There is a newly published paper by George Borjas and Kirk Doran, entitled “The Collapse of the Soviet Union and the Productivity of American Mathematicians”, here is the abstract:

It has been difficult to open up the black box of knowledge production. We use unique international data on the publications, citations, and affiliations of mathematicians to examine the impact of a large, post-1992 influx of Soviet mathematicians on the productivity of their U.S. counterparts. We find a negative productivity effect on those mathematicians whose research overlapped with that of the Soviets. We also document an increased mobility rate (to lower quality institutions and out of active publishing) and a reduced likelihood of producing “home run” papers. Although the total product of the preexisting American mathematicians shrank, the Soviet contribution to American mathematics filled in the gap. However, there is no evidence that the Soviets greatly increased the size of the “mathematics pie.” Finally, we find that there are significant international differences in the productivity effects of the collapse of the Soviet Union, and these international differences can be explained by both differences in the size of the émigré flow into the various countries and in how connected each country is to the global market for mathematical publications.

The link is here, possibly gated, there are earlier and ungated versions here.

For the pointer I thank Stuart Harty.

‘We use unique international data on the publications, citations, and affiliations of mathematicians to examine the impact of a large, post-1992 influx of Soviet mathematicians on the productivity of their U.S. counterparts.’

Fascinating – but how does one actually measure ground breaking work (Mandelbrot’s work into fractal geometry comes to mind as an example) by comparing the production of publications? Or to put it another way – does the massive citation of the sort of work Turing did a sign of ‘productivity?’

Except, of course, that much of his work remained classified for decades. Which is equally true of much of the mathematical work sponsored by both the American and Soviet government during the cold war era. Illutrated by the history of public key cryptography –

‘In 1997, it was publicly disclosed that asymmetric key algorithms were secretly developed by James H. Ellis, Clifford Cocks, and Malcolm Williamson at the Government Communications Headquarters (GCHQ) in the UK in 1973.[4] These researchers independently developed Diffie–Hellman key exchange, and a special case of RSA. The GCHQ cryptographers referred to the technique as “non-secret encryption”. This work was named an IEEE Milestone in 2010.[5]

An asymmetric-key cryptosystem was published in 1976 by Whitfield Diffie and Martin Hellman who, influenced by Ralph Merkle’s work on public-key distribution, disclosed a method of public-key agreement. This method of key exchange, which uses exponentiation in a finite field, came to be known as Diffie–Hellman key exchange. This was the first published practical method for establishing a shared secret-key over an authenticated (but not private) communications channel without using a prior shared secret. Merkle’s “public-key-agreement technique” became known as Merkle’s Puzzles, and was invented in 1974 and published in 1978.

A generalization of Cocks’s scheme was independently invented in 1977 by Ron Rivest, Adi Shamir and Leonard Adleman, all then at MIT. The latter authors published their work in 1978, and the algorithm appropriately came to be known as RSA. RSA uses exponentiation modulo, a product of two very large primes, to encrypt and decrypt, performing both public key encryption and public key digital signature. Its security is connected to the (presumed) extreme difficulty of factoring large integers, a problem for which there is no known efficient (i.e. practicably fast) general technique. In 1979, Michael O. Rabin published a related cryptosystem that is provably secure, at least as long as the factorization of the public key remains difficult – it remains an assumption that RSA also enjoys this security.’

http://en.wikipedia.org/wiki/Public-key_cryptography#History

So anyone looking at the history of ‘productivity’ of the mathematics of public key encryption in 1995 would have been incorrect in their fundamental assumptions of its invention and its citations. To think that this would not be the case in a post-Soviet world is naive – the KGB and other state organs were renamed, they did not disappear, and the Russian government would not allow its best secret researchers to resettle in the West.

Hmm, so a similar argument might wonder if the NSA hired extra US mathematicians after the 1992 influx, and if that’s where any larger size of the mathematician pie went, besides mathematicians in industry.

Isn’t the number of publications across the entire field going to be pretty independent of ‘productivity’? It seems like the forces that will drive journals to publish more papers (or for more journals to open up) are more likely to be funding related, which I don’t expect an influx of soviet mathematicians to influence one way or the other. To me all of this appears to show is that in a field with a fixed number of jobs, opening up the field to new entrants is bad for existing entrants. Big surprise. Fortunately, most of the economy doesn’t work this way.

Also, even in such a field with a fixed-number of jobs, what might be bad for existing entrants might be good for the field as a whole.

And mathematicians, like other academics, remain very pro-immigration, because what’s good for the field is important. Since you really have to believe in the field to go into academia.

“because what’s good for the field is important.”

In Russia, they don’t have blackboards and chalk?

I’m sure there are other specialties (e.g., sub-atomic particle experimentation) where relocating the best brains from a country that can’t afford the latest atom smasher to one that can would make a positive improvement in the field’s global productivity, but math seems at the opposite end of that spectrum.

Not surprisingly, therefore, Russian mathematicians in Russia were doing work that was good for the field as a global whole. Relocating them to America, however, apparently didn’t do much for global math productivity.

If they are using number of publications to measure productivity that’s a silly metric.

Also, even assuming global productivity unchanged it’s surely a plus for American mathematics to have the best Russian brains come in? As an American, I’d rather have the top-notch Russians prove theorems on my blackboard with my chalk.

I don’t see what’s so non-obvious about trying to collect the best talent in ones own organization.

Clearly, importing Jewish atomic physicists in the 1930s and Nazi rocket scientists in the 1940s was crucial to America developing a world-intimidating ICBM force in the 1950s.

How is a total collapse of one of the most active mathematical cultures in the world supposed to be good for the field as a whole? Soviet scientists were not rich by absolute standards, but they were incredibly well off by relative standards. They had a lot of talent to draw from, and they made a priority of developing it. Then the system collapsed, and everybody who could get out did get out.

Suppose the state of California went bankrupt tomorrow and abruptly closed the entire UC system. Would you expect the field as a whole to benefit or suffer?

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