Reflecting on @geoffreyhinton's flawed view of math as a "closed system", here are 3 key aspects of math that the general public (including physics Nobel prize winners) tends to get wrong:⤵️ 1. Proving theorems does matter, but it's just one aspect of math. It's arguably the most publicized one, but not the most important one.

Here's an essential quote by Fields medallist Bill Thurston: "The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat's Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding."
(from mathoverflow.net/questions/4369…)

This viral post by @paulg was based on a visual by @cremieuxrecueil. Taken at face value, it seemed to prove that IQ is almost entirely determined by genes. But when you look at the actual sources, you realize that this conclusion is fundamentally wrong.⤵️ The first crazy thing: the yellow dataset (Burt) is known to be a fabrication. I have no clue why @cremieuxrecueil decided to include it, as the Burt fraud is one of the biggest and most documented scandal in the history of science.
en.wikipedia.org/wiki/Cyril_Burt

Now a completely subjective of books that will forever change your views on logic and/or mathematics.
The first one is so short that you have no excuse not to read it.⤵️ The second one is long and rambling (and confused and paranoid), but the first 200-300 pages are fabulous.

Bill Thurston learnt to see in 4 and 5 dimensions. Here's how he did it: ⤵️ Thurston's story illuminates the nature vs nurture debate: davidbessis.substack.com/p/beyond-natur…

The math equivalent of a celebrity selfie: a picture I took in the summer of 2000, at the Yale Math Dept (you can see my reflection in the glass.) Many are gone now. Getting the chance to know them and have ongoing conversations was a life-changing experience. Most people probably recognize Mandelbrot, so there's no need to explain who he was. With Serge Lang and me, he was one of the three francophones on the list, so we often chatted during tea.

How I woke up one day and decided to solve a math conjecture from the 1970s ⤵️ Until my early 30s, I considered myself a decent, second-rate mathematician. I had published nice papers in nice journals, but had never thought of myself as someone capable of solving “big” problems.

Why you don't understand math — and what you can do about it. ⤵️ Math isn't just hard; it’s also confusing. Some people struggle with it. Others are stunningly good and can’t figure out why.
Meanwhile, the “unreasonable effectiveness of math” fascinates everyone.
en.wikipedia.org/wiki/The_Unrea…

Wow, this *really* blew up! Thank you all for your interest and feedback.

I can’t reply to all individual comments, but here’s a follow-up with tentative responses to the most frequent objections and requests for clarification.

https://twitter.com/davidbessis/status/1816459931995840984

Objection #1: couldn’t we imagine a complex expression mechanism that would take the Gaussian input and transform it into a power law?
— I'm getting this one a lot, from smart people, and they have a fair point.

A simple math proof that math talent isn’t primarily driven by genetics. ⤵️ Besides wealth, math talent is the most unbelievable form of inequality I’ve ever been faced with.

My most ambitious post ever: we've been *wrong* about math for 2300 years and I’m going to *fix this* in a single Twitter thread. From the time of Euclid, there has been two competing approaches to defining math:
1/ through what it studies: numbers, shapes, structures…
2/ through how it functions: axioms, theorems, logical deduction…

Incompetence in one figure: UN 2024 projection for India TFR:
- fertility has declined at constant slope for 60 years
- all recent data points toward a continuing decline
- no other country succeeded at stopping TFR decline
=> yet UN predicts TFR to magically stabilize overnight I find it amazing that the UN's entire "Population Division" is capable of MISSING the global collapse of fertility rates — a world-redefining phenomenon that anyone with a Wikipedia access can figure out in 10 minutes.
It paints a scary picture of how useless UN really is.

Si vous entendez dire que Maryna Viazovska a reçu la médaille Fields parce qu'elle est une femme et ukrainienne (comme dans le commentaires affligeants sous ce post de @lemondefr), voici quelques arguments pour répondre: 🧵

https://twitter.com/lemondefr/status/1544227657335934976

En 1611, le grand Johannes Kepler a formulé une conjecture devenue très célèbre... fr.wikipedia.org/wiki/Johannes_…