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Lisa Sauermann is the world's best high school math competitor
July 30, 2011 1:35 PM   Subscribe

Lisa Sauermann of Germany has won her fourth gold medal at the International Mathematical Olympiad, making her the top performer in the high school math competition's history. The IMO has been has been run continuously since 1959. Sauermann scored a perfect 42 on this year's exam, the only contestant in the world to do so. Not impressed yet? Here are this year's problems: day 1 and day 2. Watch a bunch of mathematicians wrestle with problem 2 in real time at the polymath blog.
posted by escabeche (64 comments total) 28 users marked this as a favorite

 
This is so wonderful on so many levels - I'm glad it breaks all the stereotypes of what kind of person would be so good at math.
posted by infini at 1:37 PM on July 30, 2011


What do you mean? What kind of person is she?
posted by cmoj at 1:42 PM on July 30, 2011 [1 favorite]


Is she from East Germany?
posted by Crabby Appleton at 1:45 PM on July 30, 2011 [1 favorite]


Good for her!
posted by carter at 1:45 PM on July 30, 2011 [1 favorite]


infini, I hate to break it to you, but yes, she does wear glasses. No stereotypes broken here.

Also, I am not the same person who took the Putnam exam years ago. He would have been all over these. Me, I'm going to go watch Hot Tub Time Machine and drink iced coffee.
posted by benito.strauss at 1:49 PM on July 30, 2011 [7 favorites]


This is pretty great. This year, there were 564 contestants and only 57 were female, so I really hope her example encourages more girls to take part in the IMO.
posted by Joey Joe Joe Junior Shabadoo at 1:57 PM on July 30, 2011 [1 favorite]


I'm thrilled to read the comments. This means that there are no more stereotypes of math nerds, their gender or ethnic origins in the 30 years or so since I was in high school.
posted by infini at 1:59 PM on July 30, 2011


"It might be fun to use projective duality..." Mathematicians are awesome.
posted by sleepcrime at 2:00 PM on July 30, 2011 [1 favorite]


Crabby Appleton, she is from Dresden which is in Saxony. I’m not sure what this “East Germany” you are talking about is.
posted by michael.ka at 2:03 PM on July 30, 2011


First-Place Sweep by American Girls at First Google Science Fair.
posted by cmoj at 2:05 PM on July 30, 2011


My best friend shared a dorm room in the building with one of the kids from the 1994 team. I believe this was the only team in the history of the game to score perfect 7s. He was a HS junior when he entered Harvard, and according to my friend (also a math major) he could basically answer anything. He was one of those math polyglots like Feynman that could answer any mathematical question in under two minutes using only paper and pencil. A savant. They should do a movie about that '94 team, they were all savants.
posted by Civil_Disobedient at 2:05 PM on July 30, 2011


What do you mean? What kind of person is she?


non-Asian?
posted by gyc at 2:21 PM on July 30, 2011


I see stringy hair, a self-conscious smile, and glasses. She doesn't seem to be breaking any stereotypes.
posted by Ardiril at 2:34 PM on July 30, 2011 [1 favorite]


On the windmill problem (#2), I'm confused and don't see how it's right.

Consider a set S of size N in which N-1 points are arranged in a circle, with the Nth point occupying a non-collinear location somewhere inside the circle.

Choose the first pivot point as any of the points on the circle, with the initial line normal to the radius from the circle.

Given the parameters of the question, doesn't that fit within the requirements while at the same time giving an example of a point (N) that will never get windmilled? As each line processes to the clockwise-next point on the circle, the Nth point is never touched.
posted by felix at 2:43 PM on July 30, 2011


Lawrence Summers can suck it.
posted by Sublimity at 2:46 PM on July 30, 2011 [7 favorites]


I seriously am not understanding the point of people pretending that it there isn't a widely-held stereotype that men are better then women at math, nor am I understanding the point in pretending that one of 57 women in a field of 567 contestants winning with a perfect score is not remarkable.

