A Complete Guide to St. John’s Mathematics 

By Michal Kennell, Santa Fe class of 2023 

One of the primary concerns for high school students considering St. John’s is the way we study mathematics. Mathematics is a challenging subject, and the way that St. John’s takes the principles all the way back to Ancient Greece can be quite intimidating. So, today I am here to strip away some of the mystery surrounding our math program! 

To all the students who feel unprepared for freshman math, you are not alone. Be assured, no one is prepared. Each student follows Euclid blindly through a jungle of geometry, re-learning what lines, points, and planes are. With the classroom full of uncertain freshmen, it explodes with new insights and questions the experienced mathematician would never think to ask! This year is a process of unlearning everything you have been taught in order to build a vital foundation for what you will discover in the years to come, and no one expects you to understand every proposition at first glance.  

Sophomore, junior, and senior year open a floodgate of ideas, theories, and complex proofs that rely heavily on Euclid’s Elements. My favorite year mathematically speaking is the sophomore year. We begin by examining Ptolemy, Copernicus, and Kepler. These masters use the principles Euclid established in order to evaluate and unravel the mystery of the celestial bodies. Eventually, Copernicus discovers that the Earth revolves around the Sun and Kepler that the planets do not move in perfect circles as Ptolemy thought, but ellipses instead. We work our way through the metamorphosis of astronomy, allowing us to broaden our minds and fully comprehend the value of being wrong. 

The discovery of the true movement of the planets brings our studies to another ancient mathematician, Apollonius of Perga. He introduces the conic sections to the picture, allowing us now to properly understand what an ellipse is and therefore the geometry behind planetary motion. Moreover, over the course of the second semester the principles Apollonius champions evolve into the foundation for modern algebra and calculus, directly affecting the study of Descartes’ Geometry, Galileo’s Two New Sciences, and Newton’s Principia. These junior year readings blend physics and geometry seamlessly and show you how to apply Euclid and Apollonius in ways that you scarcely could have imagined. Senior year picks up the tab in order to once again subvert everything you thought you knew, with quantum mathematics including Einstein’s theory of relativity. 

Working your way through almost 3,000 years of mathematics might sound impossible. You might think that if you fall behind or do not understand everything you work with in freshman year, you will never be able to do your work in junior year. This is where the philosophy of the college comes into play. We study many geniuses who spent years – even decades — developing and perfecting incredibly complex proofs. Our professors (whom we call tutors) do not expect their students to perfectly reenact all of Newton’s work. In fact, your tutor may be learning the proofs right alongside you! The function of a St. John’s classroom in such a circumstance is to work as a collective to figure out the logical process and significance behind the proof at hand and elevate the entire class’s understanding of the author’s work. In addition, if you feel underconfident even after working on something in class, the school provides academic assistance that will help you fill in the gaps in your knowledge.  

Math at St. John’s can be challenging, for certain. However, the faculty at St. John’s works to provide all the resources necessary to succeed in your classes. The ultimate goal of this sort of education is to allow your mind to make new connections and develop new ways of understanding and processing the world around you. So, my advice: have as much fun as you can! Mathematics can be incredibly fun and enlightening, if only you allow your mind to explore.