Hope you guys can help us out an a debate that’s getting nowhere (mostly because everyone involved in the debate is heavily biased towards the superiority of one or the other subject). The question is, is physics maths? If maths wasn’t available to us, would we be able to express physical concepts and ideas? Does this mean that physics is just a subset of maths?
Answers on a postcard to the usual address.
Newton developed a lot of his theories using his math of derivative calculus. It may be that he developed the new math in order to explain his other theories. Other scientists discovered that other relationships in physics can be expressed in advanced algebra or arithmetic terms.
There would have been other, as there are now, more imprecise ways of expressing physical terms, but the precision that math offers really help streamline and expanded the study of physics, more so than any other applied science.
However, I don’t think you could just reduce physics to “a subset of maths”. Physics, like any other branch of the natural sciences, must deal with entities in the real world, so physicists must perform experiments or make observations. The precision of expression afforded by mathematics may be essential to ever really getting anywhere with physics (or just about any other branch of the natural sciences), but physics is still a branch of science, not of mathematics.
All scientific theories require one to use some amount of mathematics to make predictions with it. Sociology requires statistics. Chemistry requires algebra to handle things like solubility products. A metallurgical law such as “the resiliency of a bar is proportional to its thickness squared” (I’m taking a wild guess here) would require you to square your measurement of a given bar’s thickness, divide it by the thickness of your “reference bar”, and then multiply this by the reference bar’s resiliency.
The difference with physics (particularly quantum mechanics) is that the mathematical tools required to make predictions with the theories are so complicated and take so long to learn how to use that you’ll be spending most of your time doing math in order to do physics. But ultimately, after your done making calculations based on your theory, you still have to compare those calculations with actual observed data to see if your theory holds up.
The difference between physics and mathematics is that the final judge of a physical law is agreement with observations, while the final judge of a mathematical theorem is logical consistency. It’s certainly possible to concoct a physical law that is logically consistent but totally at odds with observations.
Why the connection between physics and mathematics then? Nobody knows! But it’s a damn interesting question to ponder.