6 ms·

Hardy, Ramanujan and Taxi No. 1729

134 points by johncarlosbaez 5y ago

cortesi 5y ago
I once correctly guessed a that friend's PIN was "1729", based only on the fact that he was a maths major, a huge fan of Ramanujan, and was sure to have read this story. I still cherish the look of complete confusion on his face, more than 20 years later.
- samb1729 5y ago
  Reading this comment makes me glad I use a different (but still nerdy) pin :)
  - deleted 5y ago
    [deleted]
  - somethingsright 5y ago
    Is it in here? 4242 9801 1089 1024 3141 1415 2718 1412 1732 1428 2997 6626 6022
    - Scarblac 5y ago
      1337?
      - vba616 5y ago
        One approach to PINs is to take two numbers that are familiar, but aren't related to each other and interleave them. Basically the same principle as correct horse battery staple.
etothepii 5y ago
This is a fascinating question. This is a famous story, as a Cambridge mathematician I've heard it many times but the simple question, 'did the cab reg numbers in uk in 1919 allow for a match with ".*1.*7.*2.*9.*"' is not easily answerable.
- shawabawa3 5y ago
  Number plates at the time were in the format AB1234, so it's possible by "taxi number" he meant the number on the number plate edit: further research shows there would have been a "license number" too, which could have been 4 digits
pdevr 5y ago
>>I remember once going to see him when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” The quote above is from G. H. Hardy himself, from the book "Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work". There was no need for him to embellish the story while it was published to "cheer up" Ramanujan, since the book was published in 1940 after Ramanujan's death. Two great men can have different interests in the same field. It does not mean one of them had less ability. Hardy, since his early days, was fascinated by pure mathematics and rigor. Ramanujan was playing with numbers on pieces of paper since he was a child. That's why their contributions and intuitions, even though in the same broad field, are so different.
texteller 5y ago
Ramanujan always amazes me. Remembering my visit to the Ramanujan Museum in India, which treasures the pictures, letters, and documents focusing the greatest mathematician of the 20th Century: https://casualwalker.com/museum-for-the-man-who-knew-infinity-ramanujan-museum-royapuram-chennai-travel-guide/ https://casualwalker.com/museum-for-the-man-who-knew-infinit...
- jesuslop 5y ago
  This virtual expo is quite nice to have a look, thanks for posting!
johncarlosbaez 5y ago
I just looked into this story, and there was more to it than we usually hear.
jbandela1 5y ago
> Hardy either knew of Ramanujan’s work on this problem or noticed himself that 1729 had a special property. He wanted to cheer up his dear friend Ramanujan, who was lying deathly ill in the hospital. So he played the fool by walking in and saying that 1729 was “rather dull”. If this is the case, it really increases my respect for Hardy. Anybody can brag, but to willingly seem to be the fool, in order to help someone else (and notice how even in his retelling of the story, he still plays the fool for others as foil to Ramanujan) takes a really big person.
- actually_a_dog 5y ago
  At one point, people were saying there were 3 great English mathematicians alive: Hardy, Littlewood, and Hardy-Littlewood. https://www.youtube.com/watch?v=KY6wYQKfivE https://www.youtube.com/watch?v=KY6wYQKfivE
- janandonly 5y ago
  Interesting idea indeed: Him pretending to not know that 1729 isn't a 'dull' number at all. I head the same idea as the authors wife: he said it on purpose!
jimmyed 5y ago
> it is the smallest number expressible as the sum of two cubes in two different ways. I don't understand why satisfying this completely arbitrary condition makes it interesting. That way, you can have any number be interesting. 1730 is the smallest number greater than the smallest number expressible as the sum of two cubes in two different ways.
- MichaelBurge 5y ago
  This method is implicitly measuring the interestingness of a number by the number of symbols needed to specify it. So "interesting" is a measure, not a boolean.
  - vba616 5y ago
    The ratio of the actual Kolmogorov complexity to the superficially apparent Kolmogorov complexity? By the way...Wikipedia has something on a "naive" attempt to compute the Kolmogorov complexity of a string. It says that iterating through all strings won't work because some of them contain infinite loops and the halting problem is uncomputable. Ok, but what if you make a program to test all possible strings in "parallel", that is, on a sequential processor, but using brief time slices? That way, shouldn't you finish with all the strings that halt without letting the infinite loops hold things up? I probably don't understand something or am plagiarizing something I've forgotten, or both.
- marcianx 5y ago
  Indeed, that's exactly why there's no uninteresting number! https://en.wikipedia.org/wiki/Interesting_number_paradox https://en.wikipedia.org/wiki/Interesting_number_paradox
- gorgoiler 5y ago
  It’s a long con by the computer scientists who can’t be bothered to constrain the domains of functions beyond int, even though we know square(x: int) -> square_int. They wave their hands and say everything is interesting.
- ykonstant 5y ago
nmridul 5y ago
>> in his “second notebook”. This is one of three notebooks Ramanujan left behind after his death— Hope the present day Mathematicians, biologist etc still use physical notebooks or non-propretary format note taking apps that will make their work accessible to others after their death.
deleted 5y ago
[deleted]
divs1210 5y ago

