Sims was born and raised in Elkhart, Indiana, and received his B.S. from the University of Michigan.[3] He did his graduate studies at Harvard University, where he was a student of John G. Thompson and received his Ph.D. degree in 1963. In his thesis, he enumerated p-groups, giving sharp asymptotic upper and lower bounds. Sims is one of the founders of computational group theory and is the eponym of the Schreier–Sims algorithm. He was a faculty member at the Department of Mathematics at Rutgers University from 1965 to 2007. During that period he served, in particular, as Department Chair (1982–84) and Associate Provost for Computer Planning (1984–87). Sims retired from Rutgers in 2007 and moved to St. Petersburg, Florida.[4]