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I've only heard personal anecdotes about perceived stimuli and economic support to research in pure mathematics in the 1960s, presumably tied to the space race of the time. Is this something we can claim to have been planned by the governments engaged in the race?

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    $\begingroup$ There was a great deal of funding for all sorts of research in the 1960s. The most likely overarching explanation was the need to maintain economic power and ideological legitimacy in the face of the Soviet system, which led Western nations to engage in massive amounts of redistribution and government-directed economic activity, including massive investments into knowledge production of all possible kinds. $\endgroup$ – Steve Apr 15 at 16:11
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    $\begingroup$ (U.S. based comments) There was also a huge increase in numbers of college students in the years after WW 2, resulting in a huge increase in the number of faculty needed, along with a simultaneous increase in non-academic opportunities (even pure mathematicians were being hired by industry). The bottom fell out around 1970 or so, with the worst job situation (for pure mathematics) probably since the depression years and on par with the dismal situation in the 1990s. $\endgroup$ – Dave L Renfro Apr 15 at 17:52
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    $\begingroup$ The space race was acompanied by a development in all fields of science because of complexity of space ships. There was also increase in demand for computational power in order to run complex models, analysis and evaluations. This ignited interest in theoretical limits of computers, algorithms complexity and how to effectively solve tasks. All these paved the way to theoretical computer science, new field of a mathematics. However, this seems as natural side-effect, not originally planned by the government. $\endgroup$ – Martin Vesely Apr 15 at 21:14
  • $\begingroup$ No. Further, any "incentive" could be personal, departmental, or government funding-based. What is your real question? $\endgroup$ – Carl Witthoft Apr 16 at 14:21
  • $\begingroup$ Related: hsm.stackexchange.com/q/7195/4251 $\endgroup$ – Rodrigo de Azevedo May 12 at 15:43
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Indeed, funding of mathematics, together with other science and engineering fields experienced a sharp increase between 1957 and 1970. The number of PhD awarded in these fields in USA tripled during this period, and this was the fastest growth for any period after WWII.

https://www.nsf.gov/statistics/2018/nsf18304/static/report/nsf18304-report.pdf

But the "race to the Moon" was not the primary reason. The primary reason was arms race during the Cold war. The race to the Moon itself, is a byproduct of this arms race. This happened both in Soviet Union and in the US. Soviets demonstrated their success in ICBM development by launching the first artificial satellite in 1957. This made an enormous impression on American public, and the "space race" began. Much of mathematical research at that time was funded by the US Navy and Air Force, in the same way as it is funded nowadays by NSF. In Soviet Union itself, the sharp increase in S and E research was triggered by the race to make a nuclear bomb, and then it was stimulated by development of new weapons, like ICBM and submarines.

I am a "pure mathematician", and my career began in Soviet Union in the 1970s. Everyone around was strongly encouraged to make some contribution to research directly related to submarine warfare at that time.

Edit. In general, on my opinion, the arms race strongly benefited mathematics, especially in Soviet Union. They made the careers of professor and researcher very attractive by relatively high salaries. They developed a system of mathematical olimpiads to select talented children. The competition for students to enroll in the best math departments was high. Some top mathematicians were chosen to advise the government, and could influence some decisions. For example, the initiative of the space exploration came from scientists directly involved in defense research. The ideological interference into physics and mathematics was minimal (as compared for example to biology, and related medical and agricultural sciences, not even mentioning humanities which were under complete ideological control). And so on.

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