As a former "successful" mathlete (never did IMO or Putnam, but consistently made the top five in state competitions), I agree that competitions won't help you develop mathematical maturity, but it is interesting how how they are viewed in the wider world. It's been a number of years since my math tournament days, but people are always very impressed if I mention that I won math competitions in middle and high school. It is odd to me, because I don't really care about my math medals anymore and I've since accomplished things that I value a lot more, but there you have it.<p>Also, even though competitions won't help you develop as a mathematician, I still think it was a good experience for me to get out of school for a day and hang out with a bunch of other math nerds. That part of it was a lot more valuable than the competition itself.
I'm from that world of math Olympics. Never reached IMO, only top places on regional competitions (math, physics, programming), and know a lot of people who been there and who never participated. Some won the medals, graduated with MSc from universities and gave up with science. Some were not so good in competitions, but became very smart scientists and great math teachers. There's no rule, and I don't think this system is just a selection of the best, discouraging children who did not succeed from choosing math.<p>It's just much easier and more natural to see the beauty of mathematics while spending enough time on learning, solving problems and engaging in competitions. Oh, yes, I'm still seeing it despite years in MIPT with some real math. There's a lot of fun in it. For example, we had "mathematical battles", when two teams had to present and defend their solutions and get score points from jury. It's also a very special and friendly environment, where you can meet people, connect to universities and build social network that will serve you for the whole of your life. I still have a lot of friends from summer math schools which I attended in early 90s. For many it's also a social lift, egalitarian by it's nature, where distinction between rich and poor is almost invisible (not like on the street or a schoolyard), it allows many children from small towns across the country to enter top universities and build successful career, not necessarily in science.<p>I will never blame this system for presenting math "in wrong way". It doesn't have to show the world of grown-ups. And, by the way, we never heard the word "genius" (except applied to Pushkin or Einstein).
Like a few commenters on this thread, I participated in a lot of math contests in high school. Never made the IMO but placed at/near the top in regional and statewide competitions.<p>On the one hand, my experience mirrors some of what the article talks about: I learned very quickly that the things professional mathematicians work on are very different from math contest problems. (I went to college intending to major in math, but switched to CS as soon as I took a semester of abstract algebra.)<p>On the other hand, the article seems to imply that many great mathematicians look down on math competitions for not giving an accurate portrayal of math as a career path. I don't see why that is an issue. My high school was a math magnet school, and 100s of students participated in monthly contests like California Math League. Almost every participant that I talked to in those days did math contests because they were fun, or because they were an interesting challenge. I never met anyone who said "I want to be a mathematician, and contests are clearly the first step on that road."<p>For me, math contests are like high school sports or drama or anything else. They appeal to certain subgroups of kids, they're fun and hopefully educational/useful in some way, and they don't have to be more than that.
I was pretty good at math competitions (2x putnam fellow) but never that great at being a mathematician. But I still think math competitions are great experience. Winning at any sort of competition teaches you how to be persistent, how to work hard, how to recover from setbacks mentally, how to maintain focus for a long period of time, and how to gear up for critical moments where you need to perform.<p>For example, when I first went to the math olympiad summer program, I had trouble focusing on a single math problem that I had no clue how to solve for three hours straight. It's hard! The training program basically forces you to do that over and over, so I ended up learning a lot of how to focus for large chunks of time and do useful things to attack a problem that I didn't initially know how to solve.<p>I went into computer stuff instead of math stuff after college, and there's a lot of stuff I never used again. Algebraic topology, all the geometry theorems they don't teach you in high school, you name it. But the ability to work really hard on a single technical problem until you nail it, that's been constantly useful. Especially in startups.
