Sunday, August 02, 2009

Hadamard reexamined

Steven Hsu has a post on Hadamard's famous book "Psychology of Invention in the Mathematical Field" in Hadamard: The Mathematician's Mind and links to the very interesting article: Mathematical Discovery: Hadamard resurected. Both worth reading. I have met a few brilliant mathematicians including some Field Medallists, but the only one I saw at close quarters is my old friend M.S. Raghunathan. He does not seem to fit in to these patterns. I saw him picking up new topics in conversations and using them immediately. He would start working on any thing for arbitrary reasons even if he did not know the topic. He would start with all sorts of absurd ideas and would not listen if somebody told him that those would not work. After throwing away hundred of approaches he would come up with some thing that worked. He also missed a few by a whisker and probably missed the Fields Medal. He was like that in his younger days. Once he started on a topological topic to help me even though it was not his area. We were trying to reprove some result following a vague announcement. Since it was my area, I kept pace with him for a few days. When it came to the final hard part, our approaches differed. I thought that one approach was natural and should work and took a bet with him. If it worked, he should buy me dinner. Raghunathan did not care. He tried some absurd approach and proved the result. And after a few days, he showed my approach worked too and bought me dinner.
It seems that even for Raghunathan thinking of topics outside his area is difficult now. Last time I tried to tell him about some thing intersting in my area, he dozed off.

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