Mathematician David Bessis claims that mathematical thinking isn’t what you think it is, and that everyone can benefit from doing more of it. He argues that math is an internal process, hidden from view, and that people are capable of expanding their mathematical abilities far beyond what they think possible.
Math is a sort of dialog between these external and internal processes. It is the activity of aligning your inner representation—your intuition—with some logical, external representation.
You use a very rigid, crazy-looking formalism to test your intuition, to recalibrate, grow and reinforce it until you feel that you have a good understanding of something.
You claim that everyone is secretly doing math, even if they don’t realize it. You have to force them to become aware of their own mathematical training. Can you see a circle in your mind? Can you make it bigger, smaller? Can you move it around?
High school students are often unhappy with math because they think it requires some innate things that they don’t have. But that’s not true; really it relies on the same type of intuition we use every day.
So how can one get better at math? Whenever you spot a disconnect between what your gut is telling you and what is supposed to be rational, it’s an important opportunity to understand something new. And then you can start this game of back-and-forth. Can you articulate your gut instinct and place it within a rational discussion?
What can someone gain by improving their mathematical thinking? Joy, clarity, and self-confidence. Children do this all the time. That’s why they learn so fast.
I’m actually more extreme than just saying this is a self-help book. I’m saying that, in a way, mathematics itself is a self-help technique. Mathematicians have to be radically honest about what they don’t understand and what they think.
What we can learn from Descartes, Grothendieck and Thurston is that the nature of the mathematical process is not what people think. It’s not just about understanding things, but about understanding things in a very childish, deep, naive, super clear, obvious way.
When you do math, you’re exposed to the human thought process in a way that is really pure. It’s a scaffold for your imagination. When I look at my own life, and the way I managed to overcome personal challenges, I realize that my ability to think in a mathematical way helped.
Everyone, Bessis says, has some experience with this process, meaning that everyone has practice thinking like a mathematician. Moreover, everyone can, and should, try to improve their mathematical thinking—not necessarily to solve math problems, but as a general self-help technique.
For adults, this way of thinking can be very slow. But if you don’t give up, what you can do with your intuition is way beyond your wildest expectations. And this is universal. My book is a life lesson for all creative people, not just those who want to learn mathematical concepts.
Math should be thought of as a dialog between the two: between reason and instinct, between language and abstraction. It’s also a physical practice of sorts, like yoga or martial arts—something that can be improved through training.
Mathematician David Bessis claims that mathematical thinking isn’t what you think it is, and that everyone can benefit from doing more of it. He argues that math is an internal process, hidden from view, and that people are capable of expanding their mathematical abilities far beyond what they think possible.
Bessis believes that the nature of the mathematical process is not what people think. He cites examples of mathematicians like René Descartes, Alexander Grothendieck, and William Thurston, who all described a similar story about the importance of intuition in mathematics.
To improve mathematical thinking, Bessis suggests playing a game of back-and-forth between gut instinct and rational discussion. This can help to align intuition with reason and lead to greater understanding and self-confidence.
Bessis views mathematics as a self-help technique, one that can be used to improve creativity and imagination. He argues that the process of doing math is a physical practice that requires training and honesty about what one doesn’t understand.
Bessis has written a book titled “Mathematica: A Secret World of Intuition and Curiosity,” which explores the inner experience of humans doing math. He hopes that his book will help people understand what it means to do math and how they can improve their mathematical thinking.
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The mathematician’s message is for everyone: Look at what you can do if you don’t give up on your intuition.
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Mathematicians have to be radically honest about what they don’t understand and what they think. That might help them see, for example, that an object is defined the wrong way. Or that a different definition will make a theory simpler. Or that this is not the important notion, that one is.
