In 1958 Brown earned his Ph.D. from the University of Wisconsin-Madison under R. H. Bing.
Afterwards he became a professor at the University of Michigan at Ann Arbor.
With Barry Mazur in 1965 he won the Oswald Veblen prize[2] for their independent and nearly simultaneous proofs of the generalized Schoenflies hypothesis[3] in geometric topology.
Brown's short proof was elementary and fully general.
Mazur's proof was also elementary, but it used a special assumption which was removed via later work of Morse.