The ultimate Platonist these days is Max Tegmark, a cosmologist at the Massachusetts Institute of Technology. In talks and papers recently he has speculated that mathematics does not describe the universe — it is the universe.

Dr. Tegmark maintains that we are part of a mathematical structure, albeit one gorgeously more complicated than a hexagon, a multiplication table or even the multidimensional symmetries that describe modern particle physics. Other mathematical structures, he predicts, exist as their own universes in a sort of cosmic Pythagorean democracy, although not all of them would necessarily prove to be as rich as our own.

“Everything in our world is purely mathematical — including you,” he wrote in New Scientist.

This would explain why math works so well in describing the cosmos. It also suggests an answer to the question that Stephen Hawking, the English cosmologist, asked in his book, “A Brief History of Time”: “What is it that breathes fire into the equations and makes a universe for them to describe?” Mathematics itself is on fire.