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"I like to see how things fit together: you might see that some body of
results bears some resemblance to some other body of results, and for
no apparent reason, and you ask ``Why do these things look like these
things?. There must be some deeper reason.'' Finding out these deeper
reasons is the sort of thing that I like to do, rather than trying to
prove something is true if and only if something else is true. I like
that kind of result, but it is not really my favourite thing: I like big
structures and theories. That is reflected in the way I do mathematics.
I do mathematics by just trying to understand something, and the theorems
fall out by osmosis, if it works...
"I do it because the structures are incredibly beautiful -- complicated is
the wrong word, but they have lots of structure, so it's very elegant,
and they're very hard to exhaust -- and certainly impossible for me
to understand completely, so you always feel that you're learning
more about these things. And I suppose the other reason why I
think they're interesting to me, is that I have a body of theory and
technique coming from non-commutative noetherian rings, which is very
different from the things coming from physics, or from Lie theory, or
even from representation theory -- so you feel that you have something
to contribute.
"People think that what we do is very abstract, and they're right: but
to us, if we're doing it right, it shouldn't seem abstract, it should
seem concrete, because you're actually working with these concrete
gadgets in order to prove abstract things about them."
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