Mikhail G. Katz

Mikhail G. Katz
Name	Mikhail G. Katz
Birth date	1958
Birth place	Leningrad, Russian SFSR
Nationality	Israeli, American
Fields	Mathematics, History of Mathematics
Institutions	Bar-Ilan University, City College of New York, CUNY Graduate Center
Alma mater	Saint Petersburg State University, Tel Aviv University, Columbia University
Known for	Nonstandard analysis, history of infinitesimals, differential geometry, mathematical pedagogy

Mikhail G. Katz is a mathematician and historian of mathematics known for work on nonstandard analysis, the history of infinitesimals, and foundations of calculus. He has held positions at Bar-Ilan University, the City College of New York, and the CUNY Graduate Center, and has published on connections between classical analysis, Abraham Robinson's framework, and the historiography of Isaac Newton and Gottfried Wilhelm Leibniz. His work bridges research areas in differential geometry, algebraic topology, and mathematical pedagogy while engaging with institutions and figures across the modern history of mathematics.

Early life and education

Born in Leningrad (then part of the Russian SFSR), Katz studied mathematics at Saint Petersburg State University where he encountered traditions stemming from Andrey Kolmogorov, Israel Gelfand, and the Leningrad School of Mathematics. He emigrated to Israel and pursued graduate studies at Tel Aviv University before undertaking doctoral research in the United States, interacting with scholars at Columbia University and the Institute for Advanced Study. His formative education brought him into contact with historical sources related to Augustin-Louis Cauchy, Bernard Bolzano, Leopold Kronecker, and the archive collections of Cambridge University and the Bodleian Library.

Academic career

Katz served on the faculty of Bar-Ilan University and held visiting appointments at the City College of New York and the CUNY Graduate Center, collaborating with researchers affiliated with Princeton University, Harvard University, Yale University, and the University of Chicago. He has organized panels at conferences sponsored by the American Mathematical Society, European Mathematical Society, and the International Congress of Mathematicians, and contributed to symposia at institutions such as Oxford University, Cambridge University, Sorbonne University, and the ETH Zurich. His academic network includes interactions with scholars from Stanford University, Massachusetts Institute of Technology, University of California, Berkeley, and Columbia University.

Research contributions

Katz is noted for rigorous studies of infinitesimals within Abraham Robinson's nonstandard analysis and for historical reinterpretations of works by Gottfried Wilhelm Leibniz, Isaac Newton, Augustin-Louis Cauchy, and Karl Weierstrass. He has examined philosophical and technical aspects related to Bernard Bolzano, Nikolai Lobachevsky, Évariste Galois, and Henri Poincaré, and connected those studies to modern frameworks influenced by Andrei Kolmogorov and Stefan Banach. His mathematical research ranges across differential geometry with points of contact to themes in Élie Cartan's theory, Shing-Tung Yau's geometric analysis, and constructions resembling techniques used in Michael Atiyah and Isadore Singer index theory. Katz has addressed foundations by comparing set theory perspectives associated with Georg Cantor and Paul Cohen to model-theoretic methodologies originating with Alfred Tarski and Witold Hurewicz.

Selected publications

Katz has authored and coauthored monographs and articles appearing in venues connected to publishers and journals associated with Springer Verlag, Oxford University Press, Cambridge University Press, the Proceedings of the National Academy of Sciences, and the Journal of the American Mathematical Society. His publications discuss historical sources involving Pierre-Simon Laplace, Joseph-Louis Lagrange, Siméon Denis Poisson, Adrien-Marie Legendre, and analyses related to Cauchy's original texts. He has contributed essays on pedagogy influenced by dialogues with scholars from Johns Hopkins University, Princeton, Rutgers University, and Brown University.

Awards and honors

Katz's scholarly activity has been recognized through invitations to speak at meetings such as the International Congress of Mathematicians and colloquia at institutions including Columbia University, Harvard University, and Princeton University. He has been awarded research fellowships connected to centers like the Institute for Advanced Study, the Mathematical Sciences Research Institute, and the Newton Institute (now Isaac Newton Institute for Mathematical Sciences). His work has been cited in historiographical discussions alongside contributions by historians linked to Cambridge University Press and laureates such as David Hilbert and Emmy Noether