USA tops International Math Olympiad for first time in 21 years 141 points by tokenadult on July 18, 2015 | hide | past | favorite | 102 comments

 This is definitely off-topic, but have people taken a look at Po-Shen Loh's company expii.com? He's the coach for the US team.It says:Expii is a collection of free, interactive, explanations written by people from around the worldInteresting!
 Thanks for noticing! :) Indeed, I've been working with a certain segment of the population through my roles as the national coach of the USA IMO team and as a math professor at Carnegie Mellon University.However, after being appointed to the national coach position, I realized that the USA would not be able to consistently deliver top results unless we lifted our mathematical level across a broad base. It seemed that technology could provide the solution to that problem, in the sense that it's possible to crowd-source the scripting of automatic virtual tutors, which can then be replayed (for free) on mobile devices throughout all regions, rich or poor. Thus, expii.com was born.-- Po-Shen Loh
 That's really interesting. Deserving of a top-level submission, too, I think.May I ask what your plan is for defending lessons against cranks, crusading ideologues, and the less-than-knowledgeable once it gets more adoption? Other collaborative projects such as Wikipedia have suffered as a result of this, but I noticed in your talk that your aim is to maintain "higher" quality than Wikipedia or even Stack Exchange and Quora. I'm curious how this can be accomplished once the user base expands beyond its initial network.Congrats on this year's IMO result!
 Expii uses voting (like Reddit, Quora, Stack Overflow, etc) to identify the best content. After that, since we have the luxury of focusing only on the "heavy-hitter" topics which at least 100 million people need to know, there really aren't that many topics. When we do reach the size at which quality is an issue, we can simply moderate the topics in-house.Wikipedia cannot do this because their objective is to cover 100 million topics (breadth), and so in-house moderation doesn't scale. Our objective is depth: we ultimately want to provide the absolute best free interactive lessons on every heavy-hitter topic in the world. :)Thanks for your well-wishes!
 I gasped when I saw my acquaintance's name on HN. By coincidence, I'm wearing an expii t-shirt right now.He's really nice, and excited about improving math and science education. Expii could be called an "explorable explanations" Wikipedia[0]--one can write code (I think a subset of JS), embed videos etc in service of a better explanation.I'm also fond of him because his office has an X server (or would that be X client?). How many startups actually use X??[0] Just my two cents.
 Maybe I'm just dense. Do you mean X11 server (https://en.wikipedia.org/wiki/X_Window_System) or something else?
 Indeed X11. what I meant by my X11 server/client waffling is I think you /run/ an X11 client and servers connect to it--this is backwards to every other usage of client/server.
 A Canadian got a perfect score. Only one I found while checking around. No American nor Chinese got a perfect score.https://www.imo-official.org/participant_r.aspx?id=19624Also, only 1 person got 3 perfect scores in the history of the event: Ciprian Manolescu (3 for 3 perfect) https://www.imo-official.org/participant_r.aspx?id=3789
 Astonishing performance (3rd place) by North Korea with pop. around 25m. Not sure what incentives were in place for the contestants.
 North Korea was caught cheating twice, and is the only country to have been caught cheating at the IMOs so far, so I would take their ranking with a grain of salt.
 How does one cheat at a test of this sort?
 Interesting. Thanks for the response!
 lacker on July 18, 2015 [–] Just being able to communicate among the 6 participants would be enough to make a huge difference. It's like if 6 people took an SAT test together, they'd likely do better than any one could do individually.
 Singapore at the 10th with fewer than 6 million people is also quite noteworthy. I wonder how much it has to do with importing talents or talented families from abroad, and how much from training starting at a young age.(I know that Thailand does have a series of math competition for kids starting at grade 3. This was started less than 20 years ago, which helps explain its much improved IMO performance over the last decade.)Any Singaporeans care to explain?
