Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.

The theory of self-adjoint operator was created by von Neumann to fashion a framework for quantum mechanics... I recall in the summer of 1951 the excitement and elation of von Neumann when he learned that Kato has proved the self-adjointness of the Schrodinger operator associated with the helium atom.

And what do the physicists think of these matters? In the 1960s Friedrichs met Heisenberg, and used the occasion to express to him the deep gratitude of the com­ munity of mathematicians for having created quantum mechanics, which gave birth to the beautiful theory of operators in Hilbert space. Heisenberg allowed that this was so; Friedrichs then added that the mathematicians have, in some measure, returned the favor. Heisenberg looked noncommittal, so Friedrichs pointed out that it was a mathematician, von Neumann, who clarified the difference between a self-adjoint operator and one that is merely symmetric. ""What's the difference,"" said Heisenberg.

Tarski told me the following story. He tried to publish his theorem (the axiom of choice is equivalent to the fact that for every infinite set A, there is a bijection of A and A × A) in the Comptes Rendus Acad. Sci. Paris but Frechet and Lebesgue refused to present it. Frechet wrote that an implication between two well-known propositions is not a new result. Lebesgue wrote that an implication between two false propositions is of no interest.

But there is another difficulty of a more cultural and linguistic nature: physics texts are usually written by physicists for physicists. They speak a different dialect, use different notation, emphasize different points, and worry about different things than mathematicians do, and this makes their books hard for mathematicians to read. (Physicists have exactly the same complaint about mathematics books!)