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Great Mathematicians on Math Competitions and "Genius" (2010)

191 points by jimsojim 10y ago

abetusk 10y ago
For me, this applies equally to programming competitions and white boarding algorithms in interviews.
- barrkel 10y ago
  I've seen a correlation in working mode between pairing on a competition-style programming problem (to evaluate a job candidate) and pairing in real work. I'm not looking for leaps of insight though (I explain the insight required), and we're both in front of the IDE and can search the web to clarify simple questions. It's more communicating a problem and the outline of a solution, and seeing if someone is able to understand what you say and is fluent in turning ideas into code in their chosen language. I personally despise gotcha questions that rely on you either having seen the problem before, or getting lucky enough to spot the insight in a pressure situation.
- gautamdivgi 10y ago
  I think some folks overdo the white boarding. But I believe it is needed - may be one or two problems on the whiteboard with the rest of the interview focusing on design & software engineering (metrics, resiliency, etc.). I've seen folks who have a lot of coding skill on their resume fumble simple white board problems. I have fumbled simple white board problems when I have also interviewed (It was for a s/w engg position but I had spent the past several years in architecture and away from any real code - so it was expected). The point is white boarding is ok if you have a well defined problem solvable in 45 mins and if it is just geared to assess your familiarity with code. I don't think its a reasonable expectation to come up with new approximation algorithms for NP-complete problems and solve+prove them on a white board in 45 mins.
  - onion2k 10y ago
    I've seen folks who have a lot of coding skill on their resume fumble simple white board problems. Solving a coding problem on a whiteboard tests your ability to solve coding problems on a whiteboard. That's a bias. It makes people who get nervous standing up and being the centre of attention less likely to pass the test. If coding on a whiteboard is a part of the job then fair enough, but if it isn't then you're introducing something to the interview that filters people out based on something other than their ability to do the job - and that means you're not necessarily recruiting the best person. I believe that's a good reason not to use whiteboard tests very often.
    - skybrian 10y ago
      Finding a whiteboard and brainstorming about how to solve a problem is absolutely part of the job. Unfortunately it's hard to find problems that can be explained to anyone with a reasonable programming background and solved in 30 minutes. So anything you do under those constraints is going to be artificial.
      - JoeAltmaier 10y ago
        And if you overthink it (how can you not? no idea what they're looking for) you appear to clutch or ask too many questions. No shared context means a very artificial exchange.
      - varjag 10y ago
        > Finding a whiteboard and brainstorming about how to solve a problem is absolutely part of the job. But let's face it, this skill is trivial to an otherwise intelligent person, and it's not the reason whiteboard coding is done at the interviews. It is to assess one's problem solving or even specific coding skills. Unfortunately, in a nearly QM way, observation here affects the outcome. I did partake in CS competitions at regional level and to me they are less stressful than whiteboard tests. There you just have a console or a sheet of paper and a few hours to hash it over. No 3 pairs of eyes staring at your back. Guess it's the same for many others: the thing that turns reading a figurative newspaper chess column into chessboxing tournament. One might be good at chess and OK in boxing, but not necessarily at the same time. (and no, unfortunately I don't see a good way to fix this)
- kamaal 10y ago
  This explains why: From the article: From Terence Tao: professional mathematics is may be quite different from the reality. In elementary school I had the vague idea that professional mathematicians spent their time computing digits of pi, for instance, or perhaps devising and then solving Math Olympiad style problems. In real life its the same. You don't cook up interview coding problems and solve them whole day. You have real world work to do and often that requires a degree of productivity, not knowledge. This is even more so true given how cheap and easy access to knowledge has become because of the web. From GH Hardy: it is useless to ask a youth of twenty-two to perform original research under examination conditions, the examination necessarily degenerates into a kind of game, and instruction for it into initiation into a series of stunts and tricks. Notice how closely this matches with interviews which mandate people to demonstrate expertise in trivia. Or quickly state the Big-Oh complexity of some sorting algorithm. From Andrew Wiles: Real mathematical theorems will require the same stamina whether you measure the effort in months or in years [...] Almost any real measurement of algorithm expertise is in seeing how good a person in coming up with a new algorithm for a novel problems. What exactly is your knowledge of 100 sorting algorithms worth, when it can be searched for in a google search which takes a few milliseconds. Interview Algorithm guru's to me are no better than those smart elecs who used to show up in school having memorized multiplication tables and then demonstrate that as some kind of mathematical ability.
- rafaquintanilha 10y ago
