International Congress of Mathematicians (ICM) 2026

Math, Music and the Mind
Analysis of the performed Trio Sonatas of J. S. Bach

The music of J. S. Bach has influenced composers more than that of perhaps any other figure. His Trio Sonatas, in particular, offer some of the clearest insights into his pedagogy and have challenged generations of organists. For these reasons, they may also provide a uniquely powerful window into the structure of Bach’s music, and even into tonal music more broadly.

This talk will describe a collaborative project with the University of Michigan Organ Department to create high-precision digital recordings of these works, performed by students and faculty at varying skill levels. Using these digitization’s, together with direct representations of the musical scores, we investigate how music may be encoded in the mind.

Results challenge prevailing mathematical theories of music representation and reveal unexpected structural patterns in Bach’s compositions that invite further exploration. We also show how mathematical models of auditory processing in the brain can suggest new principles of musical composition.

Daniel B. Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics, and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan, Ann Arbor. He directs the Michigan Center for Applied and Interdisciplinary Mathematics and serves as Chief Scientific Officer of Arcascope. In 2026, he was named a Guggenheim Fellow for his work in applied mathematics and music. He is the author of Biological Rhythms, published in the MIT Press Essential Knowledge Series. Dr. Forger is also an accomplished organist and was named an Associate of the American Guild of Organists. As an undergraduate, he received the McCord Prize and was the organ scholar at the First Presbyterian Church in the City of New York.