Mathematics as Ideas or Proofs

Source: Quanta Magazine, Feb 2017

“There are two conceptions of mathematics,” Abouzaid said. “There’s mathematics as: The currency of mathematics is ideas. And there’s mathematics as: The currency of mathematics is proofs.

It’s hard for me to say on which side people stand. My personal attitude is: The most important thing in mathematics is ideas, and the proofs are there to make sure the ideas don’t go astray.”