My discussion will concern itself with mathematics, medicine and the possible relations between the two. It will be an exercise in logical analysis, a review of some sad, sad facts, and in some sense a promise of glad tidings. In short, it will be an effort to bring the immortal inhabitants of the mathematical heaven into harmonious relations with the mortal ills of man's vale of tears.

As to the curious role of mathematics with respect to the natural sciences, several preliminary observations insist on prompt consideration. It is a matter of common knowledge, for example, that mathematics is being constantly applied to physics. With great success, Galileo wedded the two in his study of motion down an inclined plane. The mathematics he used to describe the physical phenomenon involved the equation of a parabola. His daring genius thus got far beyond the conventional circles that were permitted to motion by theology. His courageous use of the then “higher mathematics” was followed by centuries of application of still higher and higher mathematics, till now a small army of mathematicians is busy almost exclusively with the problem of inventing or discovering new varieties of mathematics which could serve physics better and better. The mathematical physicist of to-day is a specialist, nine-tenths mathematician, one-tenth physicist, with the nine-tenths serving the one-tenth.