It's easy to politicize that. Abelians versus non-Abelians ;) Not all vector spaces will likely share the property seen there.184.108.40.206 23:34, 15 August 2013 (UTC)
Abelian means that ab = ba, but this distributive law is different. Both the distributive property and the Abelian property are assumed properties of numbers, i.e., accepted as true and used to prove more complicated properties. Non-Abelian examples of objects that "look" like numbers are not too hard to construct. One interesting example is where "a" abd "b" are rotating a book clockwise 90 degrees (a) and rotating the book forward 90 degrees (b). Start with the book facing you for reading and first do "a", then "b", which is written "ab". The result has the front of the book facing up. Now do "b" first, then "a", to get "ba". Now the binding of the book is facing up and the front of the book is facing to the right. So, "ab" is not "ba". The best I can think of for the distributive type of thing is for everything to make sense, except b+c is something for which multiplying by "a" is undefined.--DrMath 09:07, 22 November 2013 (UTC)
But what about cryptography? A mathematical topic, and hardly apolitical nowadays. However, I appreciate and enjoy Randall's sentiment about the purity of mathematics. 220.127.116.11 20:23, 17 January 2014 (UTC)
Politicize that? Easy. When you apply the same policies to a diverse group, the outcome differs from person to person. Just insert context and it can work in a wide range of situations. 18.104.22.168 02:12, 14 July 2014 (UTC)
Ways math can be, and often is, politicized:
- Politicians and government bureaucrats have imposed "New Math" of various types on children forced to suffer the public school system, several times.
- Don't forget the famous stories of legislators wanting to change pi to be equal to 3.0 like it is in the Old Testament, parodied on Usenet and by my favorite author in Stranger in a Strange Land.
- Mathematics is one of the biggest forms of lying that advocates of central planning use. There are lies, damned lies, and statistics.
- To expand on that last one, math is fundamentally little more than an expression of logic using a notation system as language. Many logical fallacies can be seen as mathematical fallacies. Essentially, a(b+c)=(ab)+(ac) can be complexified until it is very long and convoluted, but then tweaked so that it ceases to be true, and many will not notice the error at a glance. And this is what many verbal expressions of both formal and informal logical fallacies are essentially doing.
The Old Testament does not declare pi equal to 3.0; that's actually a common misconception (see paragraph 3).