At a purely structural level, I believe mathematics can have subtle political implications. For instance, statistics is concerned with patterns in the aggregate. Structurally, this has resonance with utilitarian philosophies ("the greatest good for the greatest number") and for big government approaches to problem solving.

On the other hand, one of the tenets of chaos theory is the large impact of small individual changes. Structurally, this has resonance with existential philosophies (the power of the individual) and with libertarian political impulses.

Going further back, we can draw a connection between the idealism of classical geometry and the corresponding idealism of a political system like Plato's Republic.

Of course, these correspondences are not exact or inevitable, but they do show that even mathematics is not entirely politically or philosophically neutral. And of course, we can further note that the world of mathematics --in terms of what gets attention, and what doesn't --is also inevitably political (as is every other area of human group endeavor).

Well, mathematical

modelscan be political, right? Climate change models, for example. But pure math ... let's see. Surely there was a huge dispute between the British and the Europeans regarding Newton versus Leibniz's priority in inventing calculus. But that's a priority dispute ... not about the math itself. Then of course there are the math pedagogy wars. New math, New new math, Common Core. But a dispute over pure math itself? Can't think of an example. Hitler considered relativity to be "Jewish physics." That's a sort-of example, but it's still not pure math. – user4894 – 2014-06-24T03:40:19.937@user4894 1) Here's your (attempted) example: http://en.wikipedia.org/wiki/Ludwig_Bieberbach#Politics 2) The Newton/Leibniz thing also caused the English mathematicians (right?) to stick to an unfortunate notation for a long time, I think.

– None – 2014-06-24T05:14:34.847It might be better to say that there can be mathematical models of political systems instead of calling those mathematical models political, because if, some other system (e.g. biological) can be modeled using the same math, than this is the same mathematical model, only with different names. – Danijel – 2014-06-24T05:22:13.077

@Watson Excellent link. I believe that is directly on point to OP. "German mathematics." – user4894 – 2014-06-24T05:23:58.350

How about single objective optimization vs. pareto optimization vs. feasible domain? Or that a concave function over a convex domain obtains its maximum at an extreme point of the boundary? Or the bang-bang principle and that stochastic strategies in games allow to control and smooth out the bang-bang behavior? (I think there are many more examples of this sort, just querying what sort of answer you are interested in here.) – Thomas Klimpel – 2014-06-24T08:23:09.737

@Klimpel:Its an exploratory question - I'm not sure what kind of answer is right here. But I'm talking about politics in the larger sense not political issues within mathematics or physics but intersecting with traditional political concerns - the state, race, religion, economics and power. – Mozibur Ullah – 2014-06-24T11:08:18.290

On that level 'the fair price' mechanism in financial mathematics, econometrics might be a possible area; but also I'm thinking of the mathematics being seen as a measure or epitome of objectivity/factualness/hardness as a political gesture of a sort. Can one argue with the numbers? – Mozibur Ullah – 2014-06-24T11:11:03.943

Bertrand Russell did a fair bit of math, politics and philosophy, but I'm not sure how they influenced one another. – Dave – 2014-06-24T16:05:42.030

Augustin Cauchy was political; he was a baron. ☺ – Geremia – 2014-06-25T02:41:00.533

I heard a talk a while back about how Jan van Heijenoort stopped being a Marxist after he read Engel's philosophy of mathematics, so there's an example of math gone bad to suit an agenda – sjmc – 2014-06-30T07:17:14.747