The world is continuous, but the mind is discrete.
Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.
My own view is that no major advance was ever found as a result of a committee's recommendation... We should be honest in telling these agencies we often don't know where some ideas are going to lead, but we hope they are going to clarify a problem.
I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.
Images of the world are Renormalization Group fixed points.
The world is a very complicated place, as babies know.
I think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.
The extreme possibilities are the most illuminating.
Logic has virtually nothing to do with the way we think.
A Noah's Ark of mathematicians, their lives, loves, hard times, and madnesses, Loving and Hating Mathematics shows our community with all its warts as well as its triumphs. I especially liked the chapter on much-hated school mathematics, 'Almost All Children Left Behind.'
Art lives on the mental plane (the real painting is not the set of dry pigments on the canvas nor is a symphony the sequence of sound waves that convey it to our ear) but, as the post-modernists insist, is reinterpreted in new contexts by each appreciator. As for gossip, which includes the vast majority of our thoughts, its essence is its relation to a unique local part of time and space.