  For such things like coding an optimal algorithm from scratch this might be true. But there are interview questions which have a more practical appealing, and this definitely does not apply to math Olympiads.
- kafkaesq 10y ago
  Love / hatred of the whiteboard process being of course a perennial topic here, there is one major distinction between Math/CS olympiads and the typical industry whiteboarding session: with the Math/CS olympiads, you can count on a reasonable degree of professionalism (in terms of forethought and judgement, and overall solidness of execution) -- not to mention basic common sense -- behind both the curation of the actual problem sets, and in the design of the test environments. These people know what they're doing, and their process is mature and generally well accepted. And the actual problem solving environment is designed for maximum efficiency and fairness. In the tech industry, however -- here and there you'll find companies that know what they're doing: they actually put a lot of though into picking reasonable problems to solve, and present the candidates with reasonable conditions for doing so. They're clear in stating both the problem and what they expect; and the interviewers are reasonably personable, and have great communication skills. But quite often, it's a total shit show: problems are often poorly stated (and sometimes ridiculously complex); combined, importantly, with a poor or completely absent statement of what is really expected from the candidate (As in -- do they want a perfect working solution, on running code? Or does it suffice to just outline the general idea, perhaps with pseudocode? Quite often this is never stated up front); along with gratuitously taxing and sometimes downright annoying conditions in which to tackle this allegedly crucially important problem you're asked to solve (among my favorites being: whiteboards with barely usable markers / erasers; or their electronic equivalent -- Google Docs, or other ridiculously unusable coding "platforms"; voice-only sessions of nearly any kind, but especially those where the interviewer clearly has limited communication skills for one reason or another; and then of course sessions where the interviewer doesn't know the language you're coding in very well, and you have to constantly pause to explain the basic facets of said language, along with the solution itself).
lintiness 10y ago
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. "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."
- wrsh07 10y ago
  But it's very hard to design a feedback loop with a short enough cycle to properly reward the latter. It makes me think of the line about raising children, that it's better to say, "I recognize that you worked really hard on that, it looks wonderful!" than "Good job! You're so smart!" [1] because one captures the reason why they did a good job. By calling that out, you can perhaps reinforce behavior with a longer view. [1]: http://www.theatlantic.com/education/archive/2015/06/the-s-word/397205/ http://www.theatlantic.com/education/archive/2015/06/the-s-w...
  - empath75 10y ago
    Yeah, my parents and all my teachers told me I was 'gifted' from 2nd grade, and I really feel like it held me back, overall. Yes, I picked stuff up quickly, but I was also lazy as hell, and given no real incentive to learn how to not be lazy until it was too late to turn around my disastrous grades. I have a son now, and I'm going to try to avoid calling him smart or gifted. Or at least not telling him that he's smarter than the other kids.
    - delazeur 10y ago
      I had a similar experience: that kind of reinforcement encouraged me to try to do the least work possible to get the same results as others in order to prove how gifted I was, instead of working hard to go above and beyond. It was a rude awakening when I got to the point in life when I wasn't competing against my peers to complete set tasks, but rather competing against them to provide the most valuable contributions to a research group or company. However, I also believe that this kind of explanation can be harmful because it puts the blame for my laziness on others. Even though the research supports the idea that this effect occurred, ultimately I got past it by focusing on my own agency.
sesm 10y ago
Note, however, that Grigori Perelman was very good at mathematical olympiads.
- papapra 10y ago
  And Terrence Tao who is quated was also extremely good at olympiads. As I see it, the olympiads are a good cost-effective way of identifying talented kids, they are in a way just IQ tests.
  - kkylin 10y ago
    I think the point being made is that the converse need not be true: kids who are not good at these sports need not feel discouraged from pursuing mathematics.
    - auntienomen 10y ago
      Yep. Success in math contests is correlated with success in producing mathematical research/getting tenure/measure what you will. But if you sample math professors, you won't find that most of them were problem solving champions. (A large minority perhaps, and probably more in number theory.) The common factor is more likely that they really like doing mathematics, and have the skills needed to suceed in secondary aspects of the job.
    - tamana 10y ago
      But what does it mean when the people preaching this claim are all Olympiad winners? The one math genius I know who despised Olympiads, ended up leaving academia over a famous but wrong proof.
      - kkylin 10y ago
