What is a point?
This might be an opening question when freshmen gather for their math tutorial on Euclid this fall. “Preparing for a math tutorial means understanding the material to the best of your ability, then letting yourself be vulnerable [to new ideas],” says Annapolis junior Erin Fitzpatrick, “to learn, for example, that a point is that which has no part.” Like all things at St. John’s, students examine the foundations of mathematics in an atmosphere of conversation and hands-on demonstration. Even those who found math daunting in high school discover that this approach transforms their understanding of the subject.
Freshmen begin their mathematical journey with Euclid’s Elements. In their study of the Greek mathematician often referred to as the "Father of Geometry," students approach mathematics as a liberal art, raising and encountering questions that arouse the imagination and lead to further inquiry. Proceeding from Euclid through Einstein during the four years of the Program, students gain a direct understanding of the succession of mathematical revolutions—and an appreciation for the beauty and truth within each—that have led to our modern conception of the universe. “Studying the Elements became better with time,” says Fitzpatrick.
As Johnnies work out solutions to mathematical problems, they contemplate what it means to come to know anything at all—and bring these ruminations to bear on their readings in seminar. “Euclid’s book on proportion was helpful for thinking about Plato's divided line in the Republic,” says Fitzpatrick. “Euclid helped me think more clearly and try to be more accountable for my ideas. I became more aware of cause-and-effect relationships and more skillful at breaking down arguments, all of which is extremely relevant as I pursue my interest in biology.”
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