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The Fifth problem: Math & Anti-Semitism in the Soviet Union
November 5, 2012 12:43 AM   Subscribe

The Fifth Problem: "If this were a boxing match, with one of the boxers pressed in the corner, bloodied, desperately trying to hold his own against the barrage of punches falling on him (many of them below the belt, I might add), that would be the equivalent of the final, deadly, blow. The problem looked innocent enough at first glance: given a circle and two points on the plane outside the circle, construct another circle passing trough those two points and touching the first circle at one point." Edward Frenkel, now Professor of Mathematics at the University of California, Berkeley, details the curiously baroque way Moscow State University chose to discriminate against talented Jewish math students: By quizzing them with fiendishly difficult math problems with deceptively simple solutions that are nearly impossible to find.

Edward Frenkel: At Berkeley, On Youtube, On IMDB, On Math, In Rites of Love and Math.

Tanya Khovanova discusses the "Jewish Problems" on her math blog. On her home page are even more of the problems--which in Russian are called "coffins"--along with more historical details and related links.

Previously.
posted by flug (41 comments total) 53 users marked this as a favorite

 
What incredible assholes those professors were.
posted by zippy at 1:20 AM on November 5, 2012 [1 favorite]


... the ones who gave out these exams, I mean,
posted by zippy at 2:21 AM on November 5, 2012


I'm trying desperately not to draw a similar line to a situation in the US, where it seems overwhelmingly obvious that supporters of one religion/political party/viewpoint are edging closer and closer every day to something this extreme.

Slippery slopes are tricky things indeed.
posted by Blue_Villain at 4:21 AM on November 5, 2012


My great-granduncle Julius Farber (on the right in the second photo, and later in life below) was denied his graduate degree by a panel of his friends and colleagues. Later, after engineering an escape from a Nazi prison camp along with several other captured Russian Jews, he made his way back to the USSR, where he was promptly arrested for having the gall not to die. He spent some time in Siberia, while my great-grandfather and great-grandmother worked to secure permission for him to return to Moscow. When that was finally granted, he went on to design most of the Russian telephone system. Later in his life, those aforementioned colleagues personally apologized to him for their actions, which were motivated by fear and politics. He died when I was only two years old (a decade after my great-grandfather), but my great-grandma admired him immensely, and would often talk about his life and exploits.
posted by cthuljew at 4:41 AM on November 5, 2012 [32 favorites]


I didn't do maths past high school, and I wouldn't even attempt most of these. But problem 3 was trivial, even for me, and I didn't need to solve it in the manner that was indicated at the end of the sheet. But perhaps that was the point: Mix the easy with the fiendish, to keep students off guard.
posted by kisch mokusch at 4:47 AM on November 5, 2012 [1 favorite]


I'm trying desperately not to draw a similar line to a situation in the US, where it seems overwhelmingly obvious that supporters of one religion/political party/viewpoint are edging closer and closer every day to something this extreme.

It's a funny illustration of the difference between the US and the USSR. The filtering of jews from Moscow State was/is done so crudely that the injustice is obvious. But there is an enormous wall of filters between say, a kid from Dayton, Ohio and going to college at Harvard that we generally consider to come down to "merit."

Just as a point of comparison .25% of mathematicians in the US are black. We don't even allow black kids to think of themselves as mathematicians.
posted by ennui.bz at 4:49 AM on November 5, 2012 [6 favorites]


[I understand the urge to draw parallels, but it would be good if this did not turn into another U.S. politics thread, because, man we sure do have a helluva lot of those already, and maybe you guys could talk about U.S. politics there?]
posted by taz at 5:07 AM on November 5, 2012 [17 favorites]


But problem 3 was trivial, even for me
I'm not sure I understand your solution from the diagram alone, little squirrel. (Not saying it's wrong, just I don't follow the order and specifics of the construction.) Are all the circles in your construction congruent? Does one of the circles pass through both A and B? Does your construction place K at the midpoint of AB? If so, how would that work in the case where, say, side BC is shorter than half the length of AB?
posted by Wolfdog at 5:18 AM on November 5, 2012


But problem 3 was trivial, even for me, and I didn't need to solve it in the manner that was indicated at the end of the sheet.

