His research interests are primarily in the philosophy of science and mathematics, and in the epistemology of religion. He received his Ph.D. in philosophy from Notre Dame and earned an M.A. in religion at Yale. He also holds an M.S. in mechanical engineering and, prior to his teaching career, worked for an international engineering firm where he earned five patents in aeroderivative gas turbine technology. In addition to biographies of Newton and Galileo, his books include A Shot of Faith (to the Head): Be a Confident Believer in an Age of Cranky Atheists, How to Be an Atheist: Why Many Skeptics Aren’t Skeptical Enough, and Calculus for Everyone: Understanding the Mathematics of Change. He was a grant recipient of the 2017-2019 Scholarship & Christianity in Oxford (SCIO): Bridging the Two Cultures of Science and the Humanities.
Plato, the Liberal Arts, and the Crisis in Contemporary Physics
The idea that beauty is a legitimate and even necessary guide to truth in physics is as old as the liberal arts tradition that began with Pythagoras and Plato. Moreover, this view’s credibility skyrocketed in the 20th century with the remarkable successes of our two main theories in physics: general relativity and quantum mechanics. These successes were claimed by their discoverers to depend significantly on aesthetic judgements. And today, proponents of supersymmetry and string theory are continuing in the footsteps of Albert Einstein, Paul Dirac, and Richard Feynman by grounding their unfailing optimism on the claim that these fledgling theories are “beautiful.” Yet at the same time, physicists are now hotly debating whether beauty should be used as guide in physics. After all, over the last few decades, physicists have found it impossible to reconcile important features of general relativity and quantum mechanics, a difficulty seen most saliently in the recent “string theory wars,” and a growing number of prominent physicists are arguing that this “stagnation” in physics may be due to physicists’ reliance on aesthetic criteria for developing new theories.
Though it can seem strange that beauty would play such a significant role in such a precise and objective discipline as physics, the classical liberal arts tradition itself was founded upon the belief that the cosmos is mathematically beautiful. By seeing the importance of this specific connection between truth and beauty, we can better understand how mathematics and physics are actually central to the great tradition, rather than ad-hoc additions that have to be shoehorned into our classical curricula.
Teaching Calculus Classically
Plato inaugurated the classical liberal arts tradition largely around the idea that both the cosmos and the human soul are fundamentally mathematical. Yet it has proven particularly difficult to see how to teach mathematics from a uniquely liberal arts perspective. Surprisingly, calculus is ideally suited to a classical liberal arts pedagogy, despite the fact that it is typically considered beyond the reach of most high school students. In this workshop, we will look at how calculus can be taught in a way that is both accessible and substantive to all students, whether or not they choose to pursue a career in STEM. By mastering the core of calculus—limits, derivatives, integrals, and their deep connection in the Fundamental Theorem of Calculus—students will not only see the big picture of calculus, but also be able to see how the details make up that picture. And in addition to the student’s deeper grasp of calculus proper, they will simultaneously understand its central place in the story of Western civilization. They will see how calculus reveals some of the most important themes of the great tradition, themes that originate in Plato’s Republic and run through the Scientific Revolution, 18th century Enlightenment, and the momentous intellectual revolutions of the 20th century.