Born and/or made

AVI linked to an essay dissecting twin studies.(*) David Bessis wrote a book (which I have not read) which sounds interesting and useful, but I suspect overclaims. "People think that it (mathematics) requires a special gift or that comprehension is a matter of genes. Yet the greatest mathematicians throughout history, from René Descartes to Alexander Grothendieck, have insisted that this is not the case. Like Albert Einstein, who famously claimed to have “no special talent,” they said that they had accomplished what they did using ordinary human doubts, weaknesses, curiosity, and imagination."

I'm not on the same level as those fellows, but I'm well better than average at math.

I only know that by comparison.

I don't feel particularly smart.

It's trivial for me to find problems that stump me. There are people who can solve those problems--and in an academic environment I meet them.

Being acutely aware that a colleague can easily deal with things that puzzle me is a ticket to imposter syndrome. I can't have the same painful awareness of the things that puzzle my colleague that I know how to deal with. Once you've solved a problem it seems easy, so the world is full of hard problems and all I solve are the easy ones.

I don't think that a researcher is always, or perhaps even often, going to be the best judge of how smart he is. An honest man or woman will be honestly humble, a member of the society of the puzzled.

Further, when you're surrounded by the best, that becomes your normal. At Princeton, Einstein didn't run into a lot of people who were no good at math.

FWIW, I suspect that most people are capable of understanding much more math than they dream. Mathematicians are born, but they need to train their minds in ways of looking at things, and with "crystallized intelligence" (standing on the shoulders of giants) even those of us who aren't great geniuses can learn how to make contributions.

I've griped before that advanced math books (and papers) often throw theorems at you without enough examples or motivation. That's not how they did the work to get there -- they played with examples, had some motivation to point them the way they did, and they did a lot of noodling around trying this approach and that.

(*) I'd always wondered how often it would happen that twins would be broken up to different homes. Among other details Bessis dug up, many of the separated twins were raised by relatives in their extended family, so their environments may not have differed that much.