Re: Srinivasa Ramanujan

Posted by DickT on September 10, 2003 at 17:33:59:

In Reply to: Re: Srinivasa Ramanujan posted by sol on September 10, 2003 at 11:11:07:

sol,

Well, in Ramanujans case we have some clues.

He spent his teenage years studying and mastering one book, on analytical function theory and analytical number theory (which are joined at birth). The format of the book was step by step: it started with (x-y)(x+y)=x² - y². You proved that and then came a slightly harder theorem of the same kind, in which the proof uses the first theorem, and so on one result building on another up to the state of the art as it was when the book was published (1880s). The book was intended to prepare or "cram" Cambridge students for the math exam known as the Tripos.

Ramanujan became not just familiar with the math in this book, it became his environment.

A recent author has suggested that math ability derives from the brain abilities used in social understanding. Think of living in a tribe or small town where "everybody knows everybody". By growing up in such an environment you know not only everyone else's name, but their preferences and personal characteristics. You are freely able to think what so-and-so and such-and-such would talk about if they had a conversation. And it is proposed that mathematicians have this same ability, only with the abstract things they think about and discuss, rather than people.

And so Ramanujan's "town" was the complex number system and the various peculiar things that could happen there. This was the focus of his imagination throughout his growing up and it is scarcely surprising that he was able to see relationships that more lazily prepared mathematicians (including great ones like Hardy) could not.

You don't have to postulate extra dimension, the depth of the human capabilities is sufficient.

Regards,
Dick

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Follow Ups: (Reload page to see most recent)

• Re: Srinivasa Ramanujan -- sol 9/11/03 (14)
  • Re: Srinivasa Ramanujan -- DickT 9/14/03 (0)
  • Re: Srinivasa Ramanujan -- DickT 9/11/03 (12)
    • Re: Srinivasa Ramanujan -- sol 9/12/03 (11)
      • Re: Srinivasa Ramanujan -- DickT 9/12/03 (10)
        • Re: Srinivasa Ramanujan -- sol 9/13/03 (9)
          • Re: Srinivasa Ramanujan -- DickT 9/13/03 (8)
            • Category Theory as a Philosphical Tool -- sol 10/03/03 (6)
              • Re: Category Theory as a Philosphical Tool -- DickT 10/03/03 (1)
                • Re: Category Theory as a Philosphical Tool -- sol 10/03/03 (0)
              • Re: Category Theory as a Philosphical Tool -- sol 10/03/03 (3)
                • Is Mathematics Created or Invented? -- sol 10/03/03 (2)
                  • Developing Intuitiveness in Geometry? -- sol 10/03/03 (1)
                    • The Shadows of Things -- sol 10/03/03 (0)
            • Re: Srinivasa Ramanujan -- sol 9/14/03 (0)

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