"The profound study of nature is the most fertile source of mathematical discoveries."

Jean Baptiste Joseph Fourier in 1822

He nailed it right on the head!  Most of the interesting math (in my opinion) was developed by physicists and those involved in the physical sciences.  Of course, I'm a physicist which makes me horribly biased.  It's still true though.  :-)

What do you get when you cross a horse and a chicken?

Horse chicken Sin(theta)

(Only people who know vector calculus will get the joke...)

When the problems in physics become difficult we may often look to the mathematicians, who may already have studied such things and have prepared a line of reasoning for us to follow.  On the other hand they may not have, in which case we have to invent our own line of reasoning.

-  Richard Feynman in The Character of Physical Law.  Chapter: The Relation of Mathematics to Physics

E   L  = mc² + 1/2 m q² + ...

Einstein, 1912 Manuscript on the Special Theory of Relativity.

In fact, it appears that he used L to represent energy in many equations, and subsequently replaced L with E.

[Regarding taking measurements and the quantum uncertainty principle:]

"What we are saying, then, is that magnetism is really a relativistic effect.  In the case of the two charges we just considered, travelling parallel to each other, we would expect to have to make relativistic corrections to their motion, with terms of order v^2/c^2.
...
"It is the near perfect cancellation of electrical effects which allowed relativity effects (that is, magnetism) to be studied and the correct equations -- to order v^2/c^2 -- to be discovered, even though physicists didn't know that's what was happening.  And that is why, when relativity was discovered, the electromagnetic laws didn't need to be changed.  They -- unlike mechanics -- were already correct to a precision of v^2/c^2"

Richard Feynman

Proof is an idol before which the mathematician tortures himself.

Sir Arthur Eddington