George Pólya claimed that the British emphasis on puzzle-solving had set British mathematics back a hundred years. He and Hardy tried to get rid of Cambridge's emphasis on the Tripos exam and the whole "Senior Wrangler" thing.[1] They didn't entirely succeed.<p>[1] <a href="https://en.wikipedia.org/wiki/Senior_Wrangler_(University_of_Cambridge)" rel="nofollow">https://en.wikipedia.org/wiki/Senior_Wrangler_(University_of...</a>
When I got to Harvard, probably the best Putnam/puzzle types of solvers there (among the students) were Don Coppersmith and Angelos Tsiromokos. Don went on to do very important work in cryptology. Angelos went on to leave mathematics; his next gig was as a translator for the common market. (He was probably better in word games/puzzles -- Scrabble, crosswords, and so on -- in English than I was, even though it was his third language.)<p>Ofer Gabber and Ron (Ran) donagi also did very well on a semi-formal Putnam, and did so at very young ages. They went on to decent math careers.<p>I also took the Putnam at very young ages, but never cracked the top 100. I went on to leave mathematics.<p>Nat Kuhn was perhaps the best of the undergrads then. He went on to be a psychiatrist.<p>Andy Gleason was perhaps the best at that kind of thing among the faculty. Wonderfully nice guy, and my de jure thesis advisor, which was a bit awkward because he never got a PhD himself and didn't quite understand my stresses; I didn't realize the no-PhD part until after the fact, when I saw his resume in connection with his election as president of the American Mathematical Society.
Nowadays the word 'coach' usually applies to athletics, but it dates to the 1830s, when Cambridge University started awarding math degrees by competitive examination. A coach was someone who gave you a straight, smooth ride to your degree, just like a horse-drawn coach on one of the new paved roads that began appearing in England around that time. So coaching was hip.<p>The high scorers on the exam were a Who's Who of British science in the 1800s. In 1854, for example, the second highest scorer was James Clerk Maxwell, the greatest physicist of the century, who gave humankind its first look at a fundamental law of nature. The guy who beat Maxwell became a coach and spent the rest of his life teaching people how to do well on the exam.
Keep in mind you can get Fields medal only if you are under 40 years old. That's more likely when going into academia maths straight away, without enjoying relatively lucrative industry jobs like most of IMO contestants I know do.
We also need to hear from an important segment of the math population: those who burned out or dropped out for reasons related to math perceptions engendered by the math-competition culture. We all know people who did great at math or science competitions in high school but just disappeared from the scene after that. One may say that there are other underlying causes that lead them to not live up to some hypothetical promises, but I strongly feel that success and failure at math competitions can be a cause in itself. A lot of space is dedicated to how math olympiad triple-gold medalists went on to become great mathematicians. We also hear about those like Grothendieck and Hardy who weren't big in the competition circuit.<p>But missing are the stories of those who didn't make it big in spite of great competition performance, and those who fell out of math because of failing at math competitions.<p>In India, for example, competition math is <i>everything</i> at the high school level. This is because competitive exams like the famed IIT JEE, etc. are essentially variations on the competitive math theme. A few serious math enthusiasts do take up broader math-specific exams for math institutes, but those numbers are minuscule. The worst affected in my experience, are the talented and the enthusiastic who were discouraged and/or dropped out altogether because of failing at optimizing their skills and learning for competitions and similar exams.
This seems like a more general portrayal of how innacurate tests demonstrate domain knowledge. It is true for Math Olympiads, but also true for a wide range of subjects. Nonetheless, this is stil relevant to provide a <i>hint</i> of what that person might know.
I participated in my state's math competition, but never made it to the finals. Yet it didn't discourage me from attending college and majoring in math.<p>I also participated in the music competition, called "solo and ensemble festival." Like the math competitions, music competitions are an artificial environment -- one student in front of a judge, rarely any audience. But in some sense they are "real world" because they mimic the auditions that are very much a real part of a music career, e.g., for getting music scholarships and entry into most orchestras. I never got that far.
Qualitatively, it's the same problem that a lot of people have in grad school. Doing homework from a textbook isn't the same as the uncertainty of research.
pardon the shitpost, but that is a compilation of one of the most profound and useful quotes i've ever seen. the difference between superficial achievement and real contribution is profound, and most of our systems are designed to reward and reinforce the first at the expense of the latter.<p>"They’ve done all things, often beautiful things in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era."