I am a little behind the times on this, but Dave Richeson recently posted a quote from Michael Atiyah:
Algebra is the offer made by the devil to the mathematician. The devil says: I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvelous machine.
Sir Michael Atiyah, 2002
I like the quote, I have a geometry prejudice, and feel the need to understand everything through pictures. Yet I felt it left something out. Maybe there is a reverse of the classic duel between god and the devil:
Nature and Nature’s laws lay hid in night:
God said, “Let Newton be!” and all was light.Alexander Pope: Epitaph intended for Sir Isaac Newton
It did not last; the devil howling
“Ho! Let Einstein be!” restored the status quo.Sir John Collins Squire A Random Walk in Science compiled by R. L. Weber, edited by E. Mendoza
In this case it is God’s turn to subtly undermine the work of the devil, offering the gift of computers to mathematicians. Algebra becomes algorithm and the geometry be revealed once more. The question is still whether mathematicians (especially Atiyah himself!) will appreciate this new gift.
Certainly there is an ongoing contest between number based ideas and geometric ones, even in their application (I’m thinking of physics here). And it does seem to be an internal conflict, which is sometimes mended by partnership (like analytic geometry).
But the quote was in the forward of a recent printing of Tobias Dantzig’s book Number. I checked my copy. It doesn’t have it. But this is not a geometry book. Do you know more about what Atiyah was getting at?
Just as an FYI, his name is Dave Richeson.
Thanks! I have updated to a correct version.