 Singapore set up NUS high school a couple of years ago to nurture development of students talented in maths and science. I remember a ex IMO coach from was hired from China to prepare for the competition. it is not surprising it stands at tenth place if you have long term plan for it. btw 6 mio people are total population out of which only 3mio are singaporean. but if you are really talented and wealthy, you can quickly become singaporean
 Thanks for posting this. I've always wondered how come we "suddenly" started performing really well in the IMOs.Considering the fact that until 2011, we had only won ONE gold medal and rarely featured in the top 30.But from 2011 onwards, have won 10 gold medals and have started to consistently appear in the top 10.Background: Singaporean who once aspired into getting into the IMO team [this was circa <=2004]. But ended up with a crappy silver medal in the informatics olympiad. Now a washed up, recovering Perl hacker.
 Thanks for your reply. From my experience teaching math to gifted students, it takes a lot longer than a couple of years to develop talents at this level though. Starting young (by elementary school) seems to be a requirement.Perhaps there might have been special tracks and/or competitions to help nurture these kids and their peers for quite a while before the NUS high school was set up?
 North Korea in 4th place: https://www.imo-official.org/year_country_r.aspx?year=2015
 South Korea, according to the article.
 North Korea placed 4th.[0]
 I think the reporting from The Guardian a few days earlier,[1] mentioned in this article, provides some good perspective on the International Mathematics Olympiad (IMO) from across the Atlantic Ocean from this Washington Post report.
 Congrats to the team! I'm curious if any of the six team members are reading HN.
 Hi. :)
 Not related to this year's competition, but you may also be interested in the hall of fame [1], which contains many well-known names.
 Russia nowhere to be seen. We used to be a powerhouse too, but it seems the education here is in absolute shambles now.
 To be fair, this contest measures the performance of six people. The education that is most directly tied to IMO performance is specific "math for the top few students in the country" stuff which is usually some specialist math camp thing. So I don't think it necessarily means that much about a whole country's math education, if their IMO team doesn't do well.
 Don't know about other countries. But in the USA, the six people who make the team are selected among high schoolers after rounds of competition. It does reflect very much a country's math education. But math education is just part of a much larger equation.
 For Problem 6 given in the OP, the claim is false:Notation: We borrow subscript and superscript notation from D. Knuth's TeX. So, a with a subscript j is written a_j.Consider the simple graph, based just on typing, below. The graph shows the first four values of a specific sequence a_j. This sequence is a contradiction to claim of Problem 6.In this graph, the values of j = 1, 2, ... are plotted on the horizontal axis with 1, 2, ..., and the values of the a_j are plotted on the vertical axis from 1 to 2015. We plot a value of a_j as just 'a'. Due to constraint (ii), we indicate by 'x' points that, due to prior values of a_j, cannot have an 'a'. So, the graph is: 2015 . . . a_j . 5 4 3 a a 2 x x ... 1 axax 123456789 j  Then the first two terms of the sequence a_j are: a_1 = 3 a_2 = 1  and generally for j = 1, 2, ..., a_j is: / | 3 if j is odd | a_j = < | | 1 if j is even \  Then for any positive integer b and j = 1, 2, ... (a_j - b) + (a_{j + 1} - b) >= 2  More generally for positive integers m and k, sum_{j = m + 1}^{m + 2k} (a_j - b) >= 2 k  Then for any positive integer N, we can set m = N and n = m + 2(1007^2) and get | sum_{j=m+1}^n (a_j - b) | = sum_{j=m+1}^n (a_j - b) = 2 (1007^2) > 1007^2  showing that the claim is false.
 There are no absolute values in the summands, so in your example pairs of consecutive terms sum to 0 when you choose b = 2.The theorem seems entirely correct to me. You can prove it with these sub-steps:(1) the set of all j + a_j is the set of nonnegative integers minus a finite number of gaps(2) thus for large enough n you can express \sum_{j=1}^n (j + a_j) as a quadratic function of n, plus a residual term e(n) of magnitude at most 1007^2/2(3) more precisely, \sum_{j=m+1}^n a_j = g (n-m) + e(n) - e(m) where g is the number of gaps in (1)Then choosing b = g solves the problem.Hope that helps.
 it is a good news. because American become more confident in educating their kids in maths and abandon the idea that you can be lawyer if you are not good at math. on the other hand, Chinese can stop believing that math is highest form of intelligence and pursue career as lawyer etc.
