Hey guys! I was recently wondering how much raw talent is necessary for success in mathematical olympiads on the IMO/Putnam level, other than just plain hard work. I understand that hard work is an absolute necessity for success, but I can’t seem to acquire the logical thinking and problem solving skills for these competitions. What are some strategies I can use to develop these essential skills?
To reach the level of IMO or Putnam, raw talent is absolutely critical. No amount of hard work can compensate for the lack of talent in that area. On the other hand, hard work is also necessary to compete at that level, unless you’re one of the rare true geniuses.
Probably more than any other endeavor, mathematics is all about intrinsic talent. Mathematicians are born, not made.
In the high school and college competition works, you can’t get any higher than IMO team member for one of the powerhouse countries, or any higher than top 15 in the Putnam. To get there, you quite literally need to be born to do it.
I do think with at least some modest talent and an immense work ethic, it is possible to get to the USAMO level, so there is hope even for mere mortals.
An enormous amount of raw talent is needed to be successful. I firmly believe that intrinsic talent is much more important (and the benefits from just working harder than others are correspondingly lower) in math than in any other subject. Techniques can be taught but figuring out how to apply them is not something anyone can learn. It’s hard to describe but the best mathematicians have a talent for visualizing and manipulating a problem in their heads to figure out the best way to tackle it.
I did math at a high level in college (including a PhD), and still enjoy solving these sorts of problems for fun 30 years later. But I was easily outclassed by the truly exceptional mathematicians amongst my classmates and teachers (I was taught by several IMO medalists and even a couple of Fields Medal winners).
Math competitions require a particular type of raw talent. My son was strong enough that he worked with some of the country’s best, but there was no way he was going to get to their level, no matter how hard he tried. In sports terms, the gulf was as large as between LeBron James and a player that barely made the NBA.
There is an eleven year old taking late undergrad math classes as a day student right now at one of HYPS. Right at the top of the class. I suspect some on this board know the kid.
My kid has a fair amount of talent, at least we thought they did until encountering the best at math camps. An eleven year old turned away from one of the camps upon arrival because he had already absorbed much of Real Analysis (using baby Rudin), another 14 year old kid who calculated probabilities of multiple poker hands in real time all the while talking and laughing, another who took a week off to attend the IMO for their home country.
I suspect that most people believe that preparation makes a huge difference because so few have done serious mathematics (that includes practically all elementary school and most high school teachers by the way). When you see what some kids can do at such a young age… it has to be innate.
Coming back to this a lot later, but I watched The Queen’s Gambit on Netflix this week and I think that gave a great representation of how good chess players and mathematicians think - dreaming about manipulating chess pieces on the ceiling is very similar to how it works for many mathematicians. I certainly did the best work in my PhD lying in bed (or the bath) half awake and half dreaming.
A friend who is now a famous math professor told me when I was an undergraduate that you needed two hours of inspiration in three years to produce a great math PhD thesis. I think that was pretty accurate (I never got to two hours though).
Haha. I can imagine. It is always those two critical hours of inspiration that can prove to be elusive.
The Queen’s Gambit is a great series, and I thoroughly enjoyed watching the fictional story of how a girl did so well in chess.
Talking about a real life example, UK sent a team of six kids to IMO this year : 5 boys and 1 girl. It is probably the fifth or sixth girl to be selected in UK IMO teams in the last 25 years. Having said that, not a single boy in this year’s UK IMO team got a gold medal while the girl got a gold!
Interestingly, IMO this year awarded 49 golds, and there is only one girl in the list of gold recipients this year - globally!
Mostly talent. But if you have a kid who has access to very good coaches who is very talented vs. a stellar mathematician, the talented one can often do well short term. At the highest levels, the kids are pure talent.
If anyone has read about the three female Hungarian chess masters ( I don’t know their names), one would question if it was talent or early learning. I don’t know enough about chess, but since it’s repetitive, it may be talent plus early learning. I read something years ago, and one of them spoke about how she was able to recall moves in her head ( visualize) the patterns. Some math people have this also.
