Probably because it's a pretty famous number, being the Hardy–Ramanujan number, and having a pretty famous story. There's quite a few videos on it [0] [1].

[0] https://www.youtube.com/watch?v=_o0cIpLQApk

[1] https://www.youtube.com/watch?v=LzjaDKVC4iY

Yeah not sure why it's hyperlinked, it's a rather dull number.

“But it’s not dull at all,” Ramanujan replies, “it’s actually the first number that can be written as the sum of two cubes, two different ways!”

But imagine he had said, "it's the number of dimensions your Fourier transform needs for the fastest way to multiply two numbers" :)

BTW who things the other person was really just baiting Ramanujan to say something like this?

The full anecdote as told by Hardy is

> I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. “No,” Ramanujan replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.

Hardy just saw it on a taxi cab and expressed sadness; Ramanujam pointed out the mathematical beauty of the number.

The real question is, did he know of this fact already or did he come up with it on the spot after hearing what Hardy said?

I suspect he knew it already. It kind of stands out as an almost-repeated digit pattern if you look at a table of cubes (in base 10), as the cube sums concerned are 10³+9³ = 1000+729 and 12³+1³ = 1728+1. Showing that it's the smallest such number is not difficult, but would take a bit of thought to come up with on the spot. You can do it by checking a few combinations of terms from your table:

   n   n³
  -------
   1    1
   2    8
   3   27
   4   64
   5  125
   6  216
   7  343
   8  512
   9  729
  10 1000
  11 1331
  12 1728

Because 1728 is an incredibly surprising number, showing up most prominently at the center of elliptic curves, modular forms, and L-functions: https://en.wikipedia.org/wiki/J-invariant

And 1729 is 1728 + 1. Not even kidding, that is a thing that happens.

I'd argue that it shouldn't be linked, because it's being used in the wrong context. It would be like linking an music album titled "Outer space" to the Wikipedia article on outer space.

I also wonder why that number. But as others said, it's a pretty famous number all by itself so it makes sense for there to be some notice paid to that- if there were no hyperlink I would've thought it's weird and maybe someone made a mistake.

1729 has no special meaning for the multiplication algorithm. In the paper Harvey writes:

> In Section 5 we establish (1.3) with the explicit constant K= 1728, and in Section 5.4 we list some optimisations that improve it to K= 8.

> In Section 5, we will simply take d:= 1729 (any constant larger than K would do)

So 1729 is the 42 of 4-digit numbers.

This is the curse, there are not enough small(ish) numbers for the enormous number of properties they could have, that we come up with :)

No mention of the number of dimensions for Fourier transform multiplication though: https://en.wikipedia.org/wiki/1729_(number)

I can't explain it, but it's the algorithm discussed here, if you want to read up on it: https://news.ycombinator.com/item?id=19474280

The 1729 link has since been removed, likely for the reasons user saagarjha stated -- wrong context.

Interestingly, the change that added it was also quite recent: https://en.wikipedia.org/w/index.php?title=Galactic_algorith...