I am in a debate with a friend about the value of string theory in physics. He is concerned that we are wasting valuable intellectual and financial resources on a path that is fanciful and can't ever hope to be verified by experiment and evidence (11 - 20 dimensions etc).
My point is not to agree with string theory but to argue that maths is powerful and capable of produce new ideas that can be verified.
His question to me is "Can maths provide new and viable ideas without an original idea based on the natural world or through observation"
I can't think of any good examples where the study of maths has resulted in new theory about physics. Can anyone?
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