 ???Wouldn't it be better for mankind ... if as many people like these kids as possible pursued math and science more vigorously ??? Especially kids like these, who have what I would term "creative" intelligence.Why would we want those people in law ??? That gives us far less than having them in math and science. And we will get the MOST by having them in art AND math and science. Then we'd really get their creativity going as they look for solutions to problems.
 American and Chinese education learns to balance each other for the average students. for the ultra smart,they do what they are good at. when I was at high school in china, I can solve complex algebra and geometry problem which I don't know how I did that today. I never thought public speaking or organisation skill etc is skill. I have the wrong belief like how you can talk about it if you are not expert of it. now in china people already start to reduce difficulties of maths problem in exam and pay a bit more attention on soft skill. in US, people might think to equip american kids with more math skill so that in future they can embrace more discipline. one example i see good programmers not willing to do computer graphics because they are worried about their math skills. maybe that is why post like maths you need to know for programming is popular
 Retric on July 18, 2015 [–] IMO, high level Math and Science is generally a waste of a lot of really smart peoples time. The LHC for example is studying particle energy's so far outside of 'reasonable' that we are not going to get useful technology from there. The same is true of a lot of esoteric Math which mostly ends up divorced from anything actually useful.That's not to say funding such things is necessarily a waste, just the focus on STEM education may be excessive. Russia for example ended up with a lot of highly educated security guards.
 The standard example of unexpected esoteric physic application is the Special and General Relativity corrections of the GPS. 100 years ago nobody thought that we would ever use that small correction or that everybody would have a special-and-general-aware device in the pocket.Another cool application is the superconductors in the NMR devices. They can see what is inside your head and even do something equivalent to a chemical analysis (with NRM spectroscopy) without opening it. The first superconductors experiments used Helium at 4K, so they were only a laboratory curiosity.For everyday use, I like the giant magnetoresistance. This is my favorite case to explain that strange quantum effects have real world direct applications. Just start talking about the spin in electrons. Then explain that some magnetic conductors have a different value of the current with spin up and the currents with spin down. Then add the sandwich with non-magnetic conductors. At this moment it looks like a weird laboratory experiment. Then suddenly explain how it is used in hard disks heads: http://en.wikipedia.org/wiki/Giant_magnetoresistance
 Don't get me wrong, QM for example was ridiculously useful. But, pointing to past and saying these tiny particle accelerators where useful let's make a multi billion dollar one feels like cargo cult science for the lack of a better phrase. We just keep piling higher and deeper without a clear reason to do so other than we can afford to do so.String theory is another example where lot's of effort from seemingly smart people with no practical basis.Dumping all of LHC's money into say a large ITER style fusion project would have also been cutting edge, but there would have at least had the possibility of useful results. Hell, even ISS would qualify as vaguely useful.How about a self sustaining bio-dome in Antarctica. Now that's probably harder and possibly more expensive, but would have real useful applications if we ever want to try and colonize Mars.PS: Not that the 13+Billion for the LHC was all that expensive, but there are a lot of similar projects out there.
 GH Hardy famously predicted that elementary number theory would have no practical applications. Lo and behold, today it is an indispensable part of web cryptography used by hundreds of millions every day. Waiting on the order of decades for a ROI on fundamental research is simply part of the game. I suspect the point where we experience diminishing returns from this is much to far in the future to even consider the question.
 Elementary number theory is the opposite of what I am talking about. RSA is from the kiddie pool of that field.Consider, we know the first five digits of the gravitational constant. So, while it might seem like the diminishing returns are a long way off. Yet, each extra digit becomes exponentially more expensive and less useful. So, actually learning g out just 9 digits is probably a huge waste of resources.Or in the words of a physicist, in 1920 second rate physicists where doing first rate research. Now, first rate physicistare doing second rate research.
