Leveraging Algebra and Logic to Model Biological Systems

Mathematics is often said to be “unreasonably effective” for modeling reality. This phrase mirrors the feeling of surprise when a particular area of mathematics, glittering with crystalline beauty, suddenly turns out to be useful. Such surprises have sprung forth again and again, yet the sense of wonder endures. “Nothing is too beautiful to be true.” Yet during the twentieth century, a curious phenomenon arose in the study of mathematics, particularly in the West. Whenever a branch of mathematics became overly useful, it was expelled from the main body of mathematics. The word expelled is not a rhetorical ourish; it was not simply a matter of a few mathematicians taking a “purer-than-thou” attitude towards some of their colleagues. The real manifestation of this expulsion was that practitioners of the new branch would migrate to a newly formed academic department with a new name, and new journals would be created to publish the work of this new community. Worst of all, the new branch would no longer be part of the postsecondary mathematics curriculum (if it ever was), and so in the usual course of study a budding mathematician would not learn about it except through serendipity. The rst branch to be so cast out was statistics; then operations research; then computer science; and now bioinformatics. When I worked as a software developer for a thermal analysis software vendor, my supervisor (one of its founders who had a doctorate in physics) was surprised to discover that, despite attaining doctoral candidacy in mathematics, I had never taken a statistics course since high school. I was relieved when another founder jumped to my defense: “Hey! That's not math!” Applied mathematics has a curious place in this story. In universities, it is sometimes a separate department from mathematics, sometimes not. But in any case, among the technocracy—those who create mathematics and those who use it—the implicit consensus is that applied mathematics consists of numerical analysis and differential equations. Although beautiful textbooks have been written elucidating each of these theories with nary an application in sight, these branches are recognized to be applied by their very nature, and their practitioners—whether in the applied mathematics department or not—are expected to be concerned with applications at least some of the time. Perhaps it is because these branches are born from that eld which is most unquestionably “real mathematics”, functional analysis, that uniquely in this instance the eld of their application has been allowed to retain the word “mathematics” in its name and, in some cases, to remain in the same department. For these mathematicians, theory and application form a continuous spectrum rather than residing in discrete compartments.