        I know plenty of very good mathematicians who did not participate seriously in this kind of thing. (Disclosure: I work as a mathematician at a research university.) I'm not sure why the only ones quoted here are mainly ex-winners. Indeed, while these competitions may have the positive effect of putting like minds together, it's possible that they have the negative effect of discouraging those w/o the aptitude for this particular kind of competitive sport (which is what it is), or who do not have access to the kind of coaching and practice that successful competitors often have.
paulpauper 10y ago
Success at mathematics requires staring at it until you can understand it, however long that takes
- kafkaesq 10y ago
  Well, no -- it's not enough to just stare at the problem / thing. What you have to do, effectively, is become at one with its true nature. Which in general is much more difficult than simply starting at it.
  - jonnybgood 10y ago
    > become at one with its true nature That's very vague.
    - kafkaesq 10y ago
      It is. Which is why it's so difficult.
delazeur 10y ago
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. 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.
- bisby 10y ago
  In high school, I participated in "WYSE - Academic Challenge" (Worlds Youth in Science/Engineering) which was test taking competitions for a variety of topics. You'd take 2 tests out of 7 subjects, and there were individual test prizes, and combined school/team prizes. I originally participated to hang out with other nerds, but wound up getting a few state competition medals in the computer science test. The multiple topic thing really helped cement my love for computer science/engineering. That was the most valuable part for me. I dont even know where my medals are even at anymore.
- auganov 10y ago
  I was running a BaaS startup for a bit. While researching our competition-to-be I remember finding out that Parse's Kevin Lacker is a 2x Putnam winner. Couldn't help but have instant respect for him and the whole company. Personally as a kid I was often "sent" to these competitions but never bothered to prepare for them at all. I stupidly assumed it was a pure IQ play. Now I regret not taking it seriously. Makes me have even more respect for people that do.
  - delazeur 10y ago
    > Personally as a kid I was often "sent" to these competitions but never bothered to prepare for them at all. I stupidly assumed it was a pure IQ play. I think this is the biggest disconnect between perception and reality of intellectual competitions (debate, math, chess, whatever). In reality, they require just as much practice to succeed as any other sport.
rafaquintanilha 10y ago
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 hint of what that person might know.
ivan_gammel 10y ago
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. 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. 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).
CurtMonash 10y ago
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.) 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. I also took the Putnam at very young ages, but never cracked the top 100. I went on to leave mathematics. Nat Kuhn was perhaps the best of the undergrads then. He went on to be a psychiatrist. 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.
- tamana 10y ago
  Elder Harvard math professors who have PhDs don't really empathize either, because they are in the very high end of the talent spectrum, and they came up in the time when massive breakthroughs were told for picking.
shas3 10y ago
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. 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. In India, for example, competition math is everything 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.
Animats 10y ago
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. [1] https://en.wikipedia.org/wiki/Senior_Wrangler_(University_of_Cambridge) https://en.wikipedia.org/wiki/Senior_Wrangler_(University_of...
zasz 10y ago
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.
imocuagau 10y ago
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.
mnemonicsloth 10y ago
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. 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.
lpolovets 10y ago
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. 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.) 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." 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.
- ianai 10y ago
  There's definitely an argument to be made that disgruntled, great mathematicians act as a barrier to entry. Being exclusionary hardly attracts anybody to an already difficult field. Besides, who's to say that whatever they describe as "the one prescribed path" must be what works for everybody? I think the will and drive to study mathematics is less cookie cutter than that.
lacker 10y ago
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. 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. 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.
- lpolovets 10y ago
  100% agree that learning focus and persistence was a very valuable result of doing math competitions. Completely random: If you're who I think you are, I still remember seeing your name on the list of perfect AHSME scores in 1998ish. I think we met briefly at an ACM competition in '03 (we played Mafia for a while in a big group, and were briefly introduced by Po-Shen Loh who was one of my ACM teammates.)
  - lacker 10y ago
    Yeah that sounds like me! ;-) Although by '03 I was in grad school; ACM stuff was probably '01 or '02.
    - lpolovets 10y ago
      You're right! It was '02, in Honolulu.
analog31 10y ago
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. 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.

