[5] Gunzburger began his career at New York University as a research scientist and assistant professor of mathematics, a position he held from receiving his Ph.D. until 1971.

He then spent two years working as a post-doctorate at the Naval Ordnance Laboratory before transferring to the Institute for Computer Applications in Science and Engineering at NASA until 1976.

[4] In 1989 he completed his influential first book, "Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice and Algorithms," ISBN 978-0-12-307350-1, which according to Google scholar has over 400 citations as of March 2009 [1] .

He also served as the chairman of the board of trustees in 2003 and has held various other SIAM positions[2][4] In 2007, issues 3–4 in volume 4 of the "International Journal of Numerical Analysis and Modeling" were dedicated to Gunzburger to honor the occasion of his 60th birthday.

and Idalia Reid Prize in Mathematics, an award given for "research in, or other contributions to, the broadly defined areas of differential equations and control theory."