Currently, biology students at most schools are required to take no more than one semester of calculus. If this is enough to learn and understand contemporary biology, it may also be the reason why biology is slow to incorporate mathematic modeling. Or, Matt asked, is there a "deeper" reason why biology has remained largely oblivious of mathematics?
To be sure, in addition to that one semester of calculus, biology students are required to learn a good deal of statistics. As a tool for organizing and describing data, however, statistics is not mathematics (by studying a great number of pizzas, for example, statisticians might discover that the circumference of a pizza tends to be a bit more than three times its diameter). Statistical modeling has already taught biologists that models do not have to be true in order to be useful. One can generate predictions by modeling selection pressures in idealized populations, for example. And yet it appears that biologists differ from physicists in that they are reluctant to introduce systematic idealizations such as frictionless planes into their theories. It is these kinds of idealizations, however, which would allow them to use, for example, differential equations in order not only to systematize or describe, but to clarify some aspect of the data or of a problem. Such modeling would yield mathematical descriptions which can stimulate experiments and issue in biological explanations.
Where mathematical models are used in biology, that modeling is often performed by people who did not start off as biologists but as physicists, mathematical physicists, or mathematicians. Oddly enough, those areas of biology where mathematical models are least pervasive are the most "physicalized" such as molecular and cellular iology. Matt thus returned to the question at the beginning: Are the reasons for this primarily sociological and related to the training of biologists, or do they relate to subject-matter of biology itself: Can mathematical models address the "real biological questions" at all; is the (relative) absence of mathematics cause or effect of the absence of "laws" in biology?
Alfred Nordmann
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