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The Accidental Astrophysicists
An anonymous reader recommends a ScienceNews story that begins: "Dmitry Khavinson and Genevra Neumann didn't know anything about astrophysics. They were just doing mathematics, like they always do, following their curiosity. But five days after they posted one of their results on a preprint server, they got an email that said 'Congratulations! You've proven Sun Hong Rhie's astrophysics conjecture on gravitational lensing!'... Turns out that when gravity causes light rays to bend, it can make one star look like many. But until Khavinson and Nuemann's work, astrophysicists weren't sure just how many. Their proof in mathematics settled the question."
I think the role of math as "leading" is oversold. I get the impression that a heck of a lot of math was inspired by physics. It seems as though the two develop in tandem. In particular, vector calc and E&M come to mind.
It can also be argued that philosophy is more basic than math. Some might say that we need our ontologies and epistemologies before we can do calculations involving them.
I agree that String Theory is hardly a theory. I call it String Musing, since all it is is thought experiments and possibilities. However, if we ignore it entirely, then there will never be any experimental evidence of it. Right now it's nothing but a mathematical curiosity, but there is no way of telling, from today's perspective based on today's knowledge, what may come of this mathematical curiosity in the future. I'm not a supporter of String Theory (not that my support would matter anyway, since my knowledge of physics is everything from highschool plus whatever I'm curious about at the time), but more research is required before we can dismiss it outright.
Admit it. You post strawman arguments as AC so you get modded Insightful for refuting them, rather than Troll
The way things look to a mathematician are probably different than the way things look to a physicist which are also probably different than the way things look to everyone else. I'm in the first group, so my opinions may be biased here =).
Firstly I don't think there are any absolutes, sometimes math and physics develop in tandem and other times there's a lag time with one or the other leading. I personally think math "leads" the way. Not because it wants to describe the physical world but because it's interesting. Just remember that the math you learn in high school is hundreds of years old, you don't get to the current stuff until grad school. Whereas a physicist uses math as his tool to achieve his goal and will only invent a new tool if his toolbox is insufficient, a mathematician creates new tools just because he wants to understand them. In other words the goal of a mathematician is to make to tools, the goal of a physicist is to apply the tools. That's personally why I think math is "leading" most of the time. I'd rather not get into naming specifics examples as there are millions and I don't believe anyone could win that argument.
As far as math being a subset of philosophy I'll have to disagree; I think they are inexorably linked but neither proper subsets. They share the same grammar, logic, but differ in their dictionaries.
Those are just my thoughts on the matter though.