Question

The brilliant Indian mathematician Ramanujan immediately answered a a question from the English mathematician Hardy. Hardy mentioned the number 1729 which was the number of a cab he had just travelled in ..He said it was'nt a very interesting number but the Indian instantly said it was and defined its unique property. Any suggestions about what it might be? It involves perfect cubes.

Answer 1

Oh, I read this once :)
I think its the lowest number that can be written as the sum of something... about perfect cubes

Answer 2

Hardy's Words
"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," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

Source: Wikipedia

Answer 3

Aww, prove it!

Answer 4

Smallest positive number, he probably meant.

Answer 5

yes - that guy was phenominal with numbers - and Hardy was probably the best english mathematician ecer

Answer 6

His later work with Laurel was also quite funny.

Answer 7

Hmm what about Euler?

Answer 8

I heard a lot of
Ramanujans work was wrong, though he was definitely great.

Answer 9

Euler wasn't english.

Answer 10

Oh Sorry

Answer 11

1^3 + 12^3 = 1729
9^3 + 10^3 = 1729

Answer 12

proof it's the smallest?

Answer 13

lol ktklown

Answer 14

that would be a good exercise turing - i suppose you could prove it using proof by exhaustion

Answer 15

You mean an list of 1728 numbers that don't work?

Answer 16

Ramanajan didn't lie proof - completely opposite to hardy's approach to math - that s why they made such a good leam

Answer 17

I know, I heard Ramanujan got divinely inspired from Krishna as to the sum of some series, which Hardy hated because he had to go and prove it, lol!
Plus Hardy was so anti-Platonism. What's that called, formalism? Ramanujan's approach is more about feeling the answer, which makes little sense from a formalist perspective, right?

Answer 18

yep - but amazingly he was correct most of the time. Unfortunately, he died in his early thirties.

Answer 19

This problem is wrong but given right numbers one way to approach is to represent any point on the line as a function of sine and cosine.
consider @ as theta
Given A(x1,y1) and slope tan@ you can find a point B on the line r units away from A as
Bx = x1+rcos@
By=y1+rsin@.
Such representation will help in this case because we have relation between points on the line with varying distances.

Answer 20

Care to elaborate on that method for calculating the smallest number that can be written as the sum of two cubes two different ways? I don't get it.

Answer 21

I am sorry the explanation was meant for different question I accidently posted it here.

Answer 22

Oh, I was gonna say...

Answer 23

for this a^3+b^3=c^3+d^3. give it to super computer to get first five sets of a,b,c,d integer values

Answer 24

...or give it to Ramanujan :D

Answer 25

true such a genius only once in a century

Answer 26

1729 is called the Hardy-Ramanujan number which can be expressed in the form of the sum of two perfect cubes in two different ways.

Answer 27

\[12^3 + 1^3 = 9^3 + 10^3\]I remember how there are other numbers like this too.