Fall reading, part I: Math matters

I guess I always thought I’d use more math in my work.

I’m trained as a scientist. I now train students in foundational biology concepts and ways in which science and scientists connect with the world. And yet, most of the math I do involves only simple arithmetic, algebraic manipulations, and elementary statistics. It turns out that teaching the math behind a genetics Punnett square, adjusting concentrations of laboratory solutions, and calculating student grades don’t require much mathematical gymnastics.

Even earlier in my career, as an active researcher in genetics and molecular biology, I was waiting for the day when I would put my math training to full use, alongside chemistry and physics, in illuminating interesting biological questions. That day never came, and I was a little surprised.

Like most young people who decide they’re interested in science in high school, I took a full complement of math courses, including algebra, geometry…all the way to scary-sounding calculus. In college, I pushed on through a second course in calculus as well as calculus-based physics, because I figured I was well prepared, and surely these would help me as I learned how to be a biologist. That physics class was useful, but I admit to having felt one step behind much of the time in my reasoning. The calculus class itself overwhelmed me a bit with new applications of formulaic skills.

Because, although I was dutiful in my pursuit of math, I did not really love it, and it did not always love me in return. I prefer to think about concepts in words and images, rather than in numbers. Layering on equations and numbers to an idea doesn’t clarify it for me. Instead, I sometimes get bogged down in processing the numbers and lose track of what the numbers are doing for me.

So maybe it’s just as well that I left all that math behind and settled comfortably into a career where words reign supreme. But I always sort of wondered why that happened. What was the point of all that math? Wasn’t math supposed to illuminate important patterns in scientific phenomena Why wasn’t calculus part of my scientific world? We tell students that math imparts analytical reasoning skills and helps them solve everyday calculations. But also: math can be used to solve new problems or reveal underlying mysteries about the universe. That’s the most interesting idea for me, and one I assumed I would be required to do if I became a scientist. But my own scientific questions never required my hard-fought calculus tool kit, and those skills faded away into the background of my brain, stored somewhere alongside the French language I learned but regrettably haven’t used in many years.

One day earlier this fall, I was glancing over the selections on the new nonfiction shelf at my local public library branch, after selecting a couple of new novels for fun. The title, Infinite Powers, jumped out at me, and its subtitle, “How CALCULUS Reveals the Secrets of the Universe,” inspired enough curiosity in me to prompt me to check out the book and bring it home.

I soon realized that I recognized its author, Steven Strogatz, from Twitter as a public science communicator, and so I figured I’d also learn more about his work by reading this book. Thus began my valiant effort around the edges of my busy life to re-educate myself about what all that math was for. Strogatz of course reminded me about various concepts I vaguely remembered from school but expanded on them in ways that made the long-forgotten (or never provided) context much clearer. Along the way, I learned interesting history about the development of different mathematical ideas, ways of thinking, and personalities behind the discoveries. I also learned some interesting applications of calculus—especially in biology—that I hadn’t been aware of.

Overall, Strogatz frames the main point of calculus as measuring infinitely small slices of samples extended back across larger, complex problems. Importantly, calculus reigns supreme when change and variation are part of the system. If the rate of something changes over time, for example, simple arithmetic lets you down. Calculus allows us to work in complex systems, which is why its applications in engineering and physics are important. Less obvious, but most interesting to me, are the contexts in which Strogatz connects calculus to modern biology, where the systems are both highly variable and sometimes hard to predict. Some of Strogatz’s own work in applied mathematics tackled questions I teach about, including circadian rhythms and the infection parameters of HIV/AIDS, so I was grateful to have some new knowledge about the mathematical models of these ideas to inform my work in the classroom.

Most of all, I appreciated that in his book, Strogatz makes an effort to really connect with people like me—who might feel overwhelmed when presented with too many equations—by using highly descriptive paragraphs, analogies, and real-life examples to bring the concepts to life through words and pictures. Only when satisfied that he’s done that does he reveal a handful of relevant equations, which fundamentally define the concept he’s describing. Strogatz also discusses how these key ideas connect with the overall curriculum of calculus classes, where the goal is to learn the mechanics of more detailed calculations through repetition, but where the forest of ideas and applications often gets obscured by the trees.

It took me many weeks of brief reading sessions to make my way through the book. I told my colleagues and students I was trying to read a book about calculus, which was met with curious looks and occasional bemused shakes of the head. I now feel good about knowing I was “this close” to maybe using calculus in my biology career, and that the process of learning it likely did enhance my ability to think about complex biological problems from an analytical angle. And with more scientific perspective, I can place the math in context now in ways I couldn’t when I was busy doing problem sets as a teenager every night.

Not everyone learns calculus, and not everyone who learns it will ever go on to use it in their life or work. But knowing that some people do, what they use it for, and that it can be an important part of a broad education are good reminders of the breadth of human understanding and the frontiers of what we don’t know. Many scientific concepts are clarified through seeing underlying mathematical relationships, which helps us recognize patterns emerging from chaos. And so the next time I read about biological systems in flux, I’ll remember there’s calculus behind it. But, honestly, I’m more than okay with letting someone else do those calculations, and awaiting the new insights they reveal.

Image credit: (Pixabay, free image)

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