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"I always try to explain things through an analogy with music. What we do
is in a way not so much about applications, but in trying to understand
the music of mathematics. We've got to play people our music, and try
to transmit the excitement that we feel.
"You do feel you are exploring a very beautiful and amazingly laid-out
landscape with so many interconnecting tunnels. It is not a boring place
to be, the mathematical world. It is an extraordinary place, with all
these tunnels that you go down and pop up in a completely different area!
It is just so surprising, this world, and it worth spending time there.
"I'm trying to use a zeta-function not to understand how prime numbers
are distributed, but to understand what sort of symmetries can exist.
It is like putting on a completely different pair of glasses. I'm looking
at the things that I want to understand, but I'll take the glasses from
number theory, and you get a completely different view of these things.
I think that's very exciting. I'll try on as many pairs of glasses as
I can!
"The interconnectedness of mathematics means that it is quite
hard to go too far without connecting to something else. So it took
ten to fifteen years, but this year I understood that these zeta-functions, which are about infinite groups, can be used to
understand how many finite groups of a particular kind exist. That
reaffirmed my faith in following something because it seemed
interesting in its own right. "
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