Sorry, but so what? You, with nothing at stake in getting the answer right, got it right. I can promise that if you were one of the Jewish students in this story, you would likely have gotten it wrong even if you got it right.

But perhaps that was the point: Mix the easy with the fiendish, to keep students off guard.


The point was to keep Jews out. It wasn't to keep them off-guard; they were set up to fail.

There was a story a not long ago about Emory University's dental school, which, under one particular dean from the late 40s through the early 60s, simply flunked a portion of its Jewish students (even though they weren't actually flunking) so that there weren't "too many" Jews in its dental program.
posted by rtha at 6:55 AM on November 5, 2012 [1 favorite]


Up to a point (the point at which people start killing other people), we Americans should thank the Germans and the Russians for their antisemitic policies, at least when it came to math and science — there is no doubt in my mind that the Germans would have beaten us to the A-bomb, with disastrous consequences, had they not eschewed "Jewish Science" and scientists. We probably owe our post-war edge in science to the Russians for similar reasons.

An amusing illustration of this (marred only slightly by the fact that Heisenberg wasn't actually Jewish) may be found here.
posted by ubiquity at 7:14 AM on November 5, 2012 [1 favorite]


I understand the urge to draw parallels

I see what you did there.
posted by flabdablet at 7:38 AM on November 5, 2012 [3 favorites]


Sorry, but so what? You, with nothing at stake in getting the answer right, got it right. I can promise that if you were one of the Jewish students in this story, you would likely have gotten it wrong even if you got it right.

The story is at, least to some extent, about the method of discrimination as well as its existence. Discussing the method is relevant, and does not trivialise or dismiss the fact of discrimination. It's a sensitive subject, I understand, but I think assuming good faith is helpful.
posted by howfar at 8:07 AM on November 5, 2012


But the method was engineered to specifically exclude certain people. It's irrelevant that someone sitting at a computer in the comfort of their home or office or coffee shop can answer one question correctly.
posted by rtha at 8:43 AM on November 5, 2012


I think the difficulty with "problem three" is indeed that it seems to have an obvious answer, but justifying that answer under all cases is in fact quite hard.

But what do I know, I majored in logic and topology, all these diagrams therefore look much the same to me. ;-)
posted by lupus_yonderboy at 8:44 AM on November 5, 2012 [2 favorites]


"I think assuming good faith is helpful" - Why? Assuming good faith is just as biased as assuming bad faith.
posted by outlandishmarxist at 9:02 AM on November 5, 2012


Assuming good faith is just as biased as assuming bad faith.

The argument for the assumption of good faith in public discourse is not a logical argument but an ethical one. It is exactly analogous, in that sense, to the assumption of innocence in a court of law. The point is not that good faith is or is not probable in a give instance, the point is that productive public discourse rapidly becomes impossible if good faith is not assumed until proven otherwise.
posted by yoink at 9:29 AM on November 5, 2012 [8 favorites]


It's worth remembering that the whole reason we have vague university admissions criteria for "Well-Rounded Students," as opposed to just admitting the most academically qualified to top schools such as Harvard, is to keep too many Jews from enrolling.
posted by LastOfHisKind at 9:33 AM on November 5, 2012 [9 favorites]


at a gut level the thing I just don't get (clearly because I'm thinking about policies like this at a social and historical distance from the events) is why any institution, from a math department to a nation-wide government, which benefits immensely from intelligent personnel would deliberately dumb-down their ranks by denying amazing applicants due to nonsense factors like ethnicity.

but when I think about it, I see that in social decision-making like hiring or admissions people generally can't think clearly about what factors will obviously matter in hindsight; rather we give weight to a bunch of factors that would only matter if we were picking a buddy or a mate or a friend for our kids. case in point: skill-free lawyer michael brown as Lord of Fema. this is a really hard problem. strong institutions i think are ones with a culture that fetishizes intelligence and competence, which obviously brings its own problems.
posted by serif at 10:08 AM on November 5, 2012 [1 favorite]


But the method was engineered to specifically exclude certain people. It's irrelevant that someone sitting at a computer in the comfort of their home or office or coffee shop can answer one question correctly.

