It’s a common theme for students who hated math or science in high school to come to St. John’s and claim one or the other as their favorite class. The math and lab programs at St. John’s are incredibly well-conceived, contextual, and, of course, discussion based–as per all the classes at the college.
We do 4 years of math here at the college. Freshman year math consists almost entirely of Euclid’s Elements, which is an absolutely perfect introduction to the math program at the college. Euclid is not terribly difficult, some students have even studied him in their earlier years. Euclid serves as such a good introduction because his system is intuitive and easily visualized. He is what many people would consider pure geometry, particularly after having taken more applied math courses in high school. Sophomore year delves into the astronomers; we study Ptolemy, Copernicus, Kepler. We study even those who are now considered wrong–partially to get the full arc of the historicity, and also because it’s a practice in thought. Where did they go wrong? Is there still something compelling about their argument? Second semester sophomore year we study Apollonius’ conic sections and then move on to Descartes, to see the beginning of where geometry becomes algebra.
Junior year math is difficult, but famously beloved–proof that the classes you take as underclassmen really do prepare you for higher levels of math. We spend the majority of the year studying Newton and talking about infinity, calculus, finding the area under a curve. But it’s different from high school calculus. Whereas in high school, one is often thrown formulas, without context, and left to wonder: where do they come from, what do they mean? At the college, we have those conversations. And since math is largely philosophical, our conversations are, too. By the time you’re a senior, you’re doing non-Euclidian geometry, Lobachevsky, Einstein’s Theory of Relativity. You even read some thinkers who argue that Euclid isn’t pure geometry, but is actually applied geometry, and to get even purer we have to find our way back to formal logic. It’s totally different from where we started freshman year, and way more abstract. But over the years you develop tools and abilities to think about abstract and non-intuitive concepts. And, studying Einstein first-hand is one of the coolest things you’ll do.
We do 3 years of lab here at the college. We take lab freshman year, then take a break from it sophomore year when we’re studying music, and then go back to it junior and senior year. Freshman year lab is similar to freshman year math insofar as it is highly intuitive and visual. The big question of the year is, what is life? What is a life? We do animal dissections and sketch plants. We try to see if form follows function, and if function follows form. It’s hands on, and fun.
When we come back to lab junior year, the math and lab programs line up really well. For a while, we study Newton in both math and lab. It’s not uncommon for different classes to bleed over into one another–since what we study is chronological, it’s often the case that authors are responding to one another, or dabbling in more than one subject. Senior year, when we’re studying the Theory of Relativity in math, we’re studying quantum mechanics in lab. A huge question is, can we reconcile these two theories? How is it possible that the laws which govern on a macro level no longer govern on the micro level? It’s deeply fulfilling to, as a senior, reach modernity and study what scientists are currently dealing with today.
The reason why, as an undergraduate, you have to take the full 4 years of classes at St. John’s, and can’t transfer credits into the college, is precisely so that you get the full thrust of the historical arc. There is so much to be gained from watching, and actively participating in, the unfolding of thought through the ages. Math and lab have always been a way for philosophers to study the world and to see if the laws and mathematical products of thought really do apply to Nature, or if we just impose them onto Nature. Math and Science are not simply applied fields of study, they are at the root of all human inquiry, religion, and philosophy.