In the fall of 1955, Rhodes entered Massachusetts Institute of Technology intending to major in physics, but he soon switched to mathematics, earning his Bachelor of Surgery in 1960 and his Doctor of Philosophy in 1962. His Doctor of Philosophy thesis, co-written with a graduate student from Harvard, Kenneth Krohn, became known as the Prime Decomposition Theorem, or more simply Krohn–Rhodes theory.
In the late 1960s Rhodes wrote The Wild Book, which quickly became an underground classic, but remained in typescript until its revision and editing by Nehaniv in 2009. The following year Springer Monographs in Mathematics published his and Benjamin Steinberg"s magnum opus, The q-theory of Finite Semigroups, a compendium of the history of the field, but more importantly the fruit of eight years" development of finite semigroup theory. In recent years Rhodes has expanded his research, bringing the insights of semigroups into matroid theory.
In 2015 he published, with Pedro V. Silva, the results of his current work in another monograph with Springer:.
After a year on an National Science Foundation fellowship in Paris, France, he became a member of the Faculty of Mathematics at the University of California, Berkeley, where he spent his entire teaching career.