I like to say that my favorite class at UC Davis was Math 16A. I enjoyed it so much that I took it twice. I managed to pass it the second time.
It wasn’t just that I was lazy. I was absolutely disinterested in calculus. I couldn’t see how it would be useful after college.
It was as if the doors of the lecture hall sealed off any connection to the real world. Attending class was like learning in a vacuum. All context was erased. It was simply calculus. It was simply suffocating.
My teacher never told us why we should drill ourselves endlessly on derivatives. It seemed the sole reason for the course was that it was required for an economics degree.
So I switched off during lecture, bored by abstract concepts that seemed applicable to nothing but the dreaded midterm and final. I skated by with a low grade my second time through, changed my major and vowed never to take the subject again.
Incidentally, the mathematician Eric Schechter voiced similar concerns in his essay, “Why Do We Study Calculus?” Devoid of context, of history, calculus can seem esoteric and purposeless.
A history class taught me more about calculus than I ever learned as an economics major. History 136 spanned the age of enlightenment, focusing on the greatest developments in physics and astronomy.
We read about thinkers like Ptolemy, Copernicus, Galileo, Kepler, Newton and Leibniz.
Tl;dr, Ptolemy thought the center of the universe was the earth, Copernicus said it was actually the sun, Galileo agreed with him, Kepler said the sun primarily dictated planetary movement, and Newton and Leibniz said it was more complicated than that. It always is.
Though Kepler was right in stating that the sun plays a massive role in planetary orbits, it is not the only influence. He could not account for anomalous movements that didn’t fit his system of understanding. When planets went temporarily off-path, Kepler could do nothing but chalk them up as “perturbations,” an astronomical term.
Newton and Leibniz came up with calculus, which offers explanations for these perturbations. They actually synthesized the idea of calculus around the same time and argued quite nastily about who was first.
More importantly, calculus could explain that functional relationships between planets of different mass influenced the complex movements of the universe. All bodies in the universe are attracted to each other, not just to the sun.
As Newton stated, the gravitational attraction between two bodies is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them.
What we have then is a way to determine how the variables of the universe interact with one another. Calculus is a kind of music that all the planets dance to. Better poetry about calculus has been written, I’m sure, but you won’t find it in a math textbook.
Since calculus spends so much time talking about functional relationships, perhaps some time in class could be spent on how the past influences the present. Giving calculus this context is indispensable to the equation.
As Schechter suggests with his essay (and I suggested with my GPA), math and history should not be separated. We should know already that a deep understanding of the past is necessary to learn in the present.
By remembering the thinkers of the past, the beginnings of calculus, perhaps we can break the vacuum seal on the doors of lecture halls. Students will breathe easier and be able to see why calculus is so relevant to our society.
We use calculus to show what will happen in economic markets, to analyze survey results, to determine rates of bacteria growth, to construct sloped structures like domes and tunnels, to compute the probability of meteor strikes and countless other applications.
I accept that failing calculus was primarily my fault. I did not try hard enough. However, I think some teachers would do better to give background on why their subject is so important. In this way, they can promote better learning.
We can see that calculus is a means for predicting the future, but that doesn’t mean it should ignore the past.
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