Mathematica
by David Bessis, Kevin Frey · first published 2024
80% recommend20% neutral
Why HN recommends it
Conveys how working mathematicians actually think, arguing intuition comes first and formal proof comes last; useful for students, learners, and anyone curious about the creative side of math.
Summarised by Claude from recommending comments
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…is this: Birds can fly, but can they use their intuition to create a theory of flight, and then use that to build a plane ? This book by Bessis paints this really well [1]. [1] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...
on “Ask HN: Why is problem solving in math still important in the AI age?” ↗Anyone else read Mathematica by David Bessis? Snagged this one recently and his hypothesis seems to jive with these findings. He suggests that really doing vs math is a largely intuitive process that is then fact checked by logic…
on “Children's arithmetic skills do not transfer between applied and academic math” ↗…is intuition - love the intuitionist focus in this book, also tying into what Bessis said in [1] I intend to read this book in depth. Author: please fix the html rendering. [1] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...
on “Practical Foundations of Mathematics” ↗I really enjoyed the book Mathematica by David Bessis, who writes about his creative process as a mathematician. He makes a case that formal math is usually the last step to refine/optimize an idea, not the starting point as is often assumed.…
on “Think in math, write in code (2019)” ↗There's also the argument that human intuition can and should be trained, rather than just dismissing it, in particular when it comes to mathematics. See, for example, the book "Mathematica" by David Bessis, or this blog post: https://davidbessis.substack.com/p/thinking-fast-slow-and-su...
on “Six Math Essentials” ↗There was a book I read a couple years back called "Mathematica: A Secret World of Intuition and Curiosity", by David Bessis. He discussed this topic and how generally it's left to those who are more notable in a field to ask the 'dumb' questions everyone else is…
on “Sabotaging projects by overthinking, scope creep, and structural diffing” ↗Mathematica: A Secret World of Intuition and Curiosity- David Bessis https://www.goodreads.com/book/show/200128457-mathematica?ac... Excellent book on mathematical thinking in the true sense - what needs to happen…
on “Ask HN: What were the best books you read this year?” ↗It's good to remind yourself of Bill Thurston's points: https://www.ams.org/journals/bull/1994-30-02/S0273-0979-1994... I love the analogy in David Bessis's wonderful book Mathematica (nothing to do with Wolfram). We all know how to tie our shoes. Now, write in words and symbols to teach someone how you tie your shoes. This is what a proof is. Often even people with STEM degrees…
on “Why formalize mathematics – more than catching errors” ↗I just finished Mathematica by David Bessis and I wish this information was presented in the way he talks about math: using words and imagery to explain what is happening, and only using the equations to prove the words are true.…
on “Learning Feynman's Trick for Integrals” ↗There are a few mathematicians that have analyzed and wrote about their process. A recent (IMO) good writing on the subject is David Bessis' "Mathematica" (I found this review https://siliconreckoner.substack.com/p/review-of-mathematica... which I haven't had a chance to fully read). It covers both a personal perspective as well as examples from Grothendieck,…
on “Cultivating a state of mind where new ideas are born” ↗You’re in a kind of compulsive ideology here. This same vein of thought and why it is harmful is described by David Bessis in the book Mathematica: A Secret World of Intuition and Curiosity. “To stop thinking in terms of “gifts” and “talents,” one has to find an alternate explanation. My way of looking at things, which has served me well throughout…
on “If math is more than proof, we need to better celebrate the rest of it” ↗You should read David Bessis's Mathematica.
on ““A Course of Pure Mathematics” – G. H. Hardy (1921) [pdf]” ↗Anyone who enjoys this should read David Bessis’s Mathematica.
on “Proofs Without Words” ↗Mathematician David Bessis describes similar exercises in his book [ref] - wherein he explores a room blindfolded to awaken other senses, or visualize the places he has been to. [ref] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...
on “Reality has a surprising amount of detail (2017)” ↗…math. So, there are faculties beyond visual imagination which are invoked, and even within visual imagination, there is a spectrum among people as to its strength, and quality. [1] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...
on “Proofs Without Words” ↗