I see that many people are confused by the interview's title, and also by my take that math talent isn't primarily a matter of genes. It may sound like naive egalitarianism, but it's not. It's a statement about the nature of math as a cognitive activity.
For the sake of clarity, let me repost my reply to someone who had objected that my take was "clickbait".
This person's comment began with a nice metaphor: 'I cannot agree. It's just "feel-good thinking." "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained. And the biological underpinning of our capabilities doesn't magically stop at the brain-blood barrier. We all do have different brains.'
Here was my reply (copy-pasted from my post buried somewhere deep in the discussion):
I'm the author of what you've just described as clickbait.
Interestingly, the 100m metaphor is extensively discussed in my book, where I explain why it should rather lead to the exact opposite of your conclusion.
The situation with math isn't that there's a bunch of people who run under 10s. It's more like the best people run in 1 nanosecond, while the majority of the population never gets to the finish line.
Highly-heritable polygenic traits like height follow a Gaussian distribution because this is what you get through linear expression of many random variations. There is no genetic pathway to Pareto-like distribution like what we see in math — they're always obtained through iterated stochastic draws where one capitalizes on past successes (Yule process).
When I claim everyone is capable of doing math, I'm not making a naive egalitarian claim.
As a pure mathematician who's been exposed to insane levels of math "genius" , I'm acutely aware of the breadth of the math talent gap. As explained in the interview, I don't think "normal people" can catch up with people like Grothendieck or Thurston, who started in early childhood. But I do think that the extreme talent of these "geniuses" is a testimonial to the gigantic margin of progression that lies in each of us.
In other words: you'll never run in a nanosecond, but you can become 1000x better at math than you thought was your limit.
There are actual techniques that career mathematicians know about. These techniques are hard to teach because they’re hard to communicate: it's all about adopting the right mental attitude, performing the right "unseen actions" in your head.
I know this sounds like clickbait, but it's not. My book is a serious attempt to document the secret "oral tradition" of top mathematicians, what they all know and discuss behind closed doors.
Feel free to dismiss my ideas with a shrug, but just be aware that they are fairly consensual among elite mathematicians.
A good number of Abel prize winners & Fields medallists have read my book and found it important and accurate. It's been blurbed by Steve Strogatz and Terry Tao.
In other words: the people who run the mathematical 100m in under a second don't think it's because of their genes. They may have a hard time putting words to it, but they all have a very clear memory of how they got there.