Am I not reading the tone of these comments correctly?
posted by DarlingBri at 2:46 PM on July 30, 2011 [26 favorites]


This year, there were 564 contestants and only 57 were female, so I really hope her example encourages more girls to take part in the IMO.

This is an interesting point. I don't think it's that girls aren't reluctant to take part in the IMO. They're getting put off long before IMO level. High school math teams tend to skew male (girls aren't encouraged to join? they've already been put off math?) and, if that's the main AMC/AIME/USAMO demographic, the answer's there. I don't know who typically takes the AMC, though. At my school, it was all the smart kids--it got you out of two hours of class, after all. No one opted out of the competition, we all got eliminated by not being very good at those sorts of problems. (One kid got to the USAMO one year. Maybe 15 to 20 took the AIME each year.)

All that said, it's also really important to tell kids that aren't good at those sorts of problems that there are plenty of people who do math who aren't. Some people have a serious knack for IMO or Putnam problems and others just don't.
posted by hoyland at 2:48 PM on July 30, 2011 [1 favorite]


Felix, you don't get to pick where the points in S are.
posted by valrus at 2:52 PM on July 30, 2011


That is only one of many stereotypes. I grew up in a small town whose only minority was the jewish woman who taught high school spanish. My advanced placement math and science classes were all half girls/half boys, about 10 of each in 8th grade and 4 of each remaining by 12th grade. Gender and race are not part of a stereotype if they play no part in developing the stereotype.
posted by Ardiril at 2:53 PM on July 30, 2011


Oops, Felix. Misunderstood your post. Sorry. Never mind.
posted by valrus at 2:55 PM on July 30, 2011


"This is so wonderful on so many levels - I'm glad it breaks all the stereotypes of what kind of person would be so good at math."
As any mathematician will tell you, the most extreme point on the tail doesn't tell you about the distribution as a whole. There's maybe reason to be grateful about a prominent example of stereotypes being broken, but making the subject of mathematics more broadly appealing to all is still needing a lot of work.
Damn fine job she's done, no matter what else is said.
posted by edd at 2:55 PM on July 30, 2011 [2 favorites]


"Is it me, or you can get a partition of the set of directed edges on this graph into admissible cycles (i.e., cycles generated by the windmill process) ? You juste have to reverse the time if necessary…"

It's you.
posted by memewit at 2:58 PM on July 30, 2011 [1 favorite]


Choose the first pivot point as any of the points on the circle, with the initial line normal to the radius from the circle.

To construct a counterexample you do get to pick where the points are, but you don't get to pick where the first pivot is. Since the claim is that you can pick a first pivot and first line s.t. the resulting windmill goes through every point infinitely many times, you'd need to demonstrate, not that you can avoid that result for some starting pivot, but that you would avoid it for all starting pivots.

Still, though, I guess I share your puzzlement. Even if you take the interior point as the starting pivot, wouldn't the windmill end up just going around the exterior points once it hit the first one?
posted by kenko at 2:59 PM on July 30, 2011


The puzzle solved!
posted by kenko at 2:59 PM on July 30, 2011


Okay. Let me try again. Felix and kenko, the problem says that it's possible to choose P and ℓ so that you windmill every point. I think in the case you're looking at, this would probably mean you start at one of the points on the radius of the circle and maybe pick ℓ so it's a chord of the circle.
posted by valrus at 3:02 PM on July 30, 2011


Lawrence Summers can suck it.

She probably solves problems by thinking in terms of mommy projective duality and baby projective duality.
posted by Ralston McTodd at 3:10 PM on July 30, 2011 [2 favorites]


I think in the case you're looking at, this would probably mean you start at one of the points on the radius of the circle and maybe pick ℓ so it's a chord of the circle.

Yes, my confusion was thinking this:

(a) if you pick an exterior initial pivot, you never get to the interior.
(b) if you pick an interior initial pivot, you only hit it once.

