About the Science Institute

The Science Institute draws on St. John’s College’s long tradition of studying science through the discussion of original texts, emphasizing hands-on involvement and experiments. Each weeklong session is an intensive immersion in landmark topics and texts, with twice-daily seminars centered on discussion among participants.

Rather than viewing science as an edifice of facts, we encounter it through the living questions it poses and, in so doing, reenact the experience of scientific discovery. By encouraging each other to express and engage with those questions, we open ourselves to the wonder of inquiry into the mysteries of nature.

The Science Institute is open to those who want to delve more deeply into the questions raised by science and mathematics.

Mr. Pesic, tutor emeritus and musician-in-residence at St. John’s College, Santa Fe, is the director of the Science Institute.

Seminar programs run concurrently with Summer Classics. Seminars meet twice daily.

Summer 2025 Science Institute Seminars

Beyond Numbers: Set Theory

Mahmoud Jalloh and Peter Pesic
Noon–2 p.m. EDT / 10 a.m.–Noon MDT and 4–6 p.m. EDT / 2–4 p.m. MDT
June 30–July 4, 2025
ONLINE

Are numbers the true foundation of mathematics? Or are there still more fundamental concepts from which numbers emerge? The most important modern candidate for this role is set theory. Using Paul Halmos’s classic exposition, Naive Set Theory, we discuss what it would mean to reconceive math in terms of sets. No prior mathematical study is presupposed; indeed, set theory is the basis of the “new math” midcentury mathematicians hoped would give children a grounding in the radical concepts and ways of thinking that have reshaped modern math over the past century. What are the powers and insights that sets allow? What is their value and conceptual price?

Texts: Paul R. Halmos, Naive Set Theory. Dover, ISBN 978-0486814872

A Week with Thinking Machines

Halley Barnet and Brendon Lasell
10 a.m.–Noon MDT and 2–4 p.m. MDT
July 7–11, 2025
IN-PERSON

In the Discourse on Method, Descartes famously predicated our existence as human beings on our ability to think: “I think therefore I am.” He went on to argue that no matter the sophistication of our mechanical imitations of man, they would forever fall short of the capacity to reason. An astute observer of recent developments in artificial intelligence might be tempted to conclude that Descartes was mistaken, that we have indeed succeeded in creating machines that can reason and think.

Our seminar studies the nature of the thinking machine. Together, we read philosophical and scientific texts from the past three centuries that have investigated and proposed machines that represent, model, and even simulate human thought—from Pascal’s calculator to ChatGPT. Texts include Diderot’s D’Alembert’s Dream, Menebrea’s “Sketch of the Analytical Engine Invented by Charles Babbage,” and Turing’s “Computing Machinery and Intelligence.”

Text: A manual will be provided.

Du Châtelet’s Foundations of Physics

Mahmoud Jalloh and Paola Villa
10 a.m.–Noon MDT and 2–4 p.m. MDT
July 14–18, 2025
IN-PERSON

Émilie le Tonnelier de Breteuil, marquise Du Châtelet-Lomont was one of the foremost scientists of her day. She is also at the center of contemporary efforts to recover the works of early women scientists. Famous both as the intellectual partner and lover of Voltaire as well as the sole French translator of Newton’s Principia, her work is of interest both in connection to the intellectual currents of her time and in its own right. Our seminar focuses on her ground breaking treatise, Foundations of Physics, which provides the philosophical foundations for the Newtonian worldview. The class includes a lab component on some relevant experiments, mathematical propositions, and related works that were of great influence on Du Châtelet, including Newton, Leibniz, and Huygens No prior knowledge of physics, philosophy, or mathematics is assumed.

Texts:

• Emilie Du Châtelet, Selected Philosophical and Scientific Writings (ed. Judith P. Zinsser). University of Chicago Press, ISBN 978-0226168074
• A manual will be provided.

Vector Space: The Crux of Modern Science

Peter Pesic and Kenneth Wolfe
10 a.m.–Noon MDT and 2–4 p.m. MDT
July 21–25, 2025
IN-PERSON

Vector space has long been one of the most important basic concepts of modern math, which we study through a slow reading of a short (but dense text by the great mathematician Hermann Weyl, aided by careful notes. A century ago, John von Neumann and his mentor, Weyl, taught physicists to use vector space as the central arena of quantum theory—“Hilbert space”—as we explore in simple examples, and time permitting,  consider the significance of vector space as the mathematical foundation of contemporary artificial intelligence (AI). We approach these matters only needing familiarity with math at the level of high-school algebra and calculus.

Texts: A manual will be provided.

About Peter Pesic

Peter Pesic is a writer, pianist, and educator. He is director of the Science Institute at St. John’s College, Santa Fe, New Mexico, where he is Musician-in-Residence and Tutor Emeritus. His writings include five books about the history of science, music, and ideas, six editions, and sixty papers. As a pianist, he has been heard in many places in the United States and in Europe.

He is the author of the following books, all published by the MIT Press:

• Sounding Bodies: Music and the Making of Biomedical Science
• Polyphonic Minds: Music of the Hemispheres
• Music and the Making of Modern Science
• Sky in a Bottle
• Abel’s Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability
• Seeing Double: Shared Identities in Physics, Philosophy, and Literature
• Labyrinth: A Search for the Hidden Meaning of Science

Peter Pesic’s books are available at the SJC Bookstore.