Great Mathematicians on Math Competitions and "Genius"

31CarlShulman

2multifoliaterose

7CarlShulman

2ThomasR

0CarlShulman

1multifoliaterose

15John_Baez

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Most who excel in the Olympiads don't go on to become Fields Medalists.

Most of those Fields Medalists who participated in the Olympiads did incredibly well, e.g. perfect scores, Terence Tao's gold at 13, etc.

Math contests are quite different from research mathematics, but are still amazingly good predictors of success in research mathematics compared to any other indicators available at that age. Similarly, pencil-and-paper IQ tests predict car accident rates, skill at assembling and disassembling guns, and success as a professional comedian, despite being quite different in their actual content.

Some who don't excel in competitions will still make great contributions to mathematics, and can be encouraged by reminders of this.

Motivational speeches to encourage low-performers, and ensure that high-performers actually learn research mathematics, won't be optimized to produce an accurate view of the facts.

There is a countersignaling/humility element involved.

As I said in my earlier comment, I agree with most of what you say here. Some specific comments and questions.

Math contests are quite different from research mathematics, but are still amazingly good predictors of success in research mathematics compared to any other indicators available at that age.

Can you make this statement more precise and give references to support it? I'm not sure what you mean by "indicators."

I'm pretty sure that high caliber mathematicians with a strong track record as advisors (like Hirzebruch, Atiyah, Thurston, Manin) would be better able to predict future success of high school students in research mathematicians by spending a few hours talking with the said students than by studying their scores on math olympiads.

Similarly, pencil-and-paper IQ tests predict car accident rates, skill at assembling and disassembling guns, and success as a professional comedian, despite being quite different in their actual content.

I've heard this from many people and believe it but have not had a chance to chase down references - do you have some handy?

If I turn the present posting into a top level posting I'll definitely take care to mention the point that you make above.

Some who don't excel in competitions will still make great contributions to mathematics, and can be encouraged by reminders of this.

Yes, this was one of my reasons for posting on the subject.

Motivational speeches to encourage low-performers, and ensure that high-performers actually learn research mathematics, won't be optimized to produce an accurate view of the facts.

I agree in principle but am not sure what you have in mind here specifically. Are there one or more particular quotations above that you find distortionary? If I turn the present posting into a top level posting I'll definitely take care to add quotations about the reality of natural talent.

Can you make this statement more precise and give references to support it? I'm not sure what you mean by "indicators."

I mean that if you were trying to select 100 kids to ensure that at least one would go on to win a Fields medal, picking out those at the top of the Math Olympiad distribution (the highest gold medal scores, youngest gold medalists) would probably suffice.

I've heard this from many people and believe it but have not had a chance to chase down references - do you have some handy?

The biggest datasets are from militaries (with the most representative ones from countries with universal conscription). Check out the APA report on intelligence by Niesser et al, this zoo of references on wikipedia, or Linda Gottfredson's website.

Concerning "predict(ing) future success of high school students in research mathematicians by spending a few hours talking": From my experience by private tutoring a wide variety of (university and other) students is that one develops an intuitive sensitivity for that. I wonder if others experience that too as quite unpleaseant: one has the feeling of an inappropriate intrusion into the personality of others, a violation of privacy, and because such intuitive guess comes very quickly, one feels to be very unjust. The obvious cause is that the human mind is less complex than usually estimated.

Thurston said:

Quickness is helpful in mathematics, but it is only one of the qualities which is helpful.

Gowers said:

The most profound contributions to mathematics are often made by tortoises rather than hares.

Gelfand said it in a more funny way:

You have to be fast only to catch fleas.

As I mentioned in Fields Medalists on School Mathematics, school mathematics usually gives a heavily distorted picture of mathematical practice. It's common for bright young people to participate in math competitions, an activity which is closer to that of mathematical practice. Unfortunately, while math competitions may be more representative of mathematical practice than school mathematics, math competitions are themselves greatly misleading. Furthermore, they've become tied to a misleading mythological conception of "genius." I've collected relevant quotations below.

Acknowledgment- I obtained some of these quotations from a collection of mathematician quotations compiled by my colleague Laurens Gunnarsen.In a 2003 interview, Fields Medalist Terence Tao answered the question

by saying

In The Case against the Mathematical Tripos mathematician GH Hardy wrote

In The Map of My Life mathematician Goro Shimura wrote of his experience teaching at a cram school

In his lecture at the 2001 International Mathematics Olympiad, Andrew Wiles gave further description of how math competitions are unrepresentative of mathematical practice

In his Mathematical Education essay, Fields Medalist William Thurston said

In his book Mathematics: A Very Short Introduction, Fields Medalist Timothy Gowers writes

In Does one have to be a genius to do maths? Terence Tao concurs with Gowers and expands on the same theme.

Fields Medalist Alexander Grothendieck describes his own relevant experience in

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