191 points by jimsojim 10y ago

abetusk 10y ago

For me, this applies equally to programming competitions and white boarding algorithms in interviews.

barrkel 10y ago
I've seen a correlation in working mode between pairing on a competition-style programming problem (to evaluate a job candidate) and pairing in real work. I'm not looking for leaps of insight though (I explain the insight required), and we're both in front of the IDE and can search the web to clarify simple questions. It's more communicating a problem and the outline of a solution, and seeing if someone is able to understand what you say and is fluent in turning ideas into code in their chosen language. I personally despise gotcha questions that rely on you either having seen the problem before, or getting lucky enough to spot the insight in a pressure situation.
gautamdivgi 10y ago
I think some folks overdo the white boarding. But I believe it is needed - may be one or two problems on the whiteboard with the rest of the interview focusing on design & software engineering (metrics, resiliency, etc.). I've seen folks who have a lot of coding skill on their resume fumble simple white board problems. I have fumbled simple white board problems when I have also interviewed (It was for a s/w engg position but I had spent the past several years in architecture and away from any real code - so it was expected). The point is white boarding is ok if you have a well defined problem solvable in 45 mins and if it is just geared to assess your familiarity with code. I don't think its a reasonable expectation to come up with new approximation algorithms for NP-complete problems and solve+prove them on a white board in 45 mins.
- onion2k 10y ago
  I've seen folks who have a lot of coding skill on their resume fumble simple white board problems. Solving a coding problem on a whiteboard tests your ability to solve coding problems on a whiteboard. That's a bias. It makes people who get nervous standing up and being the centre of attention less likely to pass the test. If coding on a whiteboard is a part of the job then fair enough, but if it isn't then you're introducing something to the interview that filters people out based on something other than their ability to do the job - and that means you're not necessarily recruiting the best person. I believe that's a good reason not to use whiteboard tests very often.
  - skybrian 10y ago
    Finding a whiteboard and brainstorming about how to solve a problem is absolutely part of the job. Unfortunately it's hard to find problems that can be explained to anyone with a reasonable programming background and solved in 30 minutes. So anything you do under those constraints is going to be artificial.
    - JoeAltmaier 10y ago
      And if you overthink it (how can you not? no idea what they're looking for) you appear to clutch or ask too many questions. No shared context means a very artificial exchange.
    - varjag 10y ago
      > Finding a whiteboard and brainstorming about how to solve a problem is absolutely part of the job. But let's face it, this skill is trivial to an otherwise intelligent person, and it's not the reason whiteboard coding is done at the interviews. It is to assess one's problem solving or even specific coding skills. Unfortunately, in a nearly QM way, observation here affects the outcome. I did partake in CS competitions at regional level and to me they are less stressful than whiteboard tests. There you just have a console or a sheet of paper and a few hours to hash it over. No 3 pairs of eyes staring at your back. Guess it's the same for many others: the thing that turns reading a figurative newspaper chess column into chessboxing tournament. One might be good at chess and OK in boxing, but not necessarily at the same time. (and no, unfortunately I don't see a good way to fix this)
kamaal 10y ago
This explains why: From the article: From Terence Tao: professional mathematics is may be quite different from the reality. In elementary school I had the vague idea that professional mathematicians spent their time computing digits of pi, for instance, or perhaps devising and then solving Math Olympiad style problems. In real life its the same. You don't cook up interview coding problems and solve them whole day. You have real world work to do and often that requires a degree of productivity, not knowledge. This is even more so true given how cheap and easy access to knowledge has become because of the web. From GH Hardy: it is useless to ask a youth of twenty-two to perform original research under examination conditions, the examination necessarily degenerates into a kind of game, and instruction for it into initiation into a series of stunts and tricks. Notice how closely this matches with interviews which mandate people to demonstrate expertise in trivia. Or quickly state the Big-Oh complexity of some sorting algorithm. From Andrew Wiles: Real mathematical theorems will require the same stamina whether you measure the effort in months or in years [...] Almost any real measurement of algorithm expertise is in seeing how good a person in coming up with a new algorithm for a novel problems. What exactly is your knowledge of 100 sorting algorithms worth, when it can be searched for in a google search which takes a few milliseconds. Interview Algorithm guru's to me are no better than those smart elecs who used to show up in school having memorized multiplication tables and then demonstrate that as some kind of mathematical ability.
rafaquintanilha 10y ago
For such things like coding an optimal algorithm from scratch this might be true. But there are interview questions which have a more practical appealing, and this definitely does not apply to math Olympiads.
kafkaesq 10y ago
Love / hatred of the whiteboard process being of course a perennial topic here, there is one major distinction between Math/CS olympiads and the typical industry whiteboarding session: with the Math/CS olympiads, you can count on a reasonable degree of professionalism (in terms of forethought and judgement, and overall solidness of execution) -- not to mention basic common sense -- behind both the curation of the actual problem sets, and in the design of the test environments. These people know what they're doing, and their process is mature and generally well accepted. And the actual problem solving environment is designed for maximum efficiency and fairness. In the tech industry, however -- here and there you'll find companies that know what they're doing: they actually put a lot of though into picking reasonable problems to solve, and present the candidates with reasonable conditions for doing so. They're clear in stating both the problem and what they expect; and the interviewers are reasonably personable, and have great communication skills. But quite often, it's a total shit show: problems are often poorly stated (and sometimes ridiculously complex); combined, importantly, with a poor or completely absent statement of what is really expected from the candidate (As in -- do they want a perfect working solution, on running code? Or does it suffice to just outline the general idea, perhaps with pseudocode? Quite often this is never stated up front); along with gratuitously taxing and sometimes downright annoying conditions in which to tackle this allegedly crucially important problem you're asked to solve (among my favorites being: whiteboards with barely usable markers / erasers; or their electronic equivalent -- Google Docs, or other ridiculously unusable coding "platforms"; voice-only sessions of nearly any kind, but especially those where the interviewer clearly has limited communication skills for one reason or another; and then of course sessions where the interviewer doesn't know the language you're coding in very well, and you have to constantly pause to explain the basic facets of said language, along with the solution itself).

