Mathematical work isn’t a series of lightning insights and strokes of genius. It’s first of all a work of reeducation based on the repetition of the same exercises of imagination. Progress is slow because the body needs time to transform itself. It doesn’t help to force it, which may end up hurting you. You just need to commit to a regular training

That which I’m unable to “see” or “feel,” even when I know it should be real, retains a special status for me. I don’t ignore the external information I get through language, but I treat it as a hypothesis, without entirely believing it. If I don’t see why something should be true, I’m wary of it. This kind of information can stay in this

what he saw on the screen was physically possible and really corresponded to what he’d done. For someone who’s never seen it done, learning to jump like Fosbury is almost as hard as inventing it yourself. Even with detailed written instructions, it’s not easy. “Jump up in the air on your back, headfirst.” Seriously? And why all these preliminary

When I speak of “truth,” I’m speaking of the truth of mathematicians, the absolute and eternal truth, what some people like to write as Truth, or TRUTH, or sometimes even TRUTH. This sort of truth is

As long as we conflate rationality and logic, as long as we reduce truth to its social and linguistic dimensions, as long as we see it only as a matter of consensus

served me well throughout my career, was to imagine that creative mathematicians were hackers who had found ways to unlock “hidden modes” of our cognition. Most of the time, they’d done so unwittingly, and were entirely incapable of explaining how.

education. It tries to make things easier rather than more difficult. You can compare it to meditation, yoga, rock climbing, or martial arts. It includes techniques to overcome our fears, conquer our flight reflex in the face of the unknown, and find pleasure in being contradicted. The method’s exact scope is actually broader than math. It’s a

Reconnecting with your early childhood capacity for learning means to stop believing in these absurd stories of gifts and talent. It means to become once again

For Descartes, truth was a matter of life and death. He perfectly embodies this singular and powerful aspect of mathematical psychology: his relationship to the truth is physical, almost carnal: I constantly felt a burning desire to learn to distinguish the true from the false, to see my actions for what they were, and to proceed with confidence