Ask cperciva: Are great mathematicians born or made?

I know you are waiting for cperciva to give you reply. But I want to tell my own experience.

I was very bad at math when I was in high school. I figured out algebra without problem but failed pretty bad in classical geometry when I was 9th grade. From my 10th to 12th grade, I just have dyslexia to what math textbook says.

Then I studied with 2 teachers for a year to prepare taking another entrance examination in my country (Taiwan). Both explained clearly two things to me that I like most later, one is physics and another is math. The math teacher taught me calculus in 2 weeks and I just started to become literate to meanings in those symbols and after that when I look back analytic geometry and classical mechanics in our high school textbooks, I just felt my mental block was removed! I did not feel any trouble in understanding the problems and I later chose my major in physics just because I like to learn more of it and went through my undergraduate pretty ok and later I found computer science and I started to work in the trench for 16 years.

I did not make any contribution to math and physics, but I still like to use the training that I received in my daily life and I still sometime open books from Dover Publishers to read and feel interested. I like the feeling in figuring out problems and find ways to solve them. And that is the joy I'm glad to had a chance to acquire due to two best teachers that enlighten me.

Long answer: From my personal experience, a lot of what some claim to be 'nature' is actually very early-age 'nurture'. So it's not that children of academics are genetically smarter, it's that they are raised by people with whom dinner or a walk in the park ends up being as educational as a university lecture. On top of that, if you consider that knowledge is like money under compound interest, I think it's possible to explain people that seem smart beyond comprehension as just having gotten a good head start on learning.

Math is also a special case for two (related) reasons: (1) emotions, especially ego, has a lot to do with learning math, and (2) math is filled with "aha" moments, where one thing which seemed incomprehensible one moment is obvious the next. Little kids have an advantage related to both of these - they (hopefully) don't yet have an ego to build or protect when it comes to knowing things, and they take a lot more pleasure from the "aha" moments.

So to answer your question - I would say it's nurture, but the kind which is (most of the time) limited to very young ages. On the other hand, given the determination and stubbornness of a 5 year old facing a challenge, it's nothing you can't do at 40. But I worry that I don't quite have that determination at 22, and will only have less of it as I am starting to worrying about becoming financially secure, starting a family, etc.

I competed in Math competitions while in high school but never made it to the IMO. My friends who went to the IMO were doubtlessly very smart, but they had something else: they had many years of training under their belts. I failed because I was an amateur, they succeeded because they trained like professional athletes.

To do Math, intelligence is required, but not sufficient. Tenacity, patience, stubborness, an obsession to figure things out, and the willingness to work very hard are also required. Prof. Terence Tao knows much more than I do on the subject and he explained things clearly:

http://terrytao.wordpress.com/career-advice/does-one-have-to...

When one is young, one does not mind feeling stupid. Understanding something in Mathematics takes a lot of time and effort. After a certain age, one does not want to feel that stupid anymore. That's why many great mathematicians did their best work before they were 30. It's more psychological than intellectual, I'd say.

25 is pretty young still I think. Thats only 3 years into a PhD, so really I wouldn't expect anyone (except super geniuses) to make many achievements by that age. I'd say 30 between 27 and 30 seems like a pretty solid age, as you've reached a peak with your PhD and you're still young and inquisitive and hopefully humble.

But I do think that success in science, mathematics, or really, anywhere, is much more a product of your habits, discipline, environment, and beliefs than is ordinarily given credit. I don't think 'nature', or 'very early nurture' is unimportant -- for example, it can play a very important role in the sorts of things you get interested in and the preferences, beliefs and skills you acquire. But conditioned on having the same beliefs, habits, and discipline as masterful scientists, business people, or researchers, if you're talking about great contributions, I think the other dimensions of talent truly shrink into irrelevance.

Three terrific links: Michael Nielsen on Extreme Thinking. http://michaelnielsen.org/blog/?p=19

(Edit: Whoops! Michael, the link is broken! Here's an archived version, http://web.archive.org/web/20061018164649/http://www.qinfo.o... )

Terry Tao's Career Advice: http://terrytao.wordpress.com/career-advice/

And the classic, Richard Hamming, You and Your Research: http://www.cs.virginia.edu/~robins/YouAndYourResearch.html