Talk:Sum of two cubes

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	This article was accepted from this draft on 4 January 2023 by reviewer Raydann (talk · contribs).

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Do we need this article?[edit]

There is already an article on taxicab numbers, so it's not clear what this article adds. Will Orrick (talk) 19:12, 4 January 2023 (UTC)[reply]

it was supposed to cover the formula of the addition of two cubes other than specific numbers that are a sum of two cubes expressed in multiple ways. Ang erxi ety 05:35, 5 January 2023 (UTC)[reply]

By "formula" I guess you mean the factorization of a³+b³. This will have some overlap with the factorization article and possibly others (e.g. geometric series), which isn't necessarily a bad thing, but it would be best to coordinate with those existing articles.

When discussing taxicab numbers, it must be made clear that the number being expressed and the cubes used to express it are required to be integers (or perhaps natural numbers). The word "number" by itself is ambiguous. For example, there is also the problem of expressing integers as sums of rational cubes, which is a very difficult problem on which recent progress has been made.

It seems that there was also an attempt (now deleted) to discuss Fermat's last theorem, but again it wasn't made clear that one was restricting to non-trivial integer cubes, and the attempted proof by example could not possibly have worked. At one point the article also contained the statement "The only integers that cannot be expressed as the sum of two cubes are 3 and 4." It was not clear to me what number system was being assumed there, but I can't think of any interpretation in which the statement is true.

Whether having an article that brings together such disparate topics is a good idea is still not clear to me. Will Orrick (talk) 06:28, 5 January 2023 (UTC)[reply]

So about the statement "The only integers that cannot be expressed as the sum of two cubes are 3 and 4", I saw in this source (later removed) that these numbers were used, and in order to make the article seem more notable, I used this statement. I thought he meant that only 3 and 4 cannot be the sums of two cubes, but he was just using these integers as an example for integers that cannot have a sum of two cubes. Ang erxi ety 15:18, 6 January 2023 (UTC)[reply]

Ramanujan[edit]

I removed the attribution of a "formula" to Ramnujan since the only formula in the article is the basic identity, and Ramanujan had nothing to do with that elementary result. Ramanujan, of course, was the central character in the taxicab-number story, but it is misleading to refer to a taxicab number as a "formula". Also, I'm unsure of the bit about the letter. As far as I am aware, the taxicab story was an anecdote told by Hardy. I don't believe taxicab numbers were mentioned in Ramunajan's letter to Hardy. Will Orrick (talk) 15:06, 26 January 2023 (UTC)[reply]