But it's a story about the method, about how it felt, what it involved. The fact that one problem was potentially soluble in a different context, without the unfairness of the "exam" actually is relevant to that. There is no reason to assume that the comment is meant to suggest that the "exam" was not in fact a tool of discrimination. If we can't talk about the matter in the fpp in a variety of ways we're not going to have a very productive discussion.
posted by howfar at 10:30 AM on November 5, 2012


We had, says this older guy, quotas against Jews in ivy colleges when I was in high school. Yale, for example, would not take in more than 10%, no matter how qualified applicants were. So too then in and around NY, where Jews finally had to open their own places to accomodate Jewish students...those schools (and hospitals) still exist, and are called City College and NYU
posted by Postroad at 11:15 AM on November 5, 2012


Hard problems with simple solutions are used to control graduate students in the present, too. See the book Disciplined Minds by Jeff Schmidt [amazon] [wikipedia].
posted by zeek321 at 11:24 AM on November 5, 2012 [2 favorites]


The fact that one problem was potentially soluble in a different context, without the unfairness of the "exam" actually is relevant to that.

But from the story, it seems clear that the author was able to solve many of the problems, not just the tricky looks-hard-but-is-really-easy one(s). I wasn't actually assuming bad faith on kisch mokusch's part; I was wondering why it mattered that someone (who admits to being bad at math, and who didn't try any of the other questions) could get one question right, in a context in which they are not being set up to fail. I can see that I come off as sounding pretty cranky, for which I blame the early morning hour, insufficient caffeine, and perhaps a thorough misreading of kisch mokusch's "tone."
posted by rtha at 12:14 PM on November 5, 2012


If they were so "talented" why should simple solutions evade them? This reads like axe-grindy revisionist history.
posted by mikoroshi at 1:14 PM on November 5, 2012


Um. What? Is there something "revisionist" about further documenting anti-Semitic practices in the Soviet Union?
posted by rtha at 1:16 PM on November 5, 2012 [1 favorite]


Yeah. That's a fairly surprising claim to pull out of nowhere, mikoroshi. It's pretty clear from the fpp that, as rtha said earlier, these students would be wrong no matter how right they were. The fact that Frenkel is now a maths professor at Berkeley should indicate that he was more than ordinarily "talented".
posted by howfar at 1:40 PM on November 5, 2012


I suspect mikorishi didn't read the first link in the FPP.

It didn't actually matter if you could get any particular question, or in fact every question right. If you were Jewish you were not going to pass the exam. Every other candidate would be given further questions as they solved the earlier ones; you would not. Examiners would nitpick your definitions. If it looked as though you were solving a question it would be taken away and you would be given a different one. Your proofs would be rejected on subjective grounds and you would not be allowed to appeal. It wasn't an unfair system, because that implies there was some way of succeeding. It was really just a filtering system to exclude Jews.

Tanya Kohanova's paper on the tricksy problems is here, linked to from her blog. Here's how she describes them:
Among problems that were used by the department to blackball unwanted candidate students, these problems are distinguished by having a simple solution that is difficult to find. Using problems with a simple solution protected the administration from extra complaints and appeals.
I should add that I, too, am surprised at his allegation of bad faith.
posted by Joe in Australia at 1:46 PM on November 5, 2012


If they were so "talented" why should simple solutions evade them? This reads like axe-grindy revisionist history.

One of the things math teachers do, particularly those responsible for teaching large classes covering basic concepts (ie, Jr High through Undergrad college level), is collect problems.