 >Elementary number theory is the opposite of what I am talking about.In number theory, what's considered 'elementary' now was cutting edge in the times of Diophantus, all the way to Fermat, to Euler, to Gauss (etc). The fact that children are now routinely conversant in it, I think, is another point in favor of the importance of making such discoveries in the first place.My point is that applications that were never envisioned for these (at the time) centuries-old-facts, are now commonplace and indispensable.I think that there is a bit of survivorship bias that warps our understanding of old science. We remember only the great discoveries because those are the most likely to be republished and read.Also, in the case of math, it is my impression that an amazing amount of very significant progress is being made in the present era.
 It was old hat 1500 years ago, and rediscovered repeatedly. I am suggesting there is a legitimate separation from what people find out in the first few years of research on a topic and what's built after that. So, you really need to pick a deeper topic if you want to defend your argument.As to survivorship bias, that's huge but it's not just based on good ideas. Copernicus was ~4,500 years late to proposing the sun was the center of the solar system. But, the pop story looks better when Darwin is breaking new ground instead of simply collecting more evidence in support of an old theory.As to Amazing progress, I would hope the ~1,000,000 active mathematicians are not all wasting their time. But again, the point is we don't need to maximizing the number of Mathematicians, we are well into diminishing returns.
 deanmen on July 19, 2015 [–] Relativity is not a good example since we could still discover the correction empirically and program it into GPS receivers without having a theory of relativity. (i.e. the corrections are just "these weird numbers that you add to make the results come out right").
 I agree. It seems no one is capable of saying that math and science are extremely important while also admitting that advanced math and science are actually not used in the day-to-day lives of most adults. Why is that so hard?
 What's happened to Germany? They used to be one of the best in mathematics. But the recent IMO results are very poor (27th this year).Has their education system declined or something else perhaps? I know they have a low birthrate....
 This makes me want to chant USA a lot more than the soccer game.
 Something about this comment really annoys me. It's like you are disparaging high achievement by others just because it's not in a field you are personally interested in?
 No I like sports. It's just boring when team USA wins again because they are always so dominant. Winning once in 21 years makes us the underdog.Getting really annoyed is silly. I try not to be easily offended by hackernews comments.
 or you could learn math & science...way better
 Actually my team from Cupertino was county champ in Math Counts and 2nd in the state. We lost to the team we beat in counties because they went through a training montage to avenge their loss. ;)
 congratulation...I see a hedge fund career for many
 I hope not. When I did math Olympiads (including the IMO) I was presented with a false dichotomy of pure math or finance. This is really unfortunate because finance in general does not use very deep math. A tiny number of people might use SDEs but by now the techniques are standard and boring anyway. Furthermore, even mainstream economists doubt that this sort of finance has positive externalities. The amount of resources that go into finance is just way out of proportion to what seems necessary for price discovery.In contrast, all of the science and engineering disciplines can make use of very interesting math. Not deep compared to research math, but used in a much more interesting way than in finance. E.g when you study the statistics of markets, you are just playing a game, and don't care that much about external reality per se. On the other hand if you study the statistics of DNA or gene expression, you are doing real science.I think the best advice to a young person studying math is what was given to me at the age when I was doing the IMO (and interestingly, after I graduated by someone else): Don't neglect statistics.
 As someone who neglected statistics as a student ( topology was a lot funner) , would you have any recommendations for self-learning tools for statistics?
 Casella & Berger's "Statistical Inference" is a nice introduction to basic probability theory and statistics. I found it pretty readable, and it's used for many 1st year graduate stat programs.Duda & Hart's "Pattern Classification" is one of the best introductions to machine learning IMO. It assumes very little in the way prerequisites, which is nice for first time exposure.Hastie & Tibshirani's "Elements of Statistical Learning" can be a little intimidating without having been exposed to the ideas of the previous two texts. Afterwards, however, it is a gem.
