Q. I just had an intuition about, for example, what functions might appear in the result. Hardy and Littlewood offered to put up some of the money themselves. But of more importance, as Ramanujan reported it, was that the “professors here… have lost their interest in mathematics owing to the present war”.
It is a romance that nothing can kill. Yet he had only the most bare education in backwaters of South India. He liked to hang out with other Indian students, sometimes going to musical events, or boating on the river. Other numbers in this series include 4104, 13832 and many more. As soon as enemy planes are sighted in the sky, the planes resting on the ground take off and fly at great speeds and dash against them resulting in destruction and death.”.
I actually went to college because of Ramanujan. Next, take the second group number and determine the closest perfect cubes to it. Once the young man arrived, Hardy and Ramanujan developed some of the most important math of the century. But back to Hardy. (Wolfram|Alpha now reports some other properties too.). It’s interesting to see in Ramanujan’s paper that even he occasionally didn’t know what was and wasn’t significant. But he said that since coming to England he had learned “their methods”, and was “trying to get new results by their methods so that I can easily publish these results without delay”.
The closest perfect cubes to 205 are 125, which is 5. . Is there, in other words, a method to this madness—for surely it was madness that drove Ramanujan to his results and then to extinction? Hardy is known for his achievements in number theory and mathematical analysis. The casual reader may find it a bit lengthy, but your personal inputs and speculations are amazing. Now of course there’s a fair amount of pure mathematics where one can’t (yet) just routinely go in and do an explicit computation to check whether or not some result is correct. But I think the first step to following in his footsteps is just to be adventurous: not to stay in the comfort of well-established mathematical theories, but instead to go out into the wider mathematical universe and start finding—experimentally—what’s true. And if one has earlier successes, those can help provide the confidence to move forward more definitively, without second guessing. Ramanujan described results; Hardy critiqued what Ramanujan said, and pushed for proofs and traditional mathematical presentation. It’s not particularly significant to come up with a conjecture about what’s true; what’s significant is to create a proof that explains why something is true, constructing a narrative that other mathematicians can understand.
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