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Based on Maggie Koerth-Baker's article, "What do Christian fundamentalists have against set theory?", it seems there are some parts of culture which put some restrictions on math education.

Historically, there were and there are several types of such limitations on the empirical sciences and philosophy. For example, in several countries, some parts of research on genetic engineering, particularly those which are related to cloning humans and animals, are not legal for ethical reasons.

My question is about current or historical examples of such cultural restrictions on research in particular fields of mathematics or mathematics in general. Please introduce references for each example.

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    $\begingroup$ In my experience with Christian fundamentalists, the answer to the title of that article is simply: "nothing". $\endgroup$
    – James S. Cook
    Aug 1, 2014 at 3:33
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    $\begingroup$ The movement "Deutsche Mathematik" could fit. I will try to give an actual answer later. $\endgroup$
    – quid ♦
    Aug 3, 2014 at 11:11
  • $\begingroup$ @quid Good example! It was one of my motivations to ask this question. I am waiting for your answer. $\endgroup$
    – user230
    Aug 4, 2014 at 23:12
  • $\begingroup$ Don't forget the language barrier as a cultural limitation. This is why Esperanto was created. $\endgroup$
    – Mike Jones
    Aug 24, 2014 at 15:08
  • $\begingroup$ A weird thing about what is described in that article is that to my knowledge, Cantor actually was a pious (Lutheran) Christian, saw his set theory as an inquiry into the divine, and occasionally stressed what he saw as its theological implications. (Still, that's arguably not the weirdest thing going on there.) $\endgroup$
    – Torsten Schoeneberg
    Sep 15, 2018 at 20:08

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A quintessential example of a cultural clash over math education in US schools, I would say, is the entire Math Wars, an ongoing struggle over standards and pedagogy in K-12 schools. It is a struggle of curriculum reformers trying to bring research-based innovations of mathematics thinking, learning, and teaching over the last three decades into schools facing opposition from some parents and mathematicians who prefer a traditionalist approach relying on outdated (or, in some cases, just frankly unscientific) understandings of a whole host of issues surrounding education.

For a thorough introduction, I recommend Schoenfeld's (2004) writing on the subject. It's 10 years old, and some people speak about it as though it is in the past (many people have tried to declare "math wars" as over) but I think some of the arguments over the Common Core State Standards have made it clear just how much Math Wars are still a reality.

The question as titled and asked is a little muddled (education is missing from the wording of the question in yellow, though prominent in the title). This addresses the (I think) intended question of an example of culture placing a restriction on mathematics education. In short: research findings conflict with traditional cultural values, resulting in some people rejecting the science and adhering to tradition.

Cited:

Schoenfeld, A. H. (2004). The Math Wars. Educational Policy, 18(1), 253–286. doi:10.1177/0895904803260042

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Perhaps this historical example fits the bill:

Khovanova, T., & Radul, A. (2012). Killer problems. American Mathematical Monthly, 119(10), 815-823.

The piece was published earlier on the arXiv as Jewish Problems. Here is the abstract:

This is a special collection of problems that were given to select applicants during oral entrance exams to the math department of Moscow State University. These problems were designed to prevent Jews and other undesirables from getting a passing grade. Among problems that were used by the department to blackball unwanted candidate students, these problems are distinguished by having a simple solution that is difficult to find. Using problems with a simple solution protected the administration from extra complaints and appeals. This collection therefore has mathematical as well as historical value.

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  • $\begingroup$ I suppose the downvoter might complain that the question was about cultural obstructions to the content of mathematics. Notice, it was not that Soviet officials could not tolerate math, the problem was they could not tolerate Jews in math. (I did not downvote) $\endgroup$
    – James S. Cook
    Aug 1, 2014 at 4:20
  • $\begingroup$ @JamesS.Cook Since the notion of an "undesirable" here is clearly a cultural construction, it certainly seems to me that this is an example of a historical/cultural restriction on mathematics/mathematics education. Still, an interesting thought; perhaps the down-voter will elucidate further. $\endgroup$
    – Benjamin Dickman
    Aug 1, 2014 at 4:39
  • $\begingroup$ Voting is anonymous. You don't get to demand that people de-anonymize themselves by explaining their votes. (I didn't vote at all.) $\endgroup$
    – David Richerby
    Aug 1, 2014 at 8:39
  • $\begingroup$ @DavidRicherby I agree with your first two sentences; indeed, there is no "demand." However, a down-vote indicates that someone (in this case, two someones) takes issue with the answer. If I knew why, then I could try to improve my response; at present, I have no insight into the objection! (As to it being "anonymous": It was not difficult to identify the latter down-voter; the -1 change on August 1st means sorting users by monthly reputation allowed me to see precisely "who" dved. I just don't know why...) $\endgroup$
    – Benjamin Dickman
    Aug 1, 2014 at 9:18
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    $\begingroup$ @BenjaminDickman upon reading the question once more, I see now the wording allows to interpret either in terms of forbidding a math topic to be taught (my original thought on the question given the link at the start) or forbidding a particular community pursue work in math (your answer). $\endgroup$
    – James S. Cook
    Aug 1, 2014 at 20:44

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