How can maths sometimes flower under repressive regimes?

Above: Maryam Mirzakhani, the first-ever female Fields Medal winner, died on 14 July 2017. Click here for Stanford University’s obituary.

A friend in Australia wrote to me: “A female mathematician who was awarded the Fields Medal died recently [and she was of] Iranian descent. I have noticed even in Australia several highly skilled Iranian engineers etc. Despite all the problems in Iran, why does it produce such experts in these fields?”

Here are my thoughts.

In general, prosperity and civil liberties are the best conditions for good scientific work.

However, there are other factors.

The Nazi regime in Germany virtually destroyed German mathematics within a matter of months, although Germany had been the centre of world mathematics for over a century before 1933. But not all repressive regimes have the same effect.

In Germany, many of the leading mathematicians were Jewish, or left-wing or at least outspokenly liberal, or both, partly I guess because they had grown up in a world of relatively wide civil liberties.

Max Zorn, famous as the originator of Zorn’s Lemma, was not Jewish, but in later life (in exile in the USA, like most German mathematicians) had a raspy voice because of a throat injury received in street-fighting against the Nazis.

Maybe in part as a reaction to anti-German chauvinism from the victors of World War I (the Allied powers refused sponsorship to any international mathematical conferences involving German mathematicians for some years after 1918, and that blockade was broken only by mathematicians deciding to hold their international conferences without official money), the Nazis wanted to promote “German mathematics” as opposed to other nationalities’ mathematics.

Such chauvinism is fatal in mathematics. The milder form in which British mathematicians insisted on shunning Leibniz’s formulations of the calculus in favour of Newton’s, which continued until broken by a student revolt at Cambridge in the second decade of the 19th century, made British mathematics a backwater for a century and a half even while other sciences were flourishing.

Not all repressive regimes promote such chauvinism in such abstract areas of thought.

Mathematics did well in the Stalinist USSR, and under the fascistic regimes in Poland and Hungary between World War 1 and World War 2. Most of the Hungarian mathematicians did their best work in exile – as did Maryam Mirzakhani, who moved to the USA when she was 22 – but the Poles and Russians did it in their home country.

Some factors involved here:

1. If there is relative freedom in mathematics – because Stalin, or Pilsudski, or Horthy, or Ayatollah Khamenei, however authoritarian in other realms, do not get the idea of laying down the law in maths – then keen researchers may choose to go for maths, while in a freer country they might have gone for another field.

2. The Hungarian mathematician Paul Erdös suggested that Hungary might have done well in maths because – although it had well-established universities and good connections with a large diaspora, as Iran has – it was a relatively poor country (poorer then than Iran is now, and with a much smaller population, around 9 million then while Iran has 80 million now). Mathematics is a cheap science. Keen researchers who might have chosen another field in a country with greater resources maybe went for maths instead.

3. Contrary to popular image, mathematics is the most social of sciences. It is very difficult and rare to make progress in maths without daily conversation and argument with other mathematicians. Thus talented mathematicians tend to appear in clusters. Where you have a few, they attract more. Where they are scarce, they remain scarce.

Much (not all) of the extraordinary flowering of Polish mathematics between World War 1 and World War 2 was down to a group of mathematicians who met in one particular café in Lviv (now part of Ukraine). The leading role of Germany in world mathematics for a century and a half before 1933 was in large part (not totally) due to work done at Göttingen, a small university in a small town in central Germany. (Mid-19th century, its “Mathematics-Physics Seminars” still had only about 15 students).

Thus there is an element of “randomness” in where clusters of mathematical advance appear. They are not spread evenly in exact proportion to advantageous general circumstances.