| Title | Mathematical Thinking Isn't What You Think It Is | |
| Date | Tuesday November 26, @05:26AM | |
| Author | hubie | |
| Topic | ||
| from the dept. | ||
Arthur T Knackerbracket has processed the following story:
David Bessis was drawn to mathematics for the same reason that many people are driven away: He didn’t understand how it worked. Unlike other creative processes, like making music, which can be heard, or painting pictures, which can be seen, math is for the most part an internal process, hidden from view. “It sounded a bit magical. I was intrigued,” he said.
His curiosity eventually led him to pursue a doctoral degree in math at Paris Diderot University in the late 1990s. He spent the next decade studying geometric group theory before leaving research mathematics and founding a machine learning startup in 2010.
Through it all, he never stopped questioning what it actually means to do math. Bessis wasn’t content to simply solve problems. He wanted to further interrogate — and help other people understand — how mathematicians think about and practice their craft.
In 2022, he published his answer — a book titled Mathematica: A Secret World of Intuition and Curiosity, which he hopes will “explain what’s going on inside the brain of someone who’s doing math,” he said. But more than that, he added, “this is a book about the inner experience of humans.” It was translated from the original French into English earlier this year.
In Mathematica, Bessis makes the provocative claim that whether you realize it or not, you’re constantly doing math — and that you’re capable of expanding your mathematical abilities far beyond what you think possible. Eminent mathematicians like Bill Thurston and Alexander Grothendieck didn’t owe their mathematical prowess to intrinsic genius, Bessis argues. Rather, they became such powerful mathematicians because they were willing to constantly question and refine their intuitions. They developed new ideas and then used logic and language to test and improve them.
According to Bessis, however, the way math is taught in school emphasizes the logic-based part of this process, when the more important element is intuition. Math should be thought of as a dialogue 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. It requires tapping into a childlike state and embracing one’s imagination, including the mistakes that come with it.
“The mathematician’s message is for everyone: Look at what you can do if you don’t give up on your intuition,” Bessis said.
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.
[...] At its core, Bessis says, mathematics is a game of back-and-forth between intuition and logic, instinct and reason.
[...] It would be dishonest to deny that there are people who are incredibly good at math. There are 5-year-olds who are already genius mathematicians. You can see it: It looks like they’re communicating with aliens from outer space.
But I do not think this is innate, even though it often manifests in early childhood. Genius is not an essence. It’s a state. It’s a state that you build by doing a certain job.
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.
[...] 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? If there’s still a disconnect, can you visualize why? As you play that game, your imagination will gradually reconfigure. And in the end, if you’re persistent, your instinct and your reason will align, and you will be smarter. This is mathematical thinking.
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.
“When you do math, you’re exposed to the human thought process in a way that is really pure,” Bessis said. “It’s not just about understanding things, but about understanding things in a very childish, deep, naïve, super clear, obvious way.”
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. 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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printed from SoylentNews, Mathematical Thinking Isn't What You Think It Is on 2025-01-13 21:23:52