David Bessis

Dear cutemonster,

I know this reply may not suffice to convince you, but unfortunately I won't be able to argue forever.

Did you ever consider the possibility that you might be the one living in a bubble?

FYI, the concept of innate talent predated IQ tests and twin studies by many millenia. Two of the authors I'm citing in my book (Descartes and Grothendieck) believed that innate talent existed and they both declared they would have loved to be naturally gifted like these or these people they knew.

You're declaring that these incredibly smart people were wrong about their own domains, which is a pretty bold claim to make. What do you have in support of this claim? A fake Einstein quote?

It's a sad fact of life that most quotes attributed to Einstein are fabricated. Next time, please check "The Ultimate Quotable Einstein", compiled by Alice Calaprice.

This may come as a shock to you, but Google page 1 isn't always a reliable resource. Nor is Wikipedia, even though it's quite often correct. As it happens, there's a pretty large "Heritability of IQ" bubble on the internet. It's active and vocal, but it's also quite weak scientifically — the page you're citing is a typical symptom, and it absolutely doesn't reflect the current scientific knowledge.

The IQ heritability claims that you're citing are based on twin studies and they have taken in serious beating in the past decade, especially in light of GWAS.

It's true that a number of people have been fooled by twin…

First up, I agree that mathematical pedagogy is usually pretty rough, more or less from Kindergarten to Postdoc.

But, this article implicitly assumes that a mathematical proof has to be utterly rigorous in order to be useful. I would assume that the author leans hard towards a "formalist" view of mathematics. I think this is an insufficient understanding of what mathematics _is_ and that embracing some amount of mathematical platonism and using "incomplete" proofs to gesture at important understandings is necessarily a valuable part of mathematical pedagogy.

My opinion is basically that of David Bessis, see a recent blog post [1], and his excellent book on the subject [2].

[1] https://davidbessis.substack.com/p/the-curious-case-of-broken-theorems

[2] https://www.goodreads.com/en/book/show/200128457-mathematica

Here’s one way to think about the difference between coming up with a formal proof and having something other mathematicians can use:

> A clear explanation can be found in Alex Kontorovich’s account of his own learning curve with formalized mathematics. In a nutshell: Mathlib, the dominant Lean library, is a human-curated formalization of an ever-growing fraction of existing human mathematics. It exposes clean APIs and abstractions, without which no autoformalization could take place. By contrast, Math Inc’s autoformalized proof of Viazovska’s results exposes no intelligible interface. Who in their right mind would merge a 200,000-line unaudited vibe-coded blob into the master branch of global human science?

https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy

Here's a research mathematician replying to pretty much exactly this question, and I think it's worth reading: https://davidbessis.substack.com/p/letter-to-a-phd-student

It's also relevant for non-AI reasons. The upshot is: Do it if you want to. You're at an age where you're supposed to be mostly learning, but over time, start transitioning into whyever you did this (which doesn't have to mean staying in academia, and in fact can mean teaching or popularisation or consulting or...).