First, thanks Dorothy. I hadn’t read the epilogue as I haven’t gotten my hands on the actual book, but rather just the official, 33 page book excerpt from the American Mathematical Society website:

http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf

and what I could see via the Google Books link I mentioned in #65.

But checking Amazon’s “Look Inside” feature, I’ve now been able to read the first page of the epilogue.

I’m not sure if later pages of the epilogue mention what happened between age 7 and working adulthood, but my take on the fact that only the children of the mathematicians ended up in math-related careers is as follows:

a) Overall, I’m not surprised. The children of mathematicians, presumably, got a lot of direct and indirect encouragement and education at home in math over and above the unusual experience of participating in a “math circle” while in preschool.

b) The bigger question for me — and, given the limited amount of the epilogue I can read, I’m not sure it’s one the epilogue answers — is whether most of the children eventually obtained an accurate sense of “true” mathematics (say, math of the sort one would find in the usual analysis, algebra, and geometry courses for college undergrads majoring in math) before they chose their careers. I say this since I myself am fine with my potential progeny choosing careers far away from math/CS/theoretical physics/etc. I just want them to have an accurate sense of the wonders of these fields before they decide to devote their lives elsewhere. (Additionally, though perhaps needless to say, I wouldn’t trust 99.9% of primary and secondary schools in the USA — be they public or private — to instill that sense.)

In closing, let me answer (to the best of my ability given the limited portion of the book I’ve been able to read) your question, Michael, about which child ended up where:

** Of the boys in the math circle **

Dima (the author’s son) — Indeed becomes research faculty in mathematics at one of the Universities of Paris

Andy (presumably revealed to be the son of a mathematician friend of the authors at some point, yes Dorothy?) — Got a degree in international economics and became a quant at a financial trading firm

Pete (presumably revealed to be the son of a non-mathematician at some point, yes Dorothy?) — Majored in Japanese as an undergrad and became an interpreter for a time in Japan, but now back to grad school for a degree in psychology

Gene (mistyped in the epilogue as “Jane” by the translator*, at least in the printing seen on Amazon, and also presumably revealed to be the son of a non-mathematician at some point) — Works with a tourist agency for domestic Russian tours of Moscow and St. Petersburg

[**Perhaps neurotically overcomplete sidenote: Rather than using a direct transliteration of the Russian names, the translator used American equivalents. Thus, Evgenii became “Gene”. But the author’s daughter, Evgenia (“Jane”) is also in the math circles. The translator’s mistake likely arose because both Evgenii and Evgenia in Russian get the nickname Zhenya.*]

** Of the girls in the math circle **

Jane (the author’s daughter) — Got a PhD in film studies

and, alas, that’s where Amazon’s preview of the epilogue ends, and so I don’t know the eventual careers of her friends Sandy, Sasha, and Dinah are revealed.

]]>technology is developing much too fast for any “academic research” to be reliable re children’s interaction with it. Quad-core processors allowing VERY smooth interaction with a tablet screen have arrived in just the last two years for example, making a qualitative difference to the experience.

Obviously children should also interact with many other real children – that’s what public schools enable. But simplistic dictates like “no more than 2 hours screen-time” are just silly – especially when the tech experience is evolving so rapidly.

What should they do instead? Play with wooden toys?

]]>I, however, am instantly identifiable as a native English speaker in the same way that we instantly picked out the German or Russian bad guys in 80s Hollywood action movies.

On the other hand, I help the kids with their Norwegian homework. It seems that my vocabulary is better in some areas, and my grammar is generally better than the kids’.

I did not learn by “immersion”, I went to classes at night for three years. I think people learn in different ways, and a pedagogical classroom approach was the right one for me. Immersion got me from 80% to where I am now (95?) but it didn’t work until I could grasp a lot of what was flying by.

]]>Among the children who didn’t go on to do math or math related things, were there any discernible correlations or patterns in the work they did end up doing?

]]>I think I can explain things briefly as follows:

A) The stratification of the positive Grassmanian:

Indeed there are two ways to look at it, a) as the matroidal stratification reduced to this part of the grassmanian; b) Start with the common refinement of Subert cells with respect to a cyclic family of permutations (for the whole grassmanian this lies between the shubert stratification and the matroid one). Then restrict it to the positive Grassmanian.

B) The amplituhedron:

Recall that every polytope is a projection of a simplex and projections with respect to totally positive matrices gives precisely the cyclic polytope.

Now replace the simplex by the positive grassmanian: The amplitutahedron is a projection of the positive grassmanian based on a totally positive matrix. (So it is a common generalization of the positive grassmanian and the cyclic polytope.)

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