The reason this isn't true is that you have to consider the whole line, extending both backwards and forwards.
posted by kenko at 3:14 PM on July 30, 2011


I'm literally in awe of people who have a knack for this sort of thing. I was a fairly high achiever in school, but I was always really awful at maths. (Although having a really bad teacher for three years straight may have had something to do with it.) I pretty much gave up on it when I enrolled in an English program in college and decided I didn't need it any more.

Who knows, maybe I'll try getting back into it at some point.
posted by anaximander at 3:19 PM on July 30, 2011 [1 favorite]


I seriously am not understanding the point of people pretending that it there isn't a widely-held stereotype that men are better then women at math, nor am I understanding the point in pretending that one of 57 women in a field of 567 contestants winning with a perfect score is not remarkable.

Yeah, I realized that was what's supposed to be remarkable about this and not the fact that a high school kid aced this crazy test. I think this stereotype only exists outside of, you know, math-doing circles. I was this kind of kid in high school, though not competing at near this level. If boys were over-represented it wasn't by much (latin competitions on the other hand... explain that with cultural bias), and I wan't even aware of jokes being made about girls not being as good at math. I assure you that if there had been any hint of that in our hormone-addled little nerdy zeitgeist it would have come out frequently.

Aside from that, it seems odd to have to say, "Remember, folks, there's a stereotype being forgotten here!"
posted by cmoj at 4:04 PM on July 30, 2011 [2 favorites]


Aside from that, it seems odd to have to say, "Remember, folks, there's a stereotype being forgotten here!"

If you ever follow debates over whether women are inferior -- sorry, different, or more homogeneously distributed -- in intellectual ability, someone invariably brings up the gender distribution of winners in the International Math Olympiad. So there really is a big stereotype being maybe not forgotten, but at least weakened, when a girl is the top all-time competitor in that very contest.
posted by Ralston McTodd at 4:34 PM on July 30, 2011


Lawrence Summers can suck it.

Lawrence Summers seems like an all-around asshole, so agreed, in principle.

However, the ratio of female to male participants in this particular competition naively provides a data point that backs his observation about the proportional representation of women in math.
posted by Blazecock Pileon at 4:41 PM on July 30, 2011


While I can sympathize with some of the sentiment here, some part of me feels this is no different than some getting excited that the spelling be wasnt won by an Indian or the NBA MVP isn't black.

Within the competion, I just don't believe people think like this. these competitions are among outliers in individual skill, not persons of some specific race or gender
posted by mulligan at 4:44 PM on July 30, 2011


Coincidence that a score of 42 is considered "perfect" on this test? I think not.
posted by secondhand pho at 4:45 PM on July 30, 2011 [8 favorites]


Bee
posted by mulligan at 4:45 PM on July 30, 2011 [1 favorite]


This is the fourth year in a row she's won, and five years ago she got the silver. The 'stereotype' commentary is only perpetuating this idea, and I'm not sure why it's happening.
posted by june made him a gemini at 5:29 PM on July 30, 2011 [1 favorite]


If boys were over-represented it wasn't by much (latin competitions on the other hand... explain that with cultural bias), and I wan't even aware of jokes being made about girls not being as good at math. I assure you that if there had been any hint of that in our hormone-addled little nerdy zeitgeist it would have come out frequently.

It's worth noting that at my school, girls were probably overrepresented in honors Latin classes, but severely underrepresented in certamen. The only all-female teams I ever saw were from girls' schools, whereas there was more than the occasional all-male team. (I think most teams averaged about one girl. My school only ever had two or three people at a level, so our gender balance was always liable to be out of whack.)

