Posted last two times[1][2] one of these stories came around, comment applicable here:<p>As a preamble there most definitely existed anti-semitism in Soviet Union. I am a Russian living in the US with Jewish family in Russia. This is a throw away account.<p>With that said, stories of anti-semitism told by Russian Jews in US should not be taken at face value. These folks are subject to a very strong selection bias. Most of them came to the US as refugees who were recognized by the US State Department as being discriminated against for being Jewish in USSR/Russia. Secondly they have interest in maintaining the story anti-seminitism because it validates their narrative and could potentially help their relatives immigrate to the US.<p>Additionally many stories of anti-semitism that I heard were something a non-jew would experience as well but attributed to anti-semitism. As a personal example, I was at first denied admission to a specialized school in very late Soviet period. They eventually let me in because my mother found out that I had the highest score on the entrance exam of any one. Their excuse was that they had to let the kids who were in the paid summer program at the school first and now the class was full. A Jewish kid's parents would have been told they already have too many Jews in the advanced program. Both cases are just the admissions persons asking for a bribe.<p>[1] <a href="https://news.ycombinator.com/item?id=4752047" rel="nofollow">https://news.ycombinator.com/item?id=4752047</a>
[2] <a href="https://news.ycombinator.com/item?id=5340553" rel="nofollow">https://news.ycombinator.com/item?id=5340553</a>
This is a well-known fact, actually.<p>My math teacher in Lithuania mentioned that back in his days (50-s) it was practically impossible for a non-Jewish student to get into any math- or physics-related faculty: Jewish families had a very strong multi-generational tradition of both in-school and additional education. He also said he was the only non-jewish in his group in Moscow State University that year.<p>So at some point it was decided to, ehm, discriminate jewish - they were supposed to be a minority in all the main universities/institutes, under 10%, I think, although this is not a precise number.<p>Note that I don't advocate anything or anyone, this is just the way it was.
In the early 1900s, Harvard was on track to be a Jewish dominated university, and they made the (then common) decision to limit Jewish enrollment.[1] In reading that article, I learned that even Richard Feynman was affected by Columbia's quota, and ended up at MIT instead. (Go MIT!) Non-meritocratic quotas exist to this day at all elite US universities, with one exception: Caltech.[2]<p>[1] <a href="https://en.wikipedia.org/wiki/Jewish_quota" rel="nofollow">https://en.wikipedia.org/wiki/Jewish_quota</a><p>[2] <a href="http://www.mindingthecampus.org/2010/12/why_caltech_is_in_a_class_by_i/" rel="nofollow">http://www.mindingthecampus.org/2010/12/why_caltech_is_in_a_...</a>
A similar story[1] was told by the mathematician Edward Frenkel. He was a Jew in Russia and took an exam with "hard" math problems designed to prevent his admission into Moscow State University. It's possible the problems shown in the paper are the ones Frenkel saw since he was a teenager during that time period. (The Cornell paper does not specifically mention Frenkel.)<p>[1]<a href="http://www.amazon.com/Love-Math-Heart-Hidden-Reality/dp/0465064957" rel="nofollow">http://www.amazon.com/Love-Math-Heart-Hidden-Reality/dp/0465...</a>
Having graduated math-oriented Moscow high school that, on one hand, had a lot of graduates go to the math department (roughly translated as MechMath) of MSU (usually, most of the math class alumni goes there), and on the other, had untypical amount of jewish students, these rings so close to home. Hell, I think they actually gave us most part of these problems in math lessons.<p>Edit: another curious source<p>> Mikhail Brin decided to study mathematics instead, and was offered a place although the entry exams for Jews were sat separately, in rooms that were notoriously known as "the gas chambers."<p><a href="http://www.haaretz.com/jewish/2.209/google-co-founder-my-family-left-russia-because-of-anti-semitism-1.246045" rel="nofollow">http://www.haaretz.com/jewish/2.209/google-co-founder-my-fam...</a>
Jews, and many other minority groups, form tight communities were they look out for each other help each other out. So Jewish businesses and organizations tend to discriminate in hiring, recommendations, etc. Happens all the time, very overtly. Since at this point Jewish organizations and businesses in the US are long established and powerful in many areas, this anti-gentile discrimination is problematic to society at large. But it's a type of discrimination that is rarely mentioned and complained about.
While we're discussing this subject, and hoping to shine a bright light away from all the negativity, the solidarity of the Jewish people is amazing and unequalled! Jews seem to show great compassion and provide unconditional help for their own.<p>There's wisdom to be gleaned from this I'm sure...
A bit preachy, sorry: Everyone frowns on discrimination by others, people in different times and/or places, but much more important than criticizing others is to do the right thing ourselves. We need to look in the mirror (myself included!).<p>To choose a prominent example, open discrimination against people who believe in Islam is socially acceptable in much of Western society. How stupid can we be? We're blatently repeating the exact same mistakes as before, the exact thing we frown upon. Some will say, 'but this time is different; we have a valid reason' - which of course is exactly what people said all those previous times, it's just a justification for acting out on fear (and it's just dumb reasoning). The old fears and rationalizations look absurd to us now but seemed just as real at the time as our current fears. Ours will look just as absurd in the future.<p>Why can't we just apply the simple, blanket rule? Don't discriminate; prejudice is cruel, unjust and unfair, and it results in very bad things. It provides no real benefits. It always ends up on the wrong side of history; the accomplishments and heroes we honor are never hate and the hateful, but those that stood up against them. When our descendents look back at us, which side will we be on?
