Mathematica

Meanwhile, mathematics remains the only academic discipline that is universally taught without anyone having agreed on what it’s supposed to be, which leads to some truly bizarre consequences. For example, many mathematicians have spoken about their feeling of having been self-taught. In light of the prominent role of math in the curriculum, this i

Official math can be found in textbooks, where it is presented in a logical and structured manner, in an esoteric language that relies on indecipherable symbols. Secret math, also known as mathematical intuition, can be found in the heads of mathematicians. It consists of mental representations and abstract sensations, often visual, that are for th

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.

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 th

It’s surprising that Wittgenstein’s philosophy isn’t more well known outside of specialized circles, as it holds a very practical life lesson: we should accept going step by step, clarifying our language as we move forward, and being regularly surprised. It’s an effective antidote for paranoia.

undeniable that mathematical creation feels magical and supernatural. But behind all that there’s necessarily a human reality that is neither supernatural nor magical.

Each time I found myself in a situation of teaching or explaining my work, I tried to bring together two levels of discourse: a formal level made of rigorous definitions and precise statements, and an intuitive level, with the right metaphors, the right drawings, the right inflection of my voice, the right way of waving my hands. These two levels c

When I stop writing down my dreams I quickly lose my ability to remember them. When I force myself to write them down again, even if it’s just a word or two, the ability gradually returns. Sometimes you have to keep it up for several weeks. The most difficult part is trying to recapture the first bit of a dream after a long period of not being able

My advice is to have no shame in starting at the beginning, with the most classical and elementary proofs. Since it won’t be easy for you to know if you really understand them, try explaining them to someone else, perhaps a child.