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 Ronnie Brown wrote:
In reply to Hasse Riemann's question (see below):
I remember being asked this kind of question at a Topology conference in Baku in 1987. It is worth discussing the background to this, as someone who has never gone for a `famous problem', but found myself trying to develop some mathematics to express some basic intuitions.
Saul Ulam remarked to me in 1964 at my first international conference (Syracuse, Sicily) that a young person may feel the most ambitious thing to do is to tackle a famous problem; but this may distract that person from developing the mathematics most appropriate to them. It was interesting that this remark came from someone as good as Ulam!
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----- Original Message ----- From: "Hasse Riemann" <rafaelb77@hotmail.com> To: "Category mailing list" <categories@mta.ca> Sent: Tuesday, June 02, 2009 5:31 PM Subject: categories: Famous unsolved problems in ordinary category theory
Hello categorists
I don't know what to make of the silence to my question. This is the easiest question i have. I can't believe it is so difficult. It is not like i am asking you to solve the problems.
There must be some important open problems in ordinary category theory. There are plenty of them in the theory of algebras and in representation theory, so there should be more of them in category theory.
Especially if you broaden the boundaries a bit of what ordinary category theory is. Take for instance: model categories, categorical logic, categorical quantization, topos theory-locales-sheaves. But i had originally pure category theory in mind.
Best regards Rafael Borowiecki
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