For one thing, I always liked tests in general, regardless of my ability in the subject being tested. This was due to my laziness. In math, as in every other subject, the exams were the place where in an hour or so I could make up for months of not having done much of my homework — a fantastic opportunity! For another thing, I often did well on the math tests. I was not competitive. At the MOP, a fellow student from a high school neighboring mine said that his goal for the last year, his motivation for long hours of hard studying, had been to do better than me.
This explicitly competitive attitude was so foreign and weird to me that I still remember it decades later.
The Contest Problem Book I: Annual High School Mathematics Examination 1950–1960
There are zero careers in math contests, even for the top people. I never lost a math contest.
Nobody loses a math contest. If you just view contests in terms of how far up the ladder you can get, you will be disappointed, for sure.
This puts math contests in pretty much the same category as everything else in life, if you ask me. I enjoyed my math contest success, but success was not a goal for me.
I was interested in those tasty mathematical treats that get collected into contest problems. And anyway, the whole reason I was there in the first place was because of math friends. Our high school had a great math team, very social and working together. Everyone at the school was on the same team. That was where I found people like me. We sent it to him, but it got sent back, because he had died in the meantime.
HCSSiM was a fantastic math place. Did we explore open-ended problems where nobody knew the solution if any? Because we were people who were interested in things like that. I am grateful to the existence of the math team for bringing like-minded souls together, and I am grateful to the math contests for making it easy for math teams to form.
So, what use are these skills now in research? The main use of the problem solving skills, outside as I am now of an explicitly problem solving field, is that when well-defined problems do come up, I can typically immediately identify them as either easily solvable or intractable or on rare occasions, in the oh so tasty thin margin in between. Not an enormous help. What I never learned, in all those years, was how to pose my own problems.
Contest problems of a medium to high level are in fact very difficult to come up with, and that skill is never taught or passed down in any way. When I went to grad school, I specifically aimed to learn the skill of posing my own problems, problems that I would find challenging but solvable. I wish this sort of thing were more actively taught.
It would have been much more helpful. Anyway, math contests are cool, because the problems on them are cool. Just like books by Coxeter are cool, because whatever you find in them will be cool.
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I just like them for what they are. I am glad there are other people like me in this world. I would be sad if math contests disappear. Now I am older.
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My kids went to a math contest. I happen to know that their scores were right in the middle of the distribution. They enjoyed the math contest. They want to do another one.
Math contests kind of suck | mathbabe
They are happy. I am happy. At ARML, we make a real effort to write beautiful problems and put them on the contest, so that many students will get to see them. In my capacity as problem writer, then, I see contests as one way to get interesting mathematics in front of kids. So I agree with the other commentators that there should be more pathways into math. That said, I have a seven-year-old boy who has discovered he loves chess tournaments.
Those of you who have seen me play chess may wonder, like I often do, where he gets this from.
BC Secondary Schools Math Contest
If he wins a trophy, he comes back elated. One last thought. Girls outnumber boys in high school graduations, college enrollments and college graduations.
Cathy, if I told you that a statistically significant proportion of Fields medalists qualified for the IMO in their respective countries and excelled at it, would that convince you that doing well in high school math competitions like IMO is a reasonably strong early predictor of future success as a mathematician? In fact, out of the 4 people awarded Fields medals in , 3 participated in the IMO. That is a logical fallacy. This hardly seems like an interesting fact to me. Whereas the statement is surely true only for sufficiently small values of X and Y.
Consequently, I think that the argument that unfolds below here is mostly tangential to the original post. I would actually agree that there is some weak correlation between math competition success and a future career in mathematics. So why not give them up sooner, rather than later, and start putting all the effort they demand into what really matters? However, the other people you mentioned were not Putnam Fellows but still did well on it.
Fefferman was probably too young to become a Putnam fellow he started college when he was 12 , and Edward Witten majored in History and Linguistics in college, so taking a math exam was probably the last thing on his mind at that time. The Putnam exam should actually be a slightly stronger predictor of future success in mathematics, because doing well on it requires a very deep and profound understanding of the fundamentals of college math, and reflects that a student has attained an unusual level of mathematical maturity for an undergraduate.
I know for a fact that many grad schools are willing to overlook lack of research experience if an undergraduate applicant had a solid performance on the Putnam exam. And that was back in ! Hardy way back in the twenties of the previous century.
Hardy was passionately and publicly committed to the complete abolition of the Tripos exam, precisely because his analysis convinced him that it had undermined generations of English mathematicians, indeed, Hardy insisted that the importance attached to the Tripos by young English mathematicians largely accounted for their negligibility in comparison with their French and German counterparts. While I agree with your general point, I think your last paragraph is a little unfair. Among those who fellowed three or more times, Bjorn Poonen, Ravi Vakil, Noam Elkies, and Kiran Kedlaya are all very prominent researchers in their fields.
Several more recent names on this list are strong mathematicians I have small personal connections to and I expect good things from them in the future. I too hope that the persons you mention will do grand and wonderful things, and I greatly respect their achievements to date.
I think there is agreement that there is room for wonderful alternative enrichment. But most of the people I knew who were successful at the competitions did indeed go on to high level mathematical careers. Angela suggests there is evidence that this correlation holds in general. Also, Qiaochu already made my point by giving examples of prominent mathematicians who were Putnam fellows multiple times.
Well Jordan, I guess I stand corrected then. Angela, I have indeed seen many, many Putnam exam questions. And the simple truth is that any mathematics problem that is guaranteed to be soluble within a half-hour is a contrivance — a puzzle devised by one clever person to entertain another.
Also see W. On the contrary, an entire industry of specialized tutors grew up around the exam, and every successful examinee relied heavily on their assistance. Have you ever studied the career of Arthur Rubin? I have no idea why he lost interest in academia, but I doubt it was due to inability to carry out original mathematics research.
Here is a rough and ready definition of a genius: somebody who can do easily, and at a young age, something that almost nobody else can do except after years of practice, if at all.