In the space of two days two different students in two different classes with two very different majors went out of their way to mention to me that the topic we just covered was at the same time being applied in another class. Our study of logarithmic scales is Contemporary Mathematics informed a Physics of Music class section on the intensity of sound and our study of the properties of the natural logarithms in Precalculus informed a General Chemistry investigation of reaction constituents using log plots.
Serendipity-yes but too rare. Mathematics provides models and tools that are useful in many fields. Particular levels of mathematical knowledge, sometimes in the form of prerequisites, are required for study of particular course material in many different fields. But the connection is loose or taken for granted. We talk too infrequently if at all to our colleagues in other department about what they really expect their students to know and so our fellow faculty must resort to teaching “just-in-time” math before they can get to the crux of the topic at hand. Or maybe the mathematical technique is turned into a set of cookbook instructions or worst, omitted altogether. To their students this can seem very ad hoc.
What could help? How about a math tutoring center that advertised for and undertook to help any student with a math problem on campus. Also if there were some way to reach out in both directions between all departments and math departments to address student math deficiencies and difficulties. Maybe fifteen minute lectures or demonstrations by math professors in chemistry classes and vice versa. Then serendipity wouldn’t be too rare. If fact it wouldn’t be serendipity.