Many of the top math kids have also had lots of exposure well beyond what is advanced. Without that coaching, it’s really hard to advance. Great thing is, kids can see who is who at competitions and camps. Also, there are some kids with raw talent who want to do other things. So interest plays a role also.
@Tamarix I have often stressed about the very few number of girls in top competitions. There are a number of factors. Boys are often pushed in that direction ( and coached). Girls at the early stages can be turned off by some of the attitudes ( particularly in the early ages during early middle school ]). But the numbers are getting better. And there are specific contests for top girls. The MIT Math Prize for Girls, for example. Still, it’s not even close to equal. Neither is the representation of North America vs. the rest of the world. That is a factor also as in many nations very young girls don’t have the same access to education beyond primary school. Hopefully, more women will go into math.
You have to have math talent to compete. However, there are another few talents that are not related to math that are required, including the ability to solve problems quickly. There are many kids who are just as talented or more so, but simply take a bit longer, and so cannot do so well in these types of competitions.
There is also an issue with the fact that having talent is not enough - you need to be trained in how to do well at these competitions. So a very talented kid who has not trained will usually lose to a kid who is somewhat less talented but has trained. So kids from low income school districts, district who do not get the opportunities to compete or kids whose parents cannot afford the cost of hours and hours of training will be at a disadvantage.
Basically, all kids competing are highly talented, but not all of the most highly talented kids have the opportunity to compete, and the kids who are the most talented in math, are, often not the kids who are the most talented in math.
Another issue is that mathematics, especially beyond undergraduate into graduate school, is not about solving existing problems which have known solutions. It is about finding problems that are important and THEN solving them, or, at very least, finding solutions to existing problems which have not yet been solved. This is not really part of the math Olympiads.
Math Olympiads are likely a good indication of how well a student will do as an undergraduate in math or engineering. It will not be a good indication of how well a student will do in grad school or research. Focusing on math Olympiads as the epitome of math skill is producing generations of Olympiad winners who get As in undergrad, but not ones who are future mathematicians who will make new and important discoveries in math.
In the past, Olympiads were where math geeks could compete in ways that could be measured. Now it is being used as an indication of whether a student is “the best” at math. In the past, math geeks spent their time doing math and then went to the Olympiads for bragging right. Now kids spend most of their time preparing for the next competition, and spend a lot less time simply engaging in math.
I do feel that the winners of the top math Olympiads of the past few years will not have the same level of achievements in math as did and yet will the winners of the 1980s and 1990s.
PS. by “somewhat less talented”, I’m still talking about very talented kids.
Interesting observation. Definitely correlates with my experience in the 1980s that we did the initial selection tests cold with zero prep up until the shortlisting for the national team. Back then I knew plenty of people with IMO medals who were absolutely top mathematicians, all the way up to Fields Medal winners.
What the “hard work” can sometimes do is unlock those native talents.
Not sure why OP is asking, whether he/she is drawn to these competitions or just feels the need to add them to the resume. But if math is fun, by all means continue testing yourself at whatever level. Enjoy it.
Math competitions at the Olympiad-level aren’t really about speed (speed is only important in middle school level competitions like MathCount), even though these competitions have to be timed (so they’re fair to all contestants). In IMO, for example, there’re only 6 problems with 9 hours to solve them. If you can’t solve a problem in an hour or two, it’s highly unlikely that you’ll be able to solve it with an extra hour, or two, or three, or even days.
There’re about a dozen IMO medalists who eventually won Field Medals, but certainly not all Field Medalists had won IMO medals or even participated in math competitions in their youth.
Participate in math competitions if you really love math and see its elegance and beauty. Don’t do it solely for the sake of college admissions. A few colleges do ask for your AMC and/or AIME scores, but they’re only used to ascertain your competency and skills in math (unless, of course, you’re one of the few IMO medalists). There’re a number of other ways to demonstrate that competency and skills without participation in these competitions.