What parts of a pure mathematics undergraduate curriculum have been discovered since 1964?1964?

What parts of an undergraduate curriculum in pure mathematics have been discovered since, say, 1964? (I’m choosing this because it’s 50 years ago). Pure mathematics textbooks from before 1964 seem to contain everything in pure maths that is taught to undergraduates nowadays.

I would like to disallow applications, so I want to exclude new discoveries in theoretical physics or computer science. For example I would class cryptography as an application. I’m much more interested in finding out what (if any) fundamental shifts there have been in pure mathematics at the undergraduate level.

One reason I am asking is my suspicion is that there is very little or nothing which mathematics undergraduates learn which has been discovered since the 1960s, or even possibly earlier. Am I wrong?


A lot of the important basic results of complexity theory postdate 1964. The most important example that comes to mind is that the formulation of NP-completeness didn’t occur until the seventies; this includes the Cook-Levin theorem, which states that SAT is NP-complete (1971) and the identification of NP-completeness as something that was important and common to many natural computational problems (Karp 1972). These results certainly appear in an undergraduate course on computability and complexity.

Ladner’s theorem, which would at least be mentioned in an undergraduate course, was proved in 1975.

(In contrast, the basic results of computability theory date to Turing, Post, Church, and Gödel in the 1930s.)

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