Garrity's research is in algebraic and differential geometry and in number theory. At Williams, Garrity teaches many different courses, including multivariable calculus, Fourier analysis, number theory, Galois theory, and algebraic geometry. He has been instrumental in the Williams' SMALL research program, which has produced more publications than any other in the country; he alone has advised 37 summer research students.
His "All the Mathematics You Missed (But Need to Know for Graduate School)," published by Cambridge University Press, is a bestseller among technical books in mathematics. It is an overview of topics covered in undergraduate mathematics including linear algebra, vector calculus, differential geometry, real analysis, point-set topology, differential equations, probability theory, complex analysis, abstract algebra, and more.
Garrity graduated from the University of Texas in 1981, earning both a B.A. with highest honors in philosophy and a B.S. with highest honors in mathematics. He received his Ph.D. from Brown University in 1986.
Before coming to Williams in 1989, he held the post-doctoral position of G.C. Evans Instructor of Mathematics at Rice University, where he received the Nicolas Salgo Outstanding Teacher Award.
He spent the 1992-93 academic year as a visiting professor at the University of Washington and the 2000-01 academic year as a visiting professor at the University of Michigan.