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.

The world is continuous, but the mind is discrete.

The world is a very complicated place, as babies know.

Logic has virtually nothing to do with the way we think.

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 think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.

Images of the world are Renormalization Group fixed points.