How smart were mathematicians in high school?

[Site]

Are there examples of modern, influential mathematicians who did not show unusual mathematical talent before college? Because today it seems like the field is pretty much closed off to college freshmen first encountering abstract mathematics, no matter how much fascination and interest they develop, because there are so many kids who have already put in thousands of hours in high school (like IMO medalists).

A sort of related question: to what extent does the 10,000 hour rule apply to the field of research math?

 

[Evo]

A sort of related question: to what extent does the 10,000 hour rule apply to the field of research math?

It's not a rule it's some failed journalist's way to sell a book. There are many books and studies that refute it, and it really applies to mastering physical/musical skills.

 

[Floid]

The "10,000 hour rule" is part real and part hype.

The reason it is part real:
If someone spends 10,000 hours doing something the average person will be pretty good at it. If they happen to also be naturally inclined in that area they will be phenomenal at it. If they are naturally gifted in that area they might be one of the best in the world at it.

Why it is some hype:
The rule tends to apply more to skill based activities like art, music, anything hand eye coordination related, some sports (golf for example)... activities that heavily rely on muscle memory. Your ability to perform at these activities is primarily dictated by how good your muscle memory is and there is no substitute for practice in obtaining muscle memory.

As you gravitate to activities that are either more pure mental (like math/physics) or pure physical (powerlifting, Olympic weightlifting, sprinting, etc) the rule starts to fall off. Practice is still important but your natural ability at those areas plays a bigger role.

If you aren't genetically gifted you can lift all the weights you want and you might get strong but you won't have a shot at even qualifying for the Olympics for weightlifting or sprinting much less winning. The same is true of the mental activities. If you spend 10,000 hours studying a subject you probably will have a pretty good knowledge of it but unless you happened to be blessed genetically you probably aren't going to be the Newton or Einstein.A little more about your question about when ability is shown. I don't know enough about modern mathematicians to be able to answer your question but probably not because of what I stated above. If a person is a well known mathematician they are probably naturally gifted at math which would have shown from an early age. This seems true in pretty much every field.

 

[SteamKing]

If these guys were really smart, they skipped high school altogether.

But, when the boundaries of knowledge are being pushed back ever so incrementally over time, it becomes harder and harder for an individual to make a significant or original contribution to the field, be it math or science, without having studied and acquired what has been discovered already. If you want a college freshman to make a significant contribution to math, he or she should probably have studied calculus in kindergarten.

 

[Permanence]

I think it depends on how we define 'smart'. I think that all of the college freshmen that walk in thinking they're masters of calculus because of AP courses are mistaken. You weren't describing those kids, but I still think they're worth mentioning. Those kids who were pushed into IMO are a weird byproduct of genius and parental-discipline. In the long run I don't think many of those kids are any significantly more prepared than a hard-working freshmen to make a contribution to a scientific field. What I'm getting at is prior experiences and formal education don't necessarily have to be everything.

 

[Adyssa]

I saw these quotes from Helen Keller last week, and I think they are appropriate here:

I long to accomplish a great and noble task, but it is my chief duty to accomplish humble tasks as though they were great and noble"

"The world is moved along, not only by the mighty shoves of its heroes, but also by the aggregate of the tiny pushes of each honest worker."

Just to illustrate that there's plenty going on in the world, and mountains of problems to solve, and just by studying a discipline and joining a profession, you can make a contribution that means something. You don't have to win the Fields Medal or the Nobel Prize to validate that.

 

[Site]

Very nice quotes, Adyssa! I'm going to put the first up on my wall. Thanks for the replies everyone!

 

[Tim92G]

http://www.ams.org/notices/201304/rnoti-p486.pdf

The girl who was the recent Morgan Prize Winner from MIT. She says that she didn't develop interest in advanced math until college. Apparently she didn't participate in any kind of math competitions while in high school in China.

To the OP: excelling in math competitions has little correlation with excelling in mathematics research.

There are many brilliant TA grad students I've met who have never done the USAMO or AIME in high school, mostly because they were not interested in pursuing a math major at that time, but have won prestigious REUs, grants, and have even been published in the American Mathematical Society. So no, it's certainly not necessary to be extremely precocious in math prior to college.