCD 217 at some point before I posted to that Mathoverflow thread; in particular I did not know the 1988 book of Sloane, Conway and Plouffe until your e-mail. I may have been the first to explain $exp(\pi )-\pi \approx 20$ by combining $exp(\pi )\approx 8\pi -2$ and $7\pi \approx 22$ --- at any rate I know of no earlier source, and didn't know of Doman's work until your e-mail either.
Sincerely,
--Noam D. Elkies
P.S. I see that Explain XKCD https://explainxkcd.com/217 now dates the explanation to 2023, citing the same Wikipedia page... It also dates the comic itself to 2007, but I did not know of XKCD until some years later.

With that, the full proof can likely be attributed to Noam Elkies, and dated to some time between 2009 and 2015, triggered by the XKCD comic, while the main part was published by him no later than 2002 (compare https://abel.math.harvard.edu/~elkies/M259.02/index.html, zeta1.pdf, page 7 from 2002; and https://abel.math.harvard.edu/~elkies/M259.98/index.html from 1998, no PDF), but is probably not original to him. I have added the new sources he provided. The addition to Explain XKCD that he mentions was made by myself in April 2024, as an IP user.

On Explain XKCD, there is an anonymous reply (not by me) from November 2024, saying:

That there is some (quite complicated) derivation of eπ − π ≈ 20 is neat, but that doesn't make it 'not a coincidence'. The fact that π ≈ 22/7 is also a coincidence anyway.

That is a position one can take. I disagree with the notion that the existence of an explanation doesn't matter. Renerpho (talk) 09:38, 21 September 2025 (UTC)