Gallian completed his Ph.D. thesis, entitled
Two-Step Centralizers in Finite p-Groups, at the
University of Notre Dame in 1971 under the supervision of Karl Kronstein. He has been a professor at the University of Minnesota Duluth since 1972. In addition to teaching math classes, he taught a humanities course called "The Lives and Music of the Beatles" for 33 years and a liberal arts course on math and sports. Gallian has authored or edited six books (Contemporary Abstract Algebra, Taylor & Francis 10th edition; For All Practical Purposes, W.H. Freeman (coauthor); Principles and Practices of Mathematics, Springer-Verlag; Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs, Editor, American Mathematical Society; Proceedings of the Conference on Promoting Undergraduate Research in Mathematics (editor), American Mathematical Society; Mathematics and Sports, Mathematical Association of America) and over 100 articles. He earned media attention in 1991 when he determined the methods used by Minnesota and many other states for assigning drivers' license numbers. Between 1977 and 2025, Gallian ran forty-six Research Experience for Undergraduates (REU) programs at the University of Minnesota Duluth. The program has been funded by the
University of Minnesota Duluth grants from the
National Science Foundation (40+ years) and the
National Security Agency (30+ years). It is one of the oldest and longest-running REUs in the country. As of the end of 2025, the program has had 292 undergraduate participants and has produced more than 330 publications in mainstream professional journals. More than 180 Duluth REU students have received a PhD degree. Gallian served a 2-year term as the President of the Mathematical Association of America starting in January 2007. In addition, he was co-director of
Project NExT from 1998 to 2012, Associate Editor of MAA OnLine since 1997, a member of the advisory board of
Math Horizons from 1993 to 2013, a member of the editorial board of the Mathematics Magazine for five years and the American Mathematical Monthly for 15 years. In 2021 he became a co-editor of the MAA Mugs to Donuts e-newsletter for Putnam competition students. ==Awards and honors==