I think girls were plenty welcome in our math team and were well-represented. However, I think there's something systemic happening even before you get to the somewhat mediocre high school math team level. Our girls were almost all in the top half of the team--the girls who weren't very good weren't joining. Whereas the lousy boys seemingly thought enough of their abilities to join anyway.
posted by hoyland at 5:39 PM on July 30, 2011 [2 favorites]


Sauermann the Wise.
posted by ShutterBun at 6:47 PM on July 30, 2011 [2 favorites]


With geekdom, I am gender-blind. I can picture my typical girl math geek and guy math geek, but geek on its own for me is not defined by gender. (Let's save the various flavors of engineering geeks for a different discussion.)
posted by Ardiril at 6:55 PM on July 30, 2011


I seriously am not understanding the point of people pretending that it there isn't a widely-held stereotype that men are better then women at math, nor am I understanding the point in pretending that one of 57 women in a field of 567 contestants winning with a perfect score is not remarkable.

Am I not reading the tone of these comments correctly?


When you're a hard-core math nerd, it's best for you to stop giving any kind of fuck what conclusions others may draw based on love of or ability in math.

And based on this woman's performance, her gender is probably the least remarkable thing about her.
posted by benito.strauss at 7:34 PM on July 30, 2011


kenko: I don't think that's correct. If you pick an external point, then the (whole) line rotates 'around' the circle; in effect, the circle rolls on the line. The center point is never touched.
posted by felix at 7:47 PM on July 30, 2011


If you pick an external point, then the (whole) line rotates 'around' the circle; in effect, the circle rolls on the line.

Not if you start with an internal point as the first pivot.
posted by kenko at 8:14 PM on July 30, 2011


kenko and felix, here is a visual demonstration of how it works.
posted by Jpfed at 8:41 PM on July 30, 2011


DarlingBri: ...nor am I understanding the point in pretending that one of 57 women in a field of 567 contestants winning with a perfect score is not remarkable.

If the genders are equally abled, then a woman winning a co-ed competition is entirely unremarkable, no matter the female percentage of the field. Unless - do you mean to imply that her victory shows that the truth of the stereotype skews the other way (i.e. women are actually better than men at math)?

The warring of stereotypes sometimes bears a pendulum's inertia upon public policy. If enlightened peoples simply behaved as though equality were an inherent truth (despite being cognizant that it is not a truth in practice) in lieu of staging public executions, the falsehood would be deprived of memetic fuel and the rationalist approach would be promoted as a practice. Regressive pundits then have less reactionary material with which to fortify their levees and are soon overtaken by a rising flood of newly normative thinking.

In other words, the best approach to forgetting about elephants is to stop talking about elephants instead of saying "DON'T THINK ABOUT ELEPHANTS!"
posted by troll at 9:52 PM on July 30, 2011 [4 favorites]


There are always idiots like 'reporter' John Stossel, saying that women are not good at math.
"Your brains work differently. Maybe you're not as good in math. Why sue me because of that?"

It should be seen as unremarkable that she is female, and if more results like this are reported, then maybe the idiots will no longer have a voice, and young women who enjoy math won't get discouraged by them.
posted by eye of newt at 10:04 PM on July 30, 2011


As any mathematician will tell you, the most extreme point on the tail doesn't tell you about the distribution as a whole.

As any mathematician will tell you, "oh, gross. Statististics."
posted by atrazine at 11:16 PM on July 30, 2011 [14 favorites]


The team from Pakistan had at least one woman in it. I think it's okay to be pleased about that.
posted by vanar sena at 1:51 AM on July 31, 2011


They've really gone all out with women's representation haven't they? Just look at their new Foreign Minister!
posted by infini at 2:02 AM on July 31, 2011


If the genders are equally abled, then a woman winning a co-ed competition is entirely unremarkable, no matter the female percentage of the field.

Well you had me until that last part. 57 out of 567 is, if my math is correct, nothing like equal. "If the genders are equally abled" then, all other things being equal, there should be 234 women in the competition. QED: All other things are not equal.

In this context the achievement of one of the 57 deserves some extra consideration.
posted by three blind mice at 3:36 AM on July 31, 2011


Note: A gold medal at the IMO does not mean coming in 1st place, everyone who scores over a certain amount of points gets one. In this case she was the highest scorer with a perfect 42 points, and thus has a gold medal and first place - but those are not the same thing and here previous gold medals were not first place finishes.