Once you've given a certain problem to hundreds or thousands of students at a certain level, you start to get a sense of which questions are easy, which are hard, which are moderate--which might be answered correctly by 999/1000 students at a certain level and which might be answered by only 1/1000 or 1/10,000.

So the fact that there are such lists of questions, easy, medium, hard, super-hard, and everything in between, and that people who teach these subjects know questions of every varying difficulty level and use them accordingly--why is this even a surprising thing in any way?

And in math (and probably many other subjects) there are indeed questions that are simple to pose, and yet very difficult to answer. This, again, to anyone who has done much mathematics is just a basic and well known fact.

And among those questions, which are simple to pose and yet very difficult to answer--would be correctly answered by, say, 1 out 10,000 entering math majors--some turn out to have very simple answers. This, again, is just a fact and one well known among people who study and teach math.

So what is interesting here is not that such questions exist--easy to pose, hard to answer, but with simple answers. What is interesting is that:

- People evidently collected such problems to use in this particular and strange way. As mentioned above, why not just set a quota? It's an interesting and strange use of highly advanced technical means to provide cover for base human machinations.

- The list of problems itself is something of an interesting curiosity. Questions that are easy to pose, very hard to answer, and yet have simple answers are something of a rarity, and a long list of them even more so.
posted by flug at 4:59 PM on November 5, 2012


If they were so "talented" why should simple solutions evade them? This reads like axe-grindy revisionist history.

The "ease" of the solution here I think means simple to write, like "x=3." The method of obtaining it may be very, very narrow (you're not going to stumble onto it, even with broad knowledge), or too complex to do on the spot, or well beyond what you have ever been taught.

Imagine another test, that of shooting an arrow at a target. The solution is obvious: the arrow is or is not in the target. The training to get the arrow into the target, however, is long and specific. If you've never trained for the problem of "arrow into the target," you're unlikely to be able to solve it on the spot.
posted by zippy at 6:30 PM on November 5, 2012


But from the story, it seems clear that the author was able to solve many of the problems, not just the tricky looks-hard-but-is-really-easy one(s).

Well, yes--I mean, that's exactly what this story was about. The problems were fiendishly difficult, they were given to him expecting that he would fail, he didn't fail, they rejected him anyway.

Most people (me, for instance, when I was entering my undergrad math program) would have been given one or two of the problems he solved, wouldn't have been able to answer any of them at all, would have been given a "fair" mark of zero for our zero accomplishment, and sent packing on our way. That was the purpose of the problems.

But here we have a guy who is both extremely adept at math and also happens to be hyper-prepared. And so he just chews right through a whole series of problems, any one of which would stump 99.99% of normal, intelligent, well-prepared students at this level.

Even on the problem where he was finally stopped, he had the line of attack all mapped out (inversion--info here for the curious)--one most students at that level wouldn't even have a clue about.

And still, after that rather amazing tour de force, they're just, "No admission for you!"

With apologies to kisch mokusch, I'm going to say that this doesn't solve problem #3 at all. It is certainly an example of a triangle where AK = KM = MC, and the circles show that this is so. But the question is to construct K and M using straightedge and compass and unless I'm missing something big and obvious, there is nothing in that diagram showing how K and M were constructed, and certainly nothing like a general method that will construct K and M for any given triangle. Which--again--is the problem to be solved.

For example, in the given example AM is perpendicular to CB, but that is definitely not true in the general case. So if the first step is 'construct AM perpendicular to CB' that's only going to work in this one specific case.

