@Visceral I think you might be slightly overstating - I don't think he believes mathematics is the best way to understand reality. In fact, he made a thread specifically about what to do given interest in both fields, and feeling that a lot of people even in mathematical physics seem to be more concerned with where their understanding of mathematics fits in, rather than the actual physics.
I think it is a slight blur, and I would even go as far as saying a lot of people don't really seem to be giving what I'd call the real reason mathematics is distinct.
The idea of "understanding reality" is fine and dandy, but it can mean almost anything. By some definition, understanding logic is the road to understanding "reality" - I think if one TRULY understood any single thing to the fullest, that would be understanding reality in the sense sought. But we all know that's realistically not happening.The problem I find with linking physics and mathematics too closely is that one clearly concerns itself with modeling something via mathematics, and that just isn't mathematics - it's applied mathematics.
But I feel like sometimes people are too quick to dismiss something as not leading to "higher truth" just because it was called applied. No, I'm not saying what you're doing is crunching numbers. Or just mindless use of formulas.
You can use tons and tons of advanced mathematics in your work, and be completely unafraid of PhD level work in mathematics, but still be a physicist if what you are interested in are physical questions. Yes, I understand Modern Physics often is severely based upon mathematics, rather than our everyday intuition, but physical intuition and everyday intuition (and mathematical intuition, for that matter) are all distinct enough things that I feel it's worth acknowledging.
Mathematics is not about describing something using mathematical structures - it is about studying mathematical structures. A mixture of mathematics, experiment, and many things is required to do physics. You may even have to invent new mathematics the way a mathematician does at times - I'm sure some of the great physicists have done exactly this. So yes, they contributed to the body of mathematics.Again, I should be very clear - just because one is studying a model constructed in the mind doesn't mean it's mathematics, unless one is studying the mathematical structure underlying the model in its own right. The pursuits lead to significantly different paths (i.e. where the questions day by day that you might be asking yourself and focusing on are different enough) that I can't say physics is just a part of pure mathematics.
In fact, it was said in a prior thread itself that Mathematical Physicists are more interested in messing around with Differential Equations, perhaps, than with understanding physics. Which is why they are traditionally put under mathematics departments.
