Graduate level Mathematics

e130478
Tue, 08 Oct 2013 23:02:43 +0000

Every now and then I will scan over the abstract of a research paper published by a notable academic of x,y,z discipline in an attempt to learn something new. I do this mostly because I’m interested in the idea of what it is academics truly spend their time doing. Typically this is a beneficial exercise.

However, one discipline whose work consistently grates my attention is mathematics. Half the time I get through one page of a massive wall of cryptic text just to put the paper down in absolute confusion. Typically the author asks me to assume a great order of indecipherable assumptions before continuing into the paper’s introduction, whereupon I refuse and mentally capitulate.

This property of the discipline makes me wonder greatly. Occam’s Razor tells us to ignore those hypothesis which require us to assume many conditions and favor those which do not. I tend to think there is a lot to say about the maxim, even as it applies to the complex realm of Mathematics. Some of the most dynamic and powerful structural arguments have also been the most intuitive. In economics, for example, the Taylor Rule, a simple polynomial expression, has been speculated to be the driving algorithm that determines the course of core monetary policy. In biology, simple exponential functions have led to a profusion of insight into how population growth effects nature, etc.

This is just my feeling. I would like to hear the opinions of those who might know better.