Reasons for mathematics in science

It is not surprising that there should be issues in science to which mathematics is relevant, since until about a century ago the whole purpose of mathematics was at some level thought of as being to provide abstract idealizations of aspects of physical reality (with the consequence that concepts like dimensions above 3 and transfinite numbers were not readily accepted as meaningful even in mathematics). But there is absolutely no reason to think that the specific concepts that have arisen so far in the history of mathematics should cover all of science, and indeed in this book I give extensive evidence that they do not. At times the role of mathematics in science has been used in philosophy as an indicator of the ultimate power of human thinking. In the mid-1900s, especially among physicists, there was occasionally some surprise expressed about the effectiveness of mathematics in the natural sciences. One explanation advanced by Albert Einstein was that the only physical laws we can recognize are ones that are easy to express in our system of mathematics.