 I would suggest "elements of statistical learning". If possible I would also try to study some econometrics which gives unparalleled insight into the correlation vs causation issue. You can think of econometrics as a branch of statistics that remained separate from the mainstream for historical reasons.
 drhodes on July 18, 2015 [–] I also neglected statistics, it seems there's no avoiding it these days. What cured me was a MOOC from edx/MITx called 6.041x. It literally had me close to tears a couple of times. There was carnage, whining and general malaise. I couldn't imagine a better course for persistent programmers who don't know when to quit.It's been offered during the spring term for the past two years, so maybe Feb 2016 will see the next run.
 I haven't finished it yet, but what I've read of Wasserman's All of Statistics I've liked. The chapters are a bit terse, so I'd plan on doing a bunch of the exercises. The good news is that there are lots of exercises and most of them feel well chosen.
 qmalxp on July 18, 2015 [–] Probably doesn't need to be said here, but I would also add in: Don't neglect computer science.
 the transition from pure math to the application of statistics to the real world (or science) requires a philosophical adjustment.In math, the model and axioms are sound (by definition) within the mathematician's world.However, in order to make judgments about reality by using statistics, one has to come up with reasonable models and assumptions, otherwise the resulting deductions can be worthless. The leads to a lot of subjectivity and grey areas for debate that a mathematician may not be accustomed to.
 A good proportion of maths olympians go into mathematics in academia rather than into industry. Industry does need problem solvers, but maths olympians develop creativity and a sense of elegance and beauty as well. Industry requires efficient solutions to technical problems, more than elegant or beautiful ones, at least relative to what is possible with full academic freedom.
 As a minor nitpick, some mathematicians see elegance in efficient solutions. It's interesting to get your head around a specific problem and come up with the solution that is optimal regarding some given metric.However, I agree that industry and mathematics are not best friends. That's because mathematicians righteously demand and require a level of freedom and support the industry is not always willing to give because of the social problem it creates with other employees and because the value of the work of a mathematician can be too hard to judge.From my experience, the fight to get the working conditions you need is not worth it. My advise to fellow mathematicians is that — when you want go into the industry — to go where there are already mathematicians.
 Just to clarify, I meant efficient from the perspective of business, not efficient from the perspective of mathematics. In industry, often a solution which "works", but is neither mathematically "efficient" or "elegant" is "good enough". By and large, industry is trying to generate revenue, not scientific knowledge.
 jcrites on July 18, 2015 [–] In software engineering, elegance is prized and is often related to efficiency in several layers.At the human layer, one expression of this idea is the principle of least astonishment: "People are part of the system. The design should match the user's experience, expectations, and mental models." (Wikipedia). A system involving people is not efficient if the people are often surprised by its design, implementation, or behavior.Efficient software solutions also tend to involve elegance. Take Git for example as an improvement over other source control systems. The conceptual primitives that Git is built upon are elegant and recognizing them as the correct basis for source control (along with a strong implementation) resulted in Git's efficiency and power.Granted, software is different from mathematics, but I find the parallel interesting. I suspect that a mathematician's desire to find an elegant formulation, and appreciation of it, is very similar to the software engineer's.
 giech on July 18, 2015 [–] My anecdotal experience is that most may start with math for their first degree, but then (or during) pivot to some related but more applied area like CS, Econ, etc.
 There was an interesting article that looked at what the USA Mathematical olympiad trainee candidates in 1980 were doing now (This batch included the famous Noam Elkies) -http://andrewgelman.com/2015/03/17/1980-math-olympiad-progra...HN Discussion: https://news.ycombinator.com/item?id=9225683A bunch of them went into academia, though not necessarily pure math. Some became engineers and only one ended up in finance.
 I looked a bit at the gender distribution for the gold and silver medalists, I would guess only 1 in 10-20 is a girl, most seemed to be from the eastern bloc countries.
 I would not read to much into it. This is a very specialized competition that selected 6 people from an entire country.Some aspects of soviet education are very conducive to these competitions (e.g. an emphasis on euclidean geometry). Because of this, a top 10% student from a former Soviet country will do much better than a top 10% American if neither have extra training in this sort of competition.If anyone is interested in discussing women in STEM in general, this article is a very poor place to do it. Eg the US has done extremely poorly up till now compared with similar English speaking country's. There are just so many idiosyncratic features at play.