Similar events happened in London in the mid-19th century. University College London (UCL), now one of the best colleges in the University of London, was founded to allow students entry through non-religious means. Consequently, it was the first college in the university to allow equal entry to both Jews and women.
Without the alternative easier exams to compare with and the grading scheme that were used, these problems do not mean much regarding the discrimination that took place. It is quite common to give good grades even when the exercises have not been solved completely, but interesting thoughts and ideas have been exposed, especially in mathematics.<p>Off topic, but regarding problem 2, a math professor once told me of a PhD student who started studying this kind of functions. He spent some time to discover their many interesting properties, until the professor made him understand why these functions were so regular, and that he had actually wasted his time. Funny to see this again.
I wonder why are Askhenazi Jews apparently more intelligent on average... seems that genetics is the main factor, not culture, but I can imagine research in this area is discouraged and controversial.
If you read the book Perfect Rigor, about Grigori Perelman (solved the Poincare Conjecture - won the fields metal, but would not accept the 1MM dollar prize on principle) they tell multiple tails of anti-semitism in the Russian math departments at the time. According to the book, Perelman was basically really lucky to be born when he was and where he was, and that is really the only reason he was given a chance to get the education he got. The world is obviously a better place for guys like this.
I found a site with some more background on this subject <a href="http://www.tanyakhovanova.com/coffins.html" rel="nofollow">http://www.tanyakhovanova.com/coffins.html</a>
Some answers:<p><pre><code> 1. Solve for positive x:
x (8 sqrt(1 - x) + sqrt(1 + x)) <= 11 sqrt(1 + x) - 16 sqrt(1 - x)
</code></pre>
The upper bound is clearly x=1 because the square roots cease to exist for x > 1 and and substituting in x = 1 - epsilon^2 gives to first order (8 e + 1) <= (11 - 16 e) which works because 8 <= 11. Does this thing have a root in [0, 1]?<p>The inverse of y = sqrt(1 + x)/sqrt(1 - x) is with some work x = (y^2 - 1)/(y^2 + 1) so when we divide through by sqrt(1-x) which we know now to be positive, and replace the above, we find:<p><pre><code> (y^2 - 1)/(y^2 + 1) * (8 + y) = 11 y - 16
</code></pre>
Expanding out we're looking for a root of<p><pre><code> -10 y^3 + 24*y^2 - 12 y + 8 = 0
</code></pre>
Dividing by -2 to normalize somewhat:<p><pre><code> 5 y^3 - 12 y^2 + 6 y - 4 = 0
</code></pre>
At this point I almost gave up (since it's a cubic and I had no guarantee that x was rational) but got lucky, I started trying positive integers to see where this transitions from negative (y=0) to positive (5y^3) and accidentally found that y=2 solves the equation. Sending it back through I find 3/5, so assuming that it doesn't double back somewhere in the interval [3/5, 1] that's the interval that we're looking for. Phew!<p><pre><code> 2. Find all functions F(x) : R -> R having the propery that for any x1 and x2,
F(x1) - F(x2) <= (x1 - x2)^2.
</code></pre>
Yeah, if you're just entering a university you're probably not going to get this one. Rewriting x1 as x + dx, x2 as x, then this says F(x + dx) - F(x) <= dx^2. With some limits and the Squeeze theorem, this restricts the functions to be differentiable with derivative zero, so they are constant functions. By inspection that is not just necessary but also sufficient.<p><pre><code> 3. Given a triangle ABC construct with a straightedge and compass a point K on
AB and a point M on BC such that AK = KM = MC.
</code></pre>
This seems in general impossible except for some very specific triangles -- is that true? For example if |AB| = 2 and |BC| = 1, it seems that the only point on AB which could possibly be a candidate for K is the midpoint, with M being B. But the only way that the distance from K to M is the same is if BCK is an equilateral triangle, which requires furthermore that the angle BAC is 60 degrees, no?<p><pre><code> 4. Solve 2 cubert(2y - 1) = y^3 + 1 for real y.
</code></pre>
So y = 1 is an obvious solution. Cubing both sides we get<p><pre><code> y^9 + 3y^6 + 3y^3 - 16 y + 9 = 0
</code></pre>
Then doing polynomial division by y-1 I get<p><pre><code> y^8 + y^7 + y^6 + 4 y^5 + 4 y^4 + 4 y^3 + 7 y^2 + 7 y - 9.
</code></pre>
At this point I got stuck and turned to automated tools, which say that this is factorizable as:<p><pre><code> (y^2 + y - 1)(y^6 + 2 y^4 + 2 y^3 + 4 y^2 + 2 y + 9)
</code></pre>
Graphing the right hand side it seems to be consistently positive, so that just leaves the left hand side, which is -1/2 +/- sqrt(5)/2. That's pretty difficult.