lintiness 10y ago

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. "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."

wrsh07 10y ago
But it's very hard to design a feedback loop with a short enough cycle to properly reward the latter. It makes me think of the line about raising children, that it's better to say, "I recognize that you worked really hard on that, it looks wonderful!" than "Good job! You're so smart!" [1] because one captures the reason why they did a good job. By calling that out, you can perhaps reinforce behavior with a longer view. [1]: http://www.theatlantic.com/education/archive/2015/06/the-s-word/397205/ http://www.theatlantic.com/education/archive/2015/06/the-s-w...
- empath75 10y ago
  Yeah, my parents and all my teachers told me I was 'gifted' from 2nd grade, and I really feel like it held me back, overall. Yes, I picked stuff up quickly, but I was also lazy as hell, and given no real incentive to learn how to not be lazy until it was too late to turn around my disastrous grades. I have a son now, and I'm going to try to avoid calling him smart or gifted. Or at least not telling him that he's smarter than the other kids.
  - delazeur 10y ago
    I had a similar experience: that kind of reinforcement encouraged me to try to do the least work possible to get the same results as others in order to prove how gifted I was, instead of working hard to go above and beyond. It was a rude awakening when I got to the point in life when I wasn't competing against my peers to complete set tasks, but rather competing against them to provide the most valuable contributions to a research group or company. However, I also believe that this kind of explanation can be harmful because it puts the blame for my laziness on others. Even though the research supports the idea that this effect occurred, ultimately I got past it by focusing on my own agency.

sesm 10y ago

Note, however, that Grigori Perelman was very good at mathematical olympiads.

papapra 10y ago
And Terrence Tao who is quated was also extremely good at olympiads. As I see it, the olympiads are a good cost-effective way of identifying talented kids, they are in a way just IQ tests.
- kkylin 10y ago
  I think the point being made is that the converse need not be true: kids who are not good at these sports need not feel discouraged from pursuing mathematics.
  - auntienomen 10y ago
    Yep. Success in math contests is correlated with success in producing mathematical research/getting tenure/measure what you will. But if you sample math professors, you won't find that most of them were problem solving champions. (A large minority perhaps, and probably more in number theory.) The common factor is more likely that they really like doing mathematics, and have the skills needed to suceed in secondary aspects of the job.
  - tamana 10y ago
    But what does it mean when the people preaching this claim are all Olympiad winners? The one math genius I know who despised Olympiads, ended up leaving academia over a famous but wrong proof.
    - kkylin 10y ago
      I know plenty of very good mathematicians who did not participate seriously in this kind of thing. (Disclosure: I work as a mathematician at a research university.) I'm not sure why the only ones quoted here are mainly ex-winners. Indeed, while these competitions may have the positive effect of putting like minds together, it's possible that they have the negative effect of discouraging those w/o the aptitude for this particular kind of competitive sport (which is what it is), or who do not have access to the kind of coaching and practice that successful competitors often have.