 It is my privilege to know (just a little) the first United States woman to gain a gold medal at the IMO. I know her mother much better and discuss mathematics education with her online frequently. In all countries, it takes a really sound elementary education in math to gain a chance at qualifying, through repeated rounds of testing that winnow down a national population, for a national team to the IMO. Most of the United States young people I know who have made it onto the United States IMO team have been deeply involved in mathematics competitions at younger age levels for many years, and the young woman whose mother I know was no exception. She was homeschooled for her primary and secondary education. East Asian countries and some eastern European countries seem culturally (compared to the United States) to have much less of a presupposition than many Americans have that girls will not do well in math, and correspondingly more girls in those places do well in math because they stay involved in math.
 Gender distribution, yes, that's what stands out. Aside from the gender imbalance, the US team looks pretty much like a typical slice of America, and the top teams are pretty much randomly scattered over the globe.
 booop on July 18, 2015 [flagged] [–] I can't believe the audacity of Po-Shen Loh to send a team exclusively of boys to the IMO. When you have to select 6 team members how can you NOT select at least 1 female? This flies in the face of all the outreach work people have been doing to get more girls into STEM, and this victory will only discourage them. It appears the top 3 teams are all 100% boys.I'm delighted that this is currently the top comment here. It shows we are clearly concerned with the right issues. I hope from now on all national teams participating in international competitions will be gender balanced. In order to remedy this situation we need: 1) A Twitter mob 2) An email campaign addressed Po-Shen to not repeat this and discredit his work and efforts. 3) A post of the team's picture to the popular twitter/tumblr account which shames all male conferences and gatherings 4) An email campaign addressed to IMO to implement rules that all teams should be gender balanced. 5) A solution to Poe's law.
 You usually send them based on performance in national comp, so there is no subjective selection, you just have to make it to top 5
 Tests are written by people and their biases recognized or unrecognized will end up in tests. What about the way math is taught? Or the perceptions of gender differentials in math? I'm thankful that I have the privilege of not being told that my gender was a handicap for my field (statistics).
 "Tests are written by people and their biases recognized or unrecognized will end up in tests"Honestly I have an extremely hard time imagining how math exams are gender biased. Have you even taken a look at this year or past imo's? You're speaking completely hypothetically and it sounds like nonsense.Here is problem 2: Determine all triples (a,b,c) of positive integers such that each of the numbers ab-c,bc-a,ca-b is a power of 2.As for: "perceptions of gender differentials in math" , sure that should be worked on. But it is not the fault of the contest organizes or team selectors who uses a series of objective exams and scores to determine the team members.
 Sure, but I doubt the same is true for all of the tests and educational materials that preceded this particular test. Or, or perhaps the teachers. Women are commonly beat down and told they suck and are inferior to men in STEM areas or tokenized or marginalized. All I'm asking for is that we examine, "why might a gender imbalance exist?"
 How could mathematical tests be biased? I mean, math is math is math. What would a non-biased math test even look like?
 You might find the results summarized in Sian Beilock's book "Choke" of interest.
 One simple way, just as a contrived counter-example are gendered questions or questions that assume gendered cultural capital.
 I'm not sure what that would look like. I mean whatever ornaments are in the word problem, the thing that matters is the math underneath. You seem to think female maths enthusiasts will get distracted by "gendered" ornamentation and find themselves unable to see the math underneath - which itself seems like an oddly sexist idea. Do you honestly think if we printed the tests on pink paper and made all the word problems about stereotypically feminine things, the results would change appreciatively. Isn't it possible that, on average, women are just less likely to be interested in mathematics competitions. Is this necessarily a bad thing so long as those that are are not discriminated against?Edit: And as for your comment below, I'm unsure of what the particularities of Thai dress and ceremony has to to with the posited inherent sexism of maths tests. And honestly do you really think women avoid maths competitions because they might eventually meet some foreign women in traditional dress?