If the genders are equally abled, then a woman winning a co-ed competition is entirely unremarkable, no matter the female percentage of the field.

If you can assign an immutable ability score to every individual and if the contestant with the highest ability score always wins the competition, then this is true. In practice neither of these things are the case, and the overall winner will also depend on factors like the exact nature of the problems and the overlap between the problems and the contestant's mathematical interests. In 2010 for instance, Ms Sauermann scored a perfect 7 on five of the six problems, but only 1 on the last. She ended up in 4th place with 36 points. I imagine that there may have been some key insight required for that problem that she wasn't familiar with even though she was "good enough" at math to win.

Given that is is the case, we can predict a contestant's score beforehand based on ability, but their actual score in the competitions will be distributed around that nominal score.

So a field with many fewer women will produce fewer perfect scores, just because perfect scores are rare even for those mathematicians who are good enough to get such a score on their best day.
posted by atrazine at 4:00 AM on July 31, 2011 [2 favorites]


On the bright side, I did as well as 20 of the contestants did, and I didn't even show up!
posted by ShutterBun at 6:18 AM on July 31, 2011 [1 favorite]


Pretending that there is not a widespread misperception that women are worse at math than men, and refusing to even discuss the matter because you believe yourself to be too enlightened even to sully your mind with the notion that such prejudices exist, will not actually make the problem go away.
posted by kyrademon at 8:05 AM on July 31, 2011 [2 favorites]


cmoj: Yeah, I realized that was what's supposed to be remarkable about this and not the fact that a high school kid aced this crazy test. I think this stereotype only exists outside of, you know, math-doing circles.

As a former attendee of a summer camp which trains high school students for the IMO*, I can assure you that my peers and I noticed that there were only two girls among about 30 boys. Most other math camps strive for gender balance, but this one based admissions on the USA Math Olympiad, which produces a similar gender distribution to that observed at the IMO.

The range of beliefs about what causes this imbalance was well-represented among these kids. I never met anyone who was a total asshole about it, but I do think there was a common belief that the imbalance was merely statistics at work and that virtue consisted in deriving no prejudice toward individuals from their gender. We were "past that," interested in math and not sociology, etc. Some readers will be apt to see decency in this -- others, callous indifference.

Fortunately, the opinions of teenagers do not carry the day, and the organizers of the camp (and the olympiads, etc.) were and are active in promoting math and math competitions to girls. But as a side effect of this focus, any girl who did achieve remarkable things got a level of attention which I would have found unmanageable -- not from her peers, but from organizers wanting to put her forward as a role model, and often for years. I am doubtful whether this was a net good. There are medals in some math contests for the top-scoring female contestant, which I think is pretty offensive and unnecessary: when there's a girl at the top, she needs no further recognition, and when there isn't, the special prize only draws attention to that fact.

So, congratulations to Ms. Sauermann for winning the damned thing outright! If she's inclined to be a role model for girls, great, but if not, then I hope she won't be pressured to serve as an exhibit.


* I know, dorky. By the way, the camp is not only for current IMO qualifiers, and I never did qualify for the IMO.
posted by aws17576 at 8:11 AM on July 31, 2011 [3 favorites]


P. S. atrazine, I am a mathematician and I love statististics
posted by aws17576 at 8:13 AM on July 31, 2011


As any mathematician will tell you, "oh, gross. Statististics."

In my undergrad probability class, our professor advised going into statistics because "only 10 people know anything about it."
posted by Ralston McTodd at 9:27 AM on July 31, 2011 [1 favorite]


Pretty cool that you had Gian-Carlo Rota teaching statistics. I remember reading some of his work on Husserl as an undergrad.
posted by atrazine at 11:06 AM on July 31, 2011


The documentary Beautiful Young Minds - which followed the selection process for the UK's 2006 IMO team - shows an official coach of the team explaining to camera that women just aren't as good at math as men because of basic differences in their brains. It also (depressingly) shows a high ranking female contestant - who made the level just below the team but not the team itself - explaining that she will probably never make the team because women's brains are just different and girls aren't as good at math as boys. SO, at least in 2006 in the UK, that stereotype was apparently alive and well among high-ranking 'math types'.

