[sls]

That is by no means an apt metaphor. Mathematicians are in the business of creating new mathematics, not in studying the "language" in which mathematics happens to be written. Of course the history of mathematics is replete with contributions from physicists and others, particularly during the period when the educated could turn their hand to nearly any such discipline and find a problem on which progress could be made.

[injb]

Yes. In fact it has often been noted by physicists that when they make a new discovery they sometimes find that mathematicians have been there before them. Like Einstein and non-euclidean geometry etc.

[ncmncm]

It more often goes the other way, and more profoundly.

Group theory.

Laplace transforms were considered an irrelevant curiosity until somebody figured out they were isomorphic to the wildly effective Heaviside D operator. Then everyone did their best to bury Heaviside's demonstrations of their utility, and pretend that Laplace had done all the heavy lifting.

[injb]

Group theory was invented by physicists?

[sriku]

... with string theory (or M-theory as you wish) offering a break by having made its own contributions to maths.