 Look carefully at the role of women in the headline photo, and you might see it. They're there only to be looked at, to adorn the men. This is a pretty basic and common representation of the reasons I believe women tend to be under-represented in situations like this.
 >gendered questions or questions that assume gendered cultural capitalQ. Prove Bob has a winning strategy against Alice.A. The Patriarchy! QED7/7Edit: Seriously, what could that even mean?
 forloop on July 18, 2015 [–] And also, to make up for the temporal inequality (the past ratio), the teams should be something like 5/6 female.And logically: until that happens, the school system isn't catering for half their population.
 Tinyyy on July 18, 2015 [–] This guy is being sarcastic, I don’t really understand the down votes. Maybe that’s just the way it is over here.
 It's a pointlessly baity answer and deserves downvoting.
 Respectfully disagree. He ridicules the simplistic solutions proposed to certain issues (lack of women in a math competition in this case). In my opinion, it adds a valid (and funny) point - you may agree or disagree with him, but it is not a reason to downvote. Sarcastic - yes, ad hominem - no.
 I skimmed over it without reading the "Poe's law" line at the end. I've deleted my comment. Have to be more careful.
 I think that line is new. I saw it earlier this morning and seriously debated whether or not it was serious.
 You forgot the Men's Rights Advocates and Gamergate brigades which immediately show up with posts like yours. (And send death threats to women posters and their families. http://www.theverge.com/2013/9/12/4693710/the-end-of-kindnes...)
 Please just call them bigots, don't let them choose the name we call them.
 This is an objective statement that provides data. Please don't down vote it.
 Congratulations to Ukraine and Bosnia-Herzegovina for being the only countries to send gender-balanced teams of three boys and three girls.
 I assume most countries picked the best candidates for their teams, as mathematical aptitude is relatively easy to quantify. If it wasn't the competition would have no meaning. Congratulating Ukraine and Bosnia for this like it's some heroic sacrifice is odd. These girls were the best choice for their teams so they were picked. I don't see much more to it than that.
 I would congratulate Ukraine and Boznia-Hertzegovina for creating the educational system in which talented girls flourished at the same level as talented boys and so which it came time to pick the the competitors, it was statistically likely that they'd end up with a gender-balanced team.
 > I assume most countries picked the best candidates for their teamsThe fact that there are statistically significantly more men among the best candidates is already enough to conclude that there was a gender bias. The bias can be in the education or in the selection process, etc.The fact that Ukraine and Bosnia-Herzegovina have gender balanced teams mean that they have managed to avoid this bias, one way or another but not necessarily though positive discrimination, maybe they simply a more balanced education, maybe they have a more extensive selection process where they retrain the students from scratch before selection etc. Eitheir way, they deserve some credit for that.
 Are you implying that it would be good if the ones sent were based on a gender balance rather than being chosen on their math ability?
 He might be suggesting that Ukraine and Bosnia-Herzegovina are to be lauded for having an educational system that doesn't end up leaving half of the population behind.
 You're talking about the U.S. educational system leaving men behind, right?Because in America, women are more likely to graduate high school [0], enroll in college [1], graduate from college [2], and even make up 3/5's of graduate students [2].
 It might be. What if there's a psychological barrier in place in a given society where a given group of people are repeatedly told either directly or implicitly through societal conventions inherited from previous centuries that they don't have the gift for science or maths in particular. In such a context, it would actually be beneficial to send "balanced teams" to such competitions so that it gives a mental boost (in the form of a symbol/token/role model that acts as a vessel) to perfectly capable people that just started with the handicap of being say "a woman", "a black" or "a redneck".As such, reasoning in terms of "ability" is fundamentally flawed because "skills" are never innate, they're the result of a lot of work and positive circumstances in a given field and starting with a handicap from the get go just makes it so much harder that it's absolutely not a level ground.
 What if they do worse than the man on the whole in some or many instances? What happens to the image you were trying to create then?