When has pure mathematics been influenced by the social context of mathematicians? - MathOverflow

When has pure mathematics been influenced by the social context of mathematicians?

2012-07-01T09:14:07Z

I recently learned that the Moscow school of descriptive set theory (Egorov, Lusin, etc.) was deeply influenced by the religious movement of Name Worshiping in Russia, as recounted in Graham and Kantor's book "Naming Infinity". What are some other interesting and well-sourced examples of when the work of pure mathematicians has been influenced by their cultural/social context?

Answer by Nik Weaver for When has pure mathematics been influenced by the social context of mathematicians?

2012-07-01T13:49:22Z

Pure mathematics has never been influenced by "social context" in any meaningful way.

Answer by Omnitic for When has pure mathematics been influenced by the social context of mathematicians?

2012-07-01T14:03:29Z

Maybe an example can be the period of enlightenment. During the enlightenment period mathematics advanced a lot in part thanks to the new division of higher education in Paris. During this period many great minds like the three L`s (Lagrange, Laplace and Legendre) came up. As well as others such as Cauchy. This time period was also favored by the creation of the encyclopedia which contained many mathematical terms thanks to the work of d'Alembert.

Answer by Joseph O'Rourke for When has pure mathematics been influenced by the social context of mathematicians?

2012-07-01T14:06:40Z

Perhaps a case could be made for advances in cryptography in the last half-century as driven by the social context of increased need for information security. I have in mind zero-knowledge proofs, and, say, the PCP theorem (PCP=probabilistic checkable proof).

Of course one could reject this as not the work of "pure mathematicians." Neal Koblitz might serve as a counterexample?

Answer by Gerald Edgar for When has pure mathematics been influenced by the social context of mathematicians?

2012-07-01T16:57:44Z

How about this paper:

MR1648209 (99h:01029)
Dauben, Joseph W.
Marx, Mao and mathematics: the politics of infinitesimals.
Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998). Doc. Math. 1998, Extra Vol. III, 799–809.

Throughout the Cultural Revolution, Mao Ze-dong promoted Marxism and dialectics to encourage reforms in all fields of endeavor, including the sciences. In mathematics, this encouraged, as it had Marx, an appreciation (with criticism) of the infinitesimal calculus. For Chinese mathematicians, application of Abraham Robinson's newly created nonstandard analysis not only rehabilitated infinitesimals in a technical sense, but (when understood within an appropriate materialist framework) could be used to justify and promote two new fields of study in China---model theory and nonstandard analysis.

Answer by Zack Wolske for When has pure mathematics been influenced by the social context of mathematicians?

2012-07-01T19:38:02Z

Certainly probability falls under this scope. Cardano's secretive work on the subject was done to help him in his professional gambling career. Soon after that, Pascal and Fermat worked out the notion of expected values to solve the Chevalier de Méré's gambling question. See Anders Hald's "A history of probability and statistics and their applications before 1750."

Answer by Blake for When has pure mathematics been influenced by the social context of mathematicians?

2012-07-01T20:35:25Z

I think there's two related issues here. I've heard some sociological theories suggest that the answers we get in math are socially influenced. This is clearly mistaken, because math is a purely logical discipline: once you pick axioms (and a system of logic, to be pedantic), your answers are fixed. Similarly in the physical sciences, once you pick your experiment, you have no control over the outcome.
The exception to this of course is when people disregard the strict rules of logic. Example: philosophers used to believe that Euclidean geometry was somehow 'automatic' (see e.g. Kant). There was a mathematician whose name escapes me who came extremely close to developing non-Euclidean geometry, but, after proving a number of theorems about it, concluded that there was a contradiction because the system was 'absurd' or something like that. But this is an example of somebody doing math 'wrongly.' Math done 'right' has consequences that are not socially influenced.

On the other hand, there's the question of what we choose to study. That is obviously going to be influenced by social and personal factors. For example I recall some stuff about how the ancient Greeks liked to think geometrically, whereas the ancient Chinese liked to think algebraically (and I think the ancient Arabic mathematicians as well). You can see this in the types of discoveries that they made. There are studies out there on what sorts of differences made this happen; I think there's even someone who conjectures that Westerners still tend to think more geometrically, and Easterners more algebraically, or something like that.