Sublime

No sooner did Gödel’s paper appear than von Neumann was presenting it to the mathematics colloquium at Princeton. Incompleteness was real. It meant that mathematics could never be proved free of self-contradiction. And “the important point,” von Neumann said, “is that this is not a philosophical principle or a plausible intellectual attitude, but t

In June 1983, Alexander Grothendieck sits down to write the preface to a mathematical manuscript called Pursuing Stacks . He is concerned by what he sees as a tacit disdain for the more “feminine side” of mathematics (which is related to what I’m calling the solitary creative state) in favor of the “hammer and chisel” of the finished theorem. By el

Physics basically says we’ll understand the universe because we’re going to extremize a function. That’s what physics does—optimization, some least-action principles. So, we’re going to minimize the time, we’ll minimize the energy, we’ll minimize the distance. We’re looking for those functions that we’re trying to extremize and we’re going to repre

It was not new experimental data that led to the great conceptual leap represented by special relativity, but rather Einstein’s faith in the conceptual appropriateness of theories that had shown themselves to be empirically adequate, their apparent contradictions notwithstanding. This reconstruction of the logic of a scientific revolution stands al

Albert Einstein declared “creativity is more important than knowledge,”

The constructive part of Descartes’s theory of knowledge is much less interesting than the earlier destructive part.

In Leibniz, if the principle is completely true and the deductions are entirely valid, all is well; but the structure is unstable, and the slightest flaw anywhere brings it down in ruins. In Locke or Hume, on the contrary, the base of the pyramid is on the solid ground of observed fact, and the pyramid tapers upward, not downward; consequently the