paulpauper 10y ago

Success at mathematics requires staring at it until you can understand it, however long that takes

kafkaesq 10y ago
Well, no -- it's not enough to just stare at the problem / thing. What you have to do, effectively, is become at one with its true nature. Which in general is much more difficult than simply starting at it.
- jonnybgood 10y ago
  > become at one with its true nature That's very vague.
  - kafkaesq 10y ago
    It is. Which is why it's so difficult.

delazeur 10y ago

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. 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.

bisby 10y ago
In high school, I participated in "WYSE - Academic Challenge" (Worlds Youth in Science/Engineering) which was test taking competitions for a variety of topics. You'd take 2 tests out of 7 subjects, and there were individual test prizes, and combined school/team prizes. I originally participated to hang out with other nerds, but wound up getting a few state competition medals in the computer science test. The multiple topic thing really helped cement my love for computer science/engineering. That was the most valuable part for me. I dont even know where my medals are even at anymore.
auganov 10y ago
I was running a BaaS startup for a bit. While researching our competition-to-be I remember finding out that Parse's Kevin Lacker is a 2x Putnam winner. Couldn't help but have instant respect for him and the whole company. Personally as a kid I was often "sent" to these competitions but never bothered to prepare for them at all. I stupidly assumed it was a pure IQ play. Now I regret not taking it seriously. Makes me have even more respect for people that do.
- delazeur 10y ago
  > Personally as a kid I was often "sent" to these competitions but never bothered to prepare for them at all. I stupidly assumed it was a pure IQ play. I think this is the biggest disconnect between perception and reality of intellectual competitions (debate, math, chess, whatever). In reality, they require just as much practice to succeed as any other sport.

rafaquintanilha 10y ago

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 hint of what that person might know.

ivan_gammel 10y ago

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. 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. 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).

CurtMonash 10y ago

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.) 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. I also took the Putnam at very young ages, but never cracked the top 100. I went on to leave mathematics. Nat Kuhn was perhaps the best of the undergrads then. He went on to be a psychiatrist. 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.

tamana 10y ago
Elder Harvard math professors who have PhDs don't really empathize either, because they are in the very high end of the talent spectrum, and they came up in the time when massive breakthroughs were told for picking.

shas3 10y ago

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. 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. In India, for example, competition math is everything 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.

Animats 10y ago

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. [1] https://en.wikipedia.org/wiki/Senior_Wrangler_(University_of_Cambridge) https://en.wikipedia.org/wiki/Senior_Wrangler_(University_of...

zasz 10y ago

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.

imocuagau 10y ago

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.

mnemonicsloth 10y ago

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. 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.

lpolovets 10y ago

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. 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.) 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." 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.

ianai 10y ago
There's definitely an argument to be made that disgruntled, great mathematicians act as a barrier to entry. Being exclusionary hardly attracts anybody to an already difficult field. Besides, who's to say that whatever they describe as "the one prescribed path" must be what works for everybody? I think the will and drive to study mathematics is less cookie cutter than that.

lacker 10y ago

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. 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. 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.

lpolovets 10y ago
100% agree that learning focus and persistence was a very valuable result of doing math competitions. Completely random: If you're who I think you are, I still remember seeing your name on the list of perfect AHSME scores in 1998ish. I think we met briefly at an ACM competition in '03 (we played Mafia for a while in a big group, and were briefly introduced by Po-Shen Loh who was one of my ACM teammates.)
- lacker 10y ago
  Yeah that sounds like me! ;-) Although by '03 I was in grad school; ACM stuff was probably '01 or '02.
  - lpolovets 10y ago
    You're right! It was '02, in Honolulu.

analog31 10y ago

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. 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.