(Note that it does not appear that there was active discrimination of any kind here - tests were graded blind - the interviewed teacher and student had clearly been asked to explain the gender distribution they saw at the top. Also, gender is in no way the focus of this film - the filmmaker's real focus is on the relationship between aspergers and math talent.)
posted by Wylla at 11:29 AM on July 31, 2011 [1 favorite]


Well you had me until that last part. 57 out of 567 is, if my math is correct, nothing like equal. "If the genders are equally abled" then, all other things being equal, there should be 234 women in the competition. QED: All other things are not equal.

To be fair, men are less skilled at identifying women with math, scince or technical talents, but fortunately, we have institutions that help us compensate for this gender-based limitation.

Also as a judge in this competition, I also would have accepted, "Go fuck yourself, Larry Summers," as an answer.
posted by mobunited at 11:31 AM on July 31, 2011


This reminded me of a recent article about Emmy Noether. (link to Wpedia, not the article). Another site remarks of her that Albert Einstein described her as "the most important woman in mathematical history, since the higher education of women began."

For the benefit of those still disinclined to recognize that nurture is responsible for their supposed edge.
posted by Twang at 11:32 AM on July 31, 2011


Just re-watched Beautiful Young Minds - and to clarify my comment above, the coach coyly cites "biological factors" that "make girls express their abilities in different ways" to explain why there are so few women on the team. When the film maker asks for further detail on what "biological factors" are, he giggles and refuses to give it on camera. It's the female candidate who gives the detail on what she's been told about brains.
posted by Wylla at 11:41 AM on July 31, 2011


Pretty cool that you had Gian-Carlo Rota teaching statistics.

Yeah, he was great, although it was actually probability. (And it just occurred to me that I might have misremembered and it could have actually been another professor, an algebraist, who thought there were only 10 people who knew anything about statistics. Either way, an underappreciated field, although I think that's changed somewhat.)
posted by Ralston McTodd at 11:42 AM on July 31, 2011


In my undergrad probability class, our professor advised going into statistics because "only 10 people know anything about it."

Is this like the whole "there are only a dozen people who know anything about the theory of relativity" meme that was common at some point in the early 20th century?
posted by madcaptenor at 12:23 PM on July 31, 2011


Getting a single question right (out of 15) on the AIME my senior year is one of my proudest moments ever. It was a truly humbling experience. I think I halfheartedly attempted a second, but knew I was out of my depths.
posted by yeti at 12:43 PM on July 31, 2011


Wylla: It's the female candidate who gives the detail on what she's been told about brains.

Reminds me of 'stereotype threat': the experience of anxiety or concern in a situation where a person has the potential to confirm a negative stereotype about their social group ... [it] has been shown to reduce the performance of individuals who belong to negatively stereotyped groups.
posted by troll at 1:20 PM on July 31, 2011 [1 favorite]


Holy balls - I have a math degree (to be fair, I stopped taking math courses as soon as I was able, but my computer science degree required a lot of them because it was in the math faculty), and even graduated with distinction, and sure, it's been 10 years since I graduated, but I am pretty sure I still wouldn't have been able to come up with answers to those questions even when I was in university. Nevermind high school.

I was in the "enhanced" class in high school, and it was pretty equally split, gender-wise. When we were taking the Waterloo Math Contests (particularly the Euclid, which was required for those of us applying to go to Waterloo), there was a pretty equal split, gender-wise. But then, my school was fairly progressive in that we had an "enhanced" class to begin with, I believe there was only one other school in the region that had anything similar. So I guess it wasn't that big a surprise that we attracted the most intelligent kids of both genders fairly equally.
posted by antifuse at 11:04 AM on August 2, 2011


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