Graduate level Mathematics

juillet
Wed, 09 Oct 2013 09:46:37 +0000

Occam’s razor does not tell us to ignore hypotheses that require us to assume many conditions; it says that among competing hypotheses, the hypothesis with the fewest assumptions should be selected. The “among competing hypotheses” is the important part. In earlier times of research (for all fields, but especially fields like mathematics which have been studied for thousands of years) the solutions to our issues may have been simpler, but as life and the problems to which math is applied become more complex, sometimes all the hypotheses we have to choose from ARE quite complex themselves.

Just the opening to the Wikipedia artcile on Occam’s razor clarifies this: “One should proceed to simpler theories until simplicity can be traded for greater explanatory power. The simplest available theory need not be most accurate. Philosophers also point out that the exact meaning of ‘simplest’ may be nuanced.”

Also, most mathematics and statistics papers begin with assumptions. You need the assumptions to continue on with the reading and understand. Many times, the “assumptions” are scientific discoveries (by the authors or others) on which the current paper is built, and you need to understand them in order to finish reading.