INTRODUCTION TO SYMPOSIUM* ON "MATHEMATICS IN THE SERVICE OF CHEMISTRY" FARRINGTON DANIELS.UNIVERSITY
O F WISCONSIN, MADISON. WISCONSIN
The object of this symposium is to further an appreciation of one of the chemist's most useful tools-mathematics. A few years ago we were still fighting for calculus for chemists, but that battle has been won and we are concerned here with higher mathematics and its application. Times are changing, as this program will show. We can see the mathematical physicist step in and solve our own problems more easily than we can solve them ourselves. Let the chemist who stopped growing in 1920 try to predict how fast a reaction will go; or give the chemical significance of an absorption or emission band; or tell how atoms are put together in molecules from the nature of the scattered light; or let him measure with precision the specific heat of oxygen up to 5000°. But these things are being done in 1931. To actually do these things, the investigator must acquire a new vocabulary of wave equations, eigenfunctions, 1s-2P electrons, nuclear spin, etc.-but all sciences are shrouded in a mystery of technical terms. I t is necessary, too, to travel a long, weary road of self-discipline and to solve thousands of problems. One cannot buy mathematical proficiency as he would buy a type K potentiometer. Many of us cannot afford, now, to take such a long road, but we can adopt a helpful attitude toward those who do and we can know where to go to solve some of our problems. I have a letter of greeting addressed to this group from Professor E. R. Hedrick, president last year of the American Mathematical Society. Among other things he states that a Committee of the Social Science Research Council has asked that the Mathematical Society coijperate in making mathematics courses more helpful to students of the social sciences and that they include social science problems as well as engineering problems. I believe that we are negligent in this respect and that we should in some way ask for the special cooperation in elementary training which the mathematicians are willing to give. Somehow our chemists must be better trained in mathematics or we shall be completely outclassed by our chemist friends in Europe. The time is coming and is now here when chemistry departments will
* This symposium was held under the auspices of the Division of Physical and Inorganic Chemistry of the A. C. S., on March 31, 1931, at Indianapolis, Indiana. In addition t o the contributions included in this issue other papers in the symposium were as follows: R. H. FOWLER, "Statistical Mechanics"; W. H. RODEBUSH, "Calculation of Chemical Equilibrium from the Data of Band Spectroscopy"; R. S. ~ ~ U L L I K E"New N, Developments in Valence"; T. R. HOGNESS, "The Strength of the Carbon Bond"; D. S. VILLARS,"The Present Status of Polymolecular Band Spectroscopy"; HENRY EYRING, "Quantum Mechanical Calculation of Heats of Activation"; H. L. JOHNSTON, "The Specific Heats of Nitric Oxide and of Oxygen. The Precise Calculation of the Degree of Dissociation of Oxygen Up to 500O0." 1060
VOL.8, No. 6
MATHEMATICS IN SERVICE OF CHEMISTRY
1061
have their professorships of mathematical chemistry. They are just as important as professorships of mathematical physics and more necessary. Most professors of physics are fairly good mathematicians and most professors of chemistry are not. Very shortly, too, we will have our consulting mathematicians who will help us, just as our consulting chemists now help the manufacturer and engineer. The program is divided into four sections. You are all familiar with the help that mathematics has given through thermodynamics in predicting chemical equilibria. You may not be so fully aware that probability constitutes the backbone of our new advances, and that statistical mechanics is waiting to serve us in this field. Quantum theory and atomic structure come next. Twenty years ago we were content to consider an atom as a hard round ball and to accept as unrelated and empirical, a whole mass of laboratory facts. With almost unbelievable speed we have crossed off from our list many of the so-called "specific properties of matter," making them functions of our new atomic models. To do this we have had to pay the price of complexity. In our evolutionary process we have accepted compressible atoms, then nests of square boxes, then elliptical orbits. Each has been more useful and more complicated than its predecessor. But now we have to abandon hope of expressing all our facts adequately with these simple pictures,* and we accept as inevitable, as complicated, but as useful-the new mathematical model.
* I t is still necessary and useful to employ pictures and models hut we have learned to take thrm less seriously. We have outgrown our three dimensions for we are concerned with more than three variables. Although it is impossible to represent all the properties with models in two or three dimensions, it is possible to represent some of them adequately and clearly with simple models. No one would think of giving up the benzene ring for a mathematical model in organic chemistry.
