Mathematica

the clarification of ideas and the refinement of language. It’s a delicate exercise of motor coordination and requires years of practice to master. The good news is that with patience and effort anyone has the ability to get better.

Our Ordinary Intuition As long as schools refuse to teach the human reality of mathematics, all mathematicians will be self-taught. Saying that math is a matter of intuition isn’t enough. You also have to explain that this intuition is accessible and describe the ways that you can develop it. Nothing is more intimidating than the myth that mathemat

Mathematics gives us examples of truths in which we can have absolute confidence. It’s not just about superficial truths, like 2 + 2 = 4, but also profound truths, truths that are extremely interesting and not at all immediately apparent. We’ll give several striking examples in the next chapter. It’s only through a relentless confrontation with dou

Through the work of writing, intuition becomes less and less vague and less and less wrong. This process is slow and gradual.

Learning to write math is learning to have clear ideas. Wouldn’t it be a shame to deprive yourself of that? By writing math yourself, you’ll get to understand why it is written in such a bizarre formalism, in this language made for robots: there’s really no other choice. To demonstrate, we’ll return to another of our favorite examples: the concept

Fear of falling and fear of walking are one and the same thing. The person who fears falling on their face is powerless to learn how to walk. It’s only when we stay on our ass that our initial clumsiness turns into physical disability.

innate. It’s not fixed. We can build it up, make it stronger day by day, as long as we follow the right method. Mathematicians are well aware that official math doesn’t tell all the story. They know that the real goal is to understand what’s in the books, to see it, to feel it. What mathematicians do on a daily basis is to develop their intuition,

It was in this context that I called an end to my scientific career. Decisions of this kind are never easy to make. Trying to pinpoint a single factor that explains it all would be naïve. Among the multitude of factors, there was, however, this particular frustration: I wasn’t able to teach math in a meaningful way. I could teach what math was supp

It seems that scrutinizing our own perplexity is the best way to mobilize our natural faculties for learning. This is precisely why math is difficult: it requires looking straight at what is beyond our comprehension. We must become genuinely interested in it. We must force ourselves to imagine it and