At Williams we believe that bringing together students and professors in small groups produces extraordinary academic outcomes. Our distinctive Oxford-style tutorial classes—in which two students are guided by a professor in deep exploration of a single topic—are a prime example. Each week the students take turns developing independent work—an essay, a problem set, a piece of art—and critiquing their partner’s work. Focused on close reading, writing, and oral defense of ideas, more than 70 tutorials a year are offered across the curriculum, with titles like “Biomedical Ethics,” “Women in National Politics,” and “Extraterrestrial Life in the Galaxy: a Sure Thing or a Snowball’s Chance?”
Imagine yourself in a tutorial at Williams. Of anyone in the world, whom would you choose to be the other student in the class, and why?
Euler once wrote out the following equation: (a+b^n)/n=x.
At first glance, this function is unremarkable; there are too many unknowns for a single solution to exist. Though there are infinite combinations of a,b,n, and x to satisfy this function, none of them are groundbreaking. Why, then, would I bring it up?
This was Euler’s proof of God.
Interestingly enough, Euler never rationalized this claim. He presented it in court, and he was never given a chance to explain himself. Euler, a mathematical genius, believed that this simple function indicated a divine power, something beyond humanity.
I’ve spent more time than I’d like to admit puzzling over this function. Despite scouring the Internet, I’ve never found logical reasoning to explain how this function could possibly prove the existence of God. Instead of accepting defeat, I dug a little deeper into Euler’s enigmatic mind and history. And, after further research, I realized Euler would be a fantastic tutorial partner.
Several of Euler’s works portray him as a pious Christian. In fact, before Bernoulli noticed Euler’s talent in mathematics, Euler was well on his way to becoming a pastor. The existence of God, to Euler, was a subject of great interest. But despite his ability to prove the power expansion for e, Euler was never able to publish a rigorous proof of the existence of God. He was never able to explain this equation to others. It appears, then, that Euler was never able to definitively find God. But that doesn’t necessarily mean that he failed.
I want to read tracts by Descartes and Plato, both of whom were philosophers and mathematicians. I want to examine texts by Walras and Cournot, both of whom brilliantly applied math to economics. Above all, I want to explore the interdisciplinary uses of math, economics, and philosophy. And who better to work with than Euler?