Thomas Francis Banchoff was born on April 7, 1938, in Trenton, New Jersey. He received his bachelor’s degree in mathematics from the University of Notre Dame in 1960, his master’s degree and then his doctorate from the University of California at Berkeley in 1962 and 1964. After teaching for two years at Harvard (1964/1966) and accepting a research appointment at the University of Amsterdam (1966/1967), he began his tenure at Brown University as assistant professor of Mathematics in 1967, rising to full professor in 1973. In addition to his teaching and research at Brown, Professor Banchoff has held visiting professorships at Yale, UCLA, and the University of Notre Dame.
His fields of specialization are differential geometry and topology. His monographic publications include: Beyond the Third Dimension (1990), Cusps of Gauss Mappings (1982), Linear Algebra through Geometry (1983), and Differential Geometry of Curves and Surfaces (2010). He has published numerous conference papers and articles in such journals as The Proceedings of the American Mathematical Society and the Journal of Differential Geometry. His teaching and research in these fields have explored ongoing innovations in the computer visualization of patterns and relationships, especially in his work with the fourth dimension. To this end, he and his colleague Charles Strauss formed their own production company, which released short films such as Flying through the Torus (1979) and The Hypercube: Projections and Slicing (1979). In 1975, the Washington Post featured a photograph of Banchoff holding a hypercube model in front of Salvador Dalí’s 1954 painting “Corpus Hypercubus”; this began a friendship between Dalí and Banchoff that grew out of their mutual fascination with the fourth dimension.
One of Banchoff's favorite books, Flatland: A Romance of Many Dimensions by Edwin A. Abbott, was made into a movie in 2007, and he served as a consultant for the movie. Banchoff wrote the introduction for the movie edition of the book, published in 2008. His research on the life of Flatland author Edwin A. Abbott comprises its own collection: Thomas Banchoff collection of materials relating to Edwin Abbott Abbott, Ms.2011.016, Brown University.
Professor Banchoff has received numerous teaching awards, among them the Brown University Teaching Excellence Award (1993), the Northeastern Section of the Mathematical Association of America Award for Distinguished Teaching of Mathematics (1995), and Rhode Island Professor of the Year Award (1997). He has served as an associate editor of Mathematics Magazine (1978-1981), associate editor of the American Mathematical Monthly (1982-1985), and president of the Mathematical Association of America (1999/2000). He has participated in many faculty and university committees dealing with such issues as the faculty role in university governance, student housing, and information resources and services.
In addition to teaching at Brown, Banchoff served as Acting Dean of Student Affairs during the 1971/1972 academic year, a time of significant organizational and social change on campus. As dean he oversaw the creation of the Transitional Year Program (which became the present Third World Transition Program in 1975).
As of July 2014, Thomas Banchoff is an emeritus professor at Brown, after 47 years of teaching. He continues to teach geometry, topology, and calculus courses at institutions such as Baylor University and Carnegie Mellon University.