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Ramanujan Surprises Again (2015)

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Re: Ramanujan Surprises Again (2015)

#81

Post by mkl »

v64 wrote: post #7

Great read! When you first hear the taxicab number story, your initial impression is to be struck by Ramanujan's innate calculating capability. It's interesting to find out that the real coincidence here is that Hardy rode in a taxicab whose number had happened to show up in Ramanujan's investigations of Fermat's last theorem.

> When you first hear the taxicab number story, your initial impression is to be struck by Ramanujan's innate calculating capability.

This is the way the story is always presented, and I think that's usually how it's intended, but I think it's quite misleading for another reason too. If you've ever made or looked at a table of cubes, the famous fact really jumps out (in base 10). I'm serious, look:

   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
The two pairs of cubes are 1000 and 729, and 1728 and 1, and 1000 and 1 make the addition trivial and the similarity obvious (and 729 and 1000 are even right next to each other, one row away from 1728!). With that observation, it doesn't take much effort to try the smaller possibilities and see that 1729 is the smallest number that can be written as the sum of two cubes two different ways. Ramanujan knew numbers and their relationships intimately, better than Hardy, who knew more theory. I think Ramanujan knew the fact about 1729 already, and that you are right about the taxi number coincidence being more surprising and, well, impressive.

(Yes, I've commented on this before: https://news.ycombinator.com/item?id=21165031)

Re: Ramanujan Surprises Again (2015)

#82

Post by scotty79 »

dntbnmpls wrote: post #45
Vinceo wrote: post #4

He credited his work to his family goddess. From wikipedia: "A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess. "An equation for me has no meaning," he once said, "unless it expresses a thought of God.""

Isaac Newton: "All my discoveries have been made in answer to prayer." People forget how religious newton was and he believed his physics was the discovery of god's physical laws. Chemistry comes from mystic alchemy. Astronomy derives from astrology. Just like there is a thin line between genius and madness, the same seems to apply to science and mysticism. Turn the dial a few degrees, you get mysticism. Turn it a fe…

I think the clear border is that if you start to make things up that go against what we solidly measured so far or you have gaps in your derivation then you are well within 'mysticism' part of the dial. I think there's even slightly audible click when you go to that part of the dial.

Re: Ramanujan Surprises Again (2015)

#83

Post by psoy »

wenc wrote: post #30
hnews_account_1 wrote: post #8

Earlier quoted context omitted.

A lot of genius stories are like this. I was also under the illusion that these guys could just do things that fast, but at some point, I read Feynman's biography where he explicitly talks about how he used to solve homework problems or something beforehand and then he used to pretend that he found the solution while solving it if his classmates asked. That threw me for a loop and I started believing shit like no one…

I think most of us are impressed by computational parlor tricks (and indeed raw computational intelligence in general -- being able to process information and compute quickly and accurately), but for me, genius goes beyond that. Genius is about having rare and useful insights that the rest of us are incapable of, and that a computer is unable to easily replicate. For instance, there was this thing on Twitter recently…

That's not an example of genius by any stretch of imagination, sorry.

Re: Ramanujan Surprises Again (2015)

#84

Post by madcaptenor »

pmoriarty wrote: post #23
dannykwells wrote: post #3

The taxi cab story is easily a top-5 math story, and is quintessential Ramanujan. Has there been a genius of his kind since? Maybe Terry Tao, but his work also lacks the ease and lack of machinery that Ramanujan had. Truly amazing.

What are the other 4 top math stories? For me one of them has to be of Évariste Galois[1], who, legend has it, hastily wrote fragments of his last mathematical discoveries on his shirt sleeves before fighting the duel that would end his life. [1] - https://en.wikipedia.org/wiki/%C3%89variste_Galois

My understanding is that this legend has been debunked, but ironically I can't find a source. (My instinct is to blame E. T. Bell.)

Re: Ramanujan Surprises Again (2015)

#85

Post by JoeAltmaier »

russellbeattie wrote: post #37
pixelpoet wrote: post #33

Earlier quoted context omitted.

I love how the article starts with the most boring facts about 1729: > 1729 is the natural number following 1728 and preceding 1730.

Heh. I've been reading HN for long enough to never be surprised by the capability of incredibly pedantic people to be incredibly pedantic.

We had to have a home somewhere :) And this is it.

Re: Ramanujan Surprises Again (2015)

#86

Post by Cpoll »

dwaltrip wrote: post #52
taberiand wrote: post #43

Earlier quoted context omitted.

This kind of coincidence is just cute, it doesn't imply anything useful mathematically right?

The fun thing about math (and science and technology as well) is that it is you can't always tell what is going to useful down the road. "Interestingness" is often as good a heuristic as any when looking for paths that lead to useful developments, although the path is often not a straight one or short one. I also like the idea of secondary and tertiary effects. One simple example: By "playing" with cute yet fun ideas…

Have any developments come out of adding the digits? My impulse is to dismiss it out of hand because it only works in base-10, which in my mind leans it towards numerology instead of math.

Re: Ramanujan Surprises Again (2015)

#87

Post by BGthaOG »

lonelappde wrote: post #50
BGthaOG wrote: post #49

Earlier quoted context omitted.

I would not be surprised if it is found to be useful. My reason for this is the Quran's mathematical composition, founded on the number 19: https://www.masjidtucson.org/quran/miracle/

That's numerological nonsense like Bible Code.

It is not; I invite you to study it before you reject it.

Re: Ramanujan Surprises Again (2015)

#88

Post by lvncelot »

dannykwells wrote: post #3

The taxi cab story is easily a top-5 math story, and is quintessential Ramanujan. Has there been a genius of his kind since? Maybe Terry Tao, but his work also lacks the ease and lack of machinery that Ramanujan had. Truly amazing.

John von Neumann is someone that often comes up in this context - there are numerous anecdotes on how he was perceived as frightingly clever; also his body of work is beyond impressive.

Re: Ramanujan Surprises Again (2015)

#89

Post by dwaltrip »

Cpoll wrote: post #86
dwaltrip wrote: post #52

Earlier quoted context omitted.

The fun thing about math (and science and technology as well) is that it is you can't always tell what is going to useful down the road. "Interestingness" is often as good a heuristic as any when looking for paths that lead to useful developments, although the path is often not a straight one or short one. I also like the idea of secondary and tertiary effects. One simple example: By "playing" with cute yet fun ideas…

Have any developments come out of adding the digits? My impulse is to dismiss it out of hand because it only works in base-10, which in my mind leans it towards numerology instead of math.

It looks like there are some applications. Checksum algorithms are probably the easiest to appreciate.

https://en.wikipedia.org/wiki/Digit_sum#Applications

Re: Ramanujan Surprises Again (2015)

#90

Post by mafaa »

Cpoll wrote: post #86
dwaltrip wrote: post #52

Earlier quoted context omitted.

The fun thing about math (and science and technology as well) is that it is you can't always tell what is going to useful down the road. "Interestingness" is often as good a heuristic as any when looking for paths that lead to useful developments, although the path is often not a straight one or short one. I also like the idea of secondary and tertiary effects. One simple example: By "playing" with cute yet fun ideas…

Have any developments come out of adding the digits? My impulse is to dismiss it out of hand because it only works in base-10, which in my mind leans it towards numerology instead of math.

I think small random uses add up to practical value although there are those who make a religion out of its 'meaning'.

some (n mod 9) can be found by (is congruent to) (sum of the digits mod 9) instead is the most obvious example

True only in base 10 although similar congruences exist for other bases and also involve adding the digits

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