We're pretty safe continuing the discussion under the assumption that the problems really are fiendishly difficult by design.

posted by flug at 7:47 PM on November 5, 2012 [1 favorite]


flug and zippy, thanks for the explanations. My math skillz are good but I forget sometimes that greater minds prevail and context is important, as well. Basically, I gave this a cursory pass and there was more to understand, ya'll helped me see the bias inherent here, I appreciate it.
posted by mikoroshi at 9:49 PM on November 5, 2012 [2 favorites]


With apologies to kisch mokusch, I'm going to say that this doesn't solve problem #3 at all. It is certainly an example of a triangle where AK = KM = MC, and the circles show that this is so. But the question is to construct K and M using straightedge and compass and unless I'm missing something big and obvious, there is nothing in that diagram showing how K and M were constructed, and certainly nothing like a general method that will construct K and M for any given triangle. Which--again--is the problem to be solved.

Draw line AK (whatever you want).
Use compass to circle around K, using A to set the radius
Pick any point on the circle for point M
Repeat using M as the centre of the circle, using K to set the radius.
Use the ruler to extend AK and CM until they merge at B.

Does this explain it? Sorry, I thought the red line would sort of lead people through it.
posted by kisch mokusch at 2:54 AM on November 6, 2012


But from the story, it seems clear that the author was able to solve many of the problems, not just the tricky looks-hard-but-is-really-easy one(s). I wasn't actually assuming bad faith on kisch mokusch's part; I was wondering why it mattered that someone (who admits to being bad at math, and who didn't try any of the other questions) could get one question right, in a context in which they are not being set up to fail. I can see that I come off as sounding pretty cranky, for which I blame the early morning hour, insufficient caffeine, and perhaps a thorough misreading of kisch mokusch's "tone."

Well I didn't say I was bad at math, I just wrote that I didn't study it past high school. These questions are at a university level, which makes it difficult to judge how hard they are. When the post implies that the questions are "fiendishly difficult math problems with deceptively simple solutions that are nearly impossible to find", one is naturally inclined to look at them. I wasn't trying to set any "tone", I was merely surprised by the ease of one of the questions and so made a minor, pedantic point in response to a specific aspect of the fpp. You evidently think my comment was off-topic (I obviously disagree) and seem to wish that I focused on the "bigger picture", as though the discussion in this (or any other) post can be controlled by your reactions to comments you don't like much.
posted by kisch mokusch at 3:22 AM on November 6, 2012


Does this explain it?

Given that the problem as stated is
Given a triangle ABC, construct, using straightedge and compass, a point K on AB and a point M on BC, such that AK = KM = MC
the fact that your process constructs the triangle ABC makes it look to me like you've got the whole thing back-arsewards.
posted by flabdablet at 3:24 AM on November 6, 2012


Ah, well that would explain it!
posted by kisch mokusch at 3:36 AM on November 6, 2012


Polya's First Principle: Understand the Problem.
posted by Wolfdog at 3:44 AM on November 6, 2012


Aka read the actual question
posted by kisch mokusch at 4:00 AM on November 6, 2012


You might still have a chance at passing this thing. Are you Jewish?
posted by flabdablet at 4:20 AM on November 6, 2012


No, which I guess means my answer would've been accepted at Moscow University anyway.
posted by kisch mokusch at 4:54 AM on November 6, 2012


Da! We admire the skill with which you constructed your bogus construction! Welcome, comrade!
posted by flabdablet at 5:35 AM on November 6, 2012 [1 favorite]


You evidently think my comment was off-topic (I obviously disagree) and seem to wish that I focused on the "bigger picture", as though the discussion in this (or any other) post can be controlled by your reactions to comments you don't like much.

I didn't need you to focus on any one particular thing (it doesn't surprise me that people would focus on the actual math problems), but you seemed to just breeze right past the context. It was weird to me and I remarked on it.
posted by rtha at 5:36 AM on November 6, 2012


The problems in Tanya Khovanova's paper all have hints and solutions, which makes them a bit less fun to work on here, but I'm a bit surprised nobody has tackled the one spelled out in the OP, which is:
Given a circle and two points on the plane outside the circle, construct another circle passing trough those two points and touching the first circle at one point.
The hint is to use this (more here--if you read it and look through the examples, it gives more hints).
posted by flug at 8:20 AM on November 6, 2012


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