Math and Science Are Not Cleanly Separable
What I, and many other physical scientists, object to is the notion that math and science are cleanly separable. That, as Wilson suggests, the mathematical matters can be passed off to independent contractors, while the scientists do the really important thinking. That may be true in his home field (though I’ve also seen a fair number of biologists rolling eyes at this), but for most of science, the separation is not so clean.
As much as I agree with Wilson’s statement about the need for detailed knowledge to constrain math, even in physics, there is also some truth to the reverse version of the statement, which I have often heard from physicists: If you don’t have a mathematical description of something, you don’t really understand it. Observations are all well and good, but without a coherent picture to hold them all together, you don’t really have anything nailed down. Big data alone will not save you, in the absence of a quantitative model.
Yeah, what he said.
I was surprised as an undergraduate how many of my fellow physics students moaned that they wanted to study physics and not mathematics. To me, even then the separation between the two was not very clear. In reverse, I am quite fond of using physics nomenclature as much as possible in mathematics; for example fibre coordinates on the cotangent bundle are called momenta.
Another interesting point, put to me by a very well established professor, was that all important ideas in mathematics really come from physics. I may blog more about that myself in due course…
I have made a latest comment today on this subject in the thread :-
Is Mathematics Alone a safe medium for exploring the frontiers of Science. Or should Observation and Hypothesis lead in front ?
This, I believe is as ajb illustrates, many well wishing physics students, and for that matter many scientists feel about this.