John, Glad you liked it! Thanks for the references to Raoul Bott. Mind you there was a serious point: how to turn abstract mathematics into machine computation? I have discussed this often with Larry Lambe. Ronnie ----- Original Message ----- From: "John Iskra" <jiskra@ehc.edu> To: "Ronnie Brown" <ronnie.profbrown@btinternet.com> Cc: "Hasse Riemann" <rafaelb77@hotmail.com>; <categories@mta.ca> Sent: Friday, June 05, 2009 3:54 AM Subject: Re: categories: Re: Famous unsolved problems in ordinary category theory
One of my favorite quotes:
The question you raise ``how can such a formulation lead to computations'' doesn't bother me in the least! Throughout my whole life as a mathematician, the possibility of making explicit, elegant computations has always come out by itself, as a byproduct of a thorough conceptual understanding of what was going on. Thus I never bothered about whether what would come out would be suitable for this or that, but just tried to understand -- and it always turned out that understanding was all that mattered.
A. Grothendieck
Raoul Bott reinforced this in a talk I had the privilige to hear back in 98. He said that mathematics, done well, never required the placing of your oar in the water (he probably put it better than that...). The idea I think is that if you continually ask and answer the questions that occur to you, and, thus, gain understanding, then you will inevitably make progress. And that is what matters, really. So often the person credited with solving a 'famous' problem only takes the final step in a hard journey of a thousand miles made by a thousand others.
Glory and fame - such as it is in the world of mathematics - are nice, but they are not, in the end, mathematics. I think it is of high importance to avoid confusing them.
John Iskra
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