A square cannot be partitioned into an odd number of triangles of equal area, a proof published by Paul Monsky in 1970 that remains central to combinatorial geometry. Born in 1936, this American mathematician established a career defined by rigorous contributions to algebraic structures, eventually serving as a professor emeritus of Mathematics at Brandeis University.
Academic Foundation
Monsky completed his undergraduate studies at Swarthmore College before pursuing advanced research. He earned his Ph.D. in 1962 from the University of Chicago. During his doctoral studies, he worked under the supervision of Walter Lewis Baily, Jr., focusing on the algebraic foundations that would inform his later research career.
Twenty questions, eight minutes on the clock, and a percentile measured against everyone who has taken it. No sign-up.
Take the IQ test →Algebraic Contributions
His primary research interests center on algebra, with significant output in the study of Hilbert–Kunz functions and Hilbert–Kunz multiplicity. He is credited with introducing the Monsky–Washnitzer cohomology. In 2007, he collaborated with Holger Brenner to produce a counterexample demonstrating that tight closure does not commute with localization, a development that challenged existing assumptions within commutative algebra.
Legal and Tax Stance
During the mid-1970s, Monsky adopted a public stance against United States military expenditures by ceasing payment of federal income taxes. He challenged income tax withholding processes by claiming unauthorized extra exemptions. This protest resulted in a criminal conviction on tax-related charges in 1980.
Fast facts
- Born: June 17, 1936
- Nationality: United States
- Alma Mater: Swarthmore College
- Ph.D. Institution: University of Chicago
- Doctoral Supervisor: Walter Lewis Baily, Jr.
- Field: Algebra
- Notable Result: Monsky's theorem
- Academic Title: Professor Emeritus, Brandeis University
Questions readers ask
What is Monsky's theorem?
It is a mathematical result, published in 1970, which proves that a square cannot be divided into an odd number of equal-area triangles.
What specific area of mathematics did Monsky study?
He focused on algebra, specifically Hilbert–Kunz functions, Hilbert–Kunz multiplicity, and the Monsky–Washnitzer cohomology.
Achievements
- Fields: algebra
