4 ms·

> 1729 Why is this hyperlinked? I was hoping the link would help explain why 1729 and not some other number, but it’s just trivia... > One immediate practical

> 1729 Why is this hyperlinked? I was hoping the link would help explain why 1729 and not some other number, but it’s just trivia... > One immediate practical effect would be to earn the discoverer a million dollar prize from the Clay Mathematics Institute. I mean, I can’t argue with the practicality of that.

ehsankia 7y ago
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 https://www.youtube.com/watch?v=_o0cIpLQApk [1] https://www.youtube.com/watch?v=LzjaDKVC4iY https://www.youtube.com/watch?v=LzjaDKVC4iY
namanyayg 7y ago
Yeah not sure why it's hyperlinked, it's a rather dull number.
- zaroth 7y ago
  “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!”
  - tripzilch 7y ago
    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?
    - n4r9 7y ago
      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.
    - namanyayg 7y ago
      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?
      - mkl 7y ago
        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
edanm 7y ago
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.
- nabla9 7y ago
  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)
  - tripzilch 7y ago
    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 :)
  - _kst_ 7y ago
    So 1729 is the 42 of 4-digit numbers.
- zeristor 7y ago
  No mention of the number of dimensions for Fourier transform multiplication though: https://en.wikipedia.org/wiki/1729_(number) https://en.wikipedia.org/wiki/1729_(number)
saagarjha 7y ago
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.
hcs 7y ago
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 https://news.ycombinator.com/item?id=19474280
BlueGh0st 7y ago
The 1729 link has since been removed, likely for the reasons user saagarjha stated -- wrong context.
- saagarjha 7y ago
  Interestingly, the change that added it was also quite recent: https://en.wikipedia.org/w/index.php?title=Galactic_algorithm&type=revision&diff=919685582&oldid=913898828 https://en.wikipedia.org/w/index.php?title=Galactic_algorith...
lidHanteyk 7y ago
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 https://en.wikipedia.org/wiki/J-invariant And 1729 is 1728 + 1. Not even kidding, that is a thing that happens.

ehsankia 7y ago

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 https://www.youtube.com/watch?v=_o0cIpLQApk [1] https://www.youtube.com/watch?v=LzjaDKVC4iY https://www.youtube.com/watch?v=LzjaDKVC4iY

namanyayg 7y ago

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

zaroth 7y ago
“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!”
- tripzilch 7y ago
  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?
  - n4r9 7y ago
    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.
  - namanyayg 7y ago
    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?
    - mkl 7y ago
      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

edanm 7y ago

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.

nabla9 7y ago
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)
- tripzilch 7y ago
  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 :)
- _kst_ 7y ago
  So 1729 is the 42 of 4-digit numbers.
zeristor 7y ago
No mention of the number of dimensions for Fourier transform multiplication though: https://en.wikipedia.org/wiki/1729_(number) https://en.wikipedia.org/wiki/1729_(number)

saagarjha 7y ago

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.

hcs 7y ago

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 https://news.ycombinator.com/item?id=19474280

BlueGh0st 7y ago

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

saagarjha 7y ago
Interestingly, the change that added it was also quite recent: https://en.wikipedia.org/w/index.php?title=Galactic_algorithm&type=revision&diff=919685582&oldid=913898828 https://en.wikipedia.org/w/index.php?title=Galactic_algorith...

lidHanteyk 7y ago

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 https://en.wikipedia.org/wiki/J-invariant And 1729 is 1728 + 1. Not even kidding, that is a thing that happens.