Katz received in 1963 from Princeton University a bachelor's degree and in 1968 from Brandeis University a Ph.D. in mathematics under Maurice Auslander with thesis The Brauer group of a regular local ring. He became at Federal City College an assistant professor and then in 1973 an associate professor and, after the merger of Federal City College into the University of the District of Columbia in 1977, a full professor there in 1980. He retired there as professor emeritus in 2005.
As a mathematician Katz specializes in algebra, but he is mainly known for his work on the history of mathematics and its uses in teaching. He wrote a textbook History of Mathematics: An Introduction (1993), for which he won in 1995 the Watson Davis and Helen Miles Davis Prize. He organized workshops and congresses for the MAA and the National Council of Teachers of Mathematics. The MAA published a collection of teaching materials by Katz as a compact disk with the title Historical Modules for the Teaching and Learning of Mathematics. With Frank Swetz, he was a founding editor of a free online journal on the history of mathematics under the aegis of the MAA; the journal is called Convergence: Where Mathematics, History, and Teaching Interact. In the journal Convergence, Katz and Swetz published a series Mathematical Treasures. For a study of the possibilities for using mathematical history in schools, Katz received a grant from the National Science Foundation.
He has been married since 1969 to Phyllis Katz (née Friedman), a science educator who developed and directed the U.S. national nonprofit organization Hands On Science Outreach, Inc. (HOSO). The couple have three children.
History of Mathematics: An Introduction, New York: Harper Collins, 1993, 3rd edition Pearson 2008 (a shortened edition was published in 2003 by Pearson)
with Karen Hunger Parshall: Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century, Princeton University Press 2014
with John B. Fraleigh: A first course in abstract algebra, Addison-Wesley 2003
The Mathematics of Egypt, Mesopotamia, China, India and Islam: A Sourcebook, Princeton University Press 2007
with Bengt Johansson, Frank Swetz, Otto Bekken, John Fauvel: Learn from the Masters, MAA 1994 (contribution by Katz: Historical ideas in teaching linear algebra, Napier's logarithms adapted for today's classroom)
Using History to Teach Mathematics: An International Perspective, MAA 2000, MAA Notes (No. 51)
with Marlow Anderson, Robin Wilson: Sherlock Holmes in Babylon and other Tales of Mathematical History, (collection of reprints from the journal Mathematics Magazine of MAA; contribution by Katz: Ideas of calculus in Islam and India), MAA 2004
with Marlow Anderson, Robin Wilson: Who gave you the epsilon? and other tales of mathematical history, MAA 2009 (continuation of the collection of essays on the history of mathematics from MAA journal; contribution by Katz: The history of Stokes' theorem)
with Constantinos Tzanakis: Recent Developments on Introducing a Historical Dimension in Mathematics Education, MAA 2011
^biographical information from American Men and Women of Science, Thomson Gale 2004
^Katz, V. J.; Swetz, F. (March 2011). "Mathematical Treasures" (PDF). HPM Newskletter. No. 76. pp. 2–4.
^Jongsma, Calvin (26 February 2015). "Review of Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century by Victor J. Katz and Karen Hunger Parshall". MAA Reviews, Mathematical Association of America.
^Chen, Jiang-Ping Jeff (March 2015). "Review of Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century by Victor J. Katz and Karen Hunger Parshall". The College Mathematics Journal. 46 (2): 149–152. doi:10.4169/college.math.j.46.2.149. S2CID 218544510.
^Montelle, Clemency (2015). "Review of The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook ed. by Victor J. Katz". Aestimatio: Critical Reviews in the History of Science. 4: 179–191. doi:10.33137/aestimatio.v4i0.25818.
^Sandifer, Ed (3 January 2001). "Review of Using History to Teach Mathematics: An International Perspective by Victor J. Katz". MAA Reviews, Mathematical Association of America.
^Deakin, Michael A. B. (2001). "Review of Using History to Teach Mathematics: An International Perspective ed. by Victor J. Katz" (PDF). Zentralblatt für Didaktik der Mathematik. 33 (5): 137–138. doi:10.1007/BF02656618.
^Gouvêa, Fernando Q. (2015). "Review of Sherlock Holmes in Babylon and Other Tales of Mathematical History ed. by Marlow Anderson, Victor Katz, and Robin Wilson". Aestimatio: Critical Reviews in the History of Science. 2: 67–79. doi:10.33137/aestimatio.v2i0.25743.
^Davis, Philip J. (18 October 2009). "Review of Who Gave You the Epsilon? & Other Tales of Mathematical History ed. by Marlow Anderson, Victor Katz, and Robin Wilson". SIAM News, Society for Industrial and Applied Mathematics.