I once correctly guessed a that friend's PIN was "1729", based only on the fact that he was a maths major, a huge fan of Ramanujan, and was sure to have read this story. I still cherish the look of complete confusion on his face, more than 20 years later.

samb1729 5y ago
Reading this comment makes me glad I use a different (but still nerdy) pin :)
- deleted 5y ago
  [deleted]
- somethingsright 5y ago
  Is it in here? 4242 9801 1089 1024 3141 1415 2718 1412 1732 1428 2997 6626 6022
  - Scarblac 5y ago
    1337?
    - vba616 5y ago
      One approach to PINs is to take two numbers that are familiar, but aren't related to each other and interleave them. Basically the same principle as correct horse battery staple.

etothepii 5y ago

This is a fascinating question. This is a famous story, as a Cambridge mathematician I've heard it many times but the simple question, 'did the cab reg numbers in uk in 1919 allow for a match with ".*1.*7.*2.*9.*"' is not easily answerable.

shawabawa3 5y ago
Number plates at the time were in the format AB1234, so it's possible by "taxi number" he meant the number on the number plate edit: further research shows there would have been a "license number" too, which could have been 4 digits

pdevr 5y ago

>>I remember once going to see him when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” The quote above is from G. H. Hardy himself, from the book "Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work". There was no need for him to embellish the story while it was published to "cheer up" Ramanujan, since the book was published in 1940 after Ramanujan's death. Two great men can have different interests in the same field. It does not mean one of them had less ability. Hardy, since his early days, was fascinated by pure mathematics and rigor. Ramanujan was playing with numbers on pieces of paper since he was a child. That's why their contributions and intuitions, even though in the same broad field, are so different.

texteller 5y ago

Ramanujan always amazes me. Remembering my visit to the Ramanujan Museum in India, which treasures the pictures, letters, and documents focusing the greatest mathematician of the 20th Century: https://casualwalker.com/museum-for-the-man-who-knew-infinity-ramanujan-museum-royapuram-chennai-travel-guide/ https://casualwalker.com/museum-for-the-man-who-knew-infinit...

jesuslop 5y ago
This virtual expo is quite nice to have a look, thanks for posting!

johncarlosbaez 5y ago

I just looked into this story, and there was more to it than we usually hear.

jbandela1 5y ago

> Hardy either knew of Ramanujan’s work on this problem or noticed himself that 1729 had a special property. He wanted to cheer up his dear friend Ramanujan, who was lying deathly ill in the hospital. So he played the fool by walking in and saying that 1729 was “rather dull”. If this is the case, it really increases my respect for Hardy. Anybody can brag, but to willingly seem to be the fool, in order to help someone else (and notice how even in his retelling of the story, he still plays the fool for others as foil to Ramanujan) takes a really big person.

actually_a_dog 5y ago
At one point, people were saying there were 3 great English mathematicians alive: Hardy, Littlewood, and Hardy-Littlewood. https://www.youtube.com/watch?v=KY6wYQKfivE https://www.youtube.com/watch?v=KY6wYQKfivE
janandonly 5y ago
Interesting idea indeed: Him pretending to not know that 1729 isn't a 'dull' number at all. I head the same idea as the authors wife: he said it on purpose!

jimmyed 5y ago

> it is the smallest number expressible as the sum of two cubes in two different ways. I don't understand why satisfying this completely arbitrary condition makes it interesting. That way, you can have any number be interesting. 1730 is the smallest number greater than the smallest number expressible as the sum of two cubes in two different ways.

MichaelBurge 5y ago
This method is implicitly measuring the interestingness of a number by the number of symbols needed to specify it. So "interesting" is a measure, not a boolean.
- vba616 5y ago
  The ratio of the actual Kolmogorov complexity to the superficially apparent Kolmogorov complexity? By the way...Wikipedia has something on a "naive" attempt to compute the Kolmogorov complexity of a string. It says that iterating through all strings won't work because some of them contain infinite loops and the halting problem is uncomputable. Ok, but what if you make a program to test all possible strings in "parallel", that is, on a sequential processor, but using brief time slices? That way, shouldn't you finish with all the strings that halt without letting the infinite loops hold things up? I probably don't understand something or am plagiarizing something I've forgotten, or both.
marcianx 5y ago
Indeed, that's exactly why there's no uninteresting number! https://en.wikipedia.org/wiki/Interesting_number_paradox https://en.wikipedia.org/wiki/Interesting_number_paradox
gorgoiler 5y ago
It’s a long con by the computer scientists who can’t be bothered to constrain the domains of functions beyond int, even though we know square(x: int) -> square_int. They wave their hands and say everything is interesting.
ykonstant 5y ago

nmridul 5y ago

>> in his “second notebook”. This is one of three notebooks Ramanujan left behind after his death— Hope the present day Mathematicians, biologist etc still use physical notebooks or non-propretary format note taking apps that will make their work accessible to others after their death.

deleted 5y ago

[deleted]

divs1210 5y ago