David Bessis's 2022 book Mathematica: Une aventure au coeur de nous-mêmes was translated into English in 2024 as Mathematica: A Secret World of Intuition and Curiosity. It's inspiring in parts, though distractingly first-person-self-indulgent and information-thin elsewhere. Among the many delightful and aphoristic bits, however, beginning in Chapter 6 ("Refusing to Read") are:
- “At a profound level, math is the only successful attempt by humanity to speak with precision about things we can’t point to with our fingers. This is one of the central themes of this book ...”
- “What is rare, and what our culture doesn't push you to do, is to be aware of your capability for synesthesia and to try to develop it systematically. Secret math is a mental yoga whose goal is to retake control over our ability for synesthesia.”
... and five rules from Chapter 11 ("The Ball and the Bat"):
- You can reprogram your intuition.
- Any misalignment between your intuition and reason is an opportunity to create within yourself a new way of seeing things.
- Don't expect it all to come at once, in real time. Developing mental images means reorganizing the connections between your neurons. This process is organic and has its own pace.
- Don't force it. Simply start from what you already easily understand, what you can already see, what you find easy, and just play with it. Try to intuitively interpret the calculations you would have written down. If it helps, scribble on a piece of paper.
- With time and patience, this activity will strengthen your intuitive capacities. It may not seem like you're making progress, until the day the right answer suddenly seems obvious.
... and later in that chapter:
- "Nothing is counterintuitive by nature: something is only ever counterintuitive temporarily, until you've found means to make it intuitive."
... and from Chapter 15 ("Awe and Magic"):
The difficulty of math, the initial shock, is only the first part of the emotional journey. The second part is the incredible feeling of wonder that arises from deep understanding, once you discover that not only is it possible, it is even easy. It was easy from the beginning, except that you couldn't see it.
Awe and then magic: this is a potent recipe for mathematical desire and a great complement to the sanitized math from the curriculum. Math isn't for the faint of heart. When we hide how scary it can be, we make it less desirable. If it wasn't for the awe, there would be no magic.
In a Quanta magazine interview (18 Nov 2024) by Kelsey Houston-Edwards with author Bessis there are some additional beautiful remarks:
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. They have to. Otherwise, I mean, nothing makes sense. I think this is also why babies are super happy — because they have epiphanies all day long. It’s wonderful.”
... and:
"Math is a journey. It’s about plasticity. I am not saying that math is easy. Math is hard. But life, whatever you do, is extremely hard.”
Eugenia Cheng's book Is Math Real? How simple questions lead us to mathematics' deepest truths is perhaps a more successful exploration of some higher dimensions in mathematical thinking, as are her comments in a July 2017 "Greater than Code" conversation.
But Bessis makes many powerful points, especially in highlighting some brilliant insights of René Descartes, William Thurston, and Alexander Grothendieck. And the translation by Kevin Frey is smooth and pellucid.
So much to ponder ...
(cf Live the Questions Now (2015-04-02), Good Mathematician vs Great Mathematician (2016-01-03), Eugenia Cheng on Thinking (2017-12-30), Is Math Real (2023-11-01), Mathematical Mantras in Toki Pona (2024-11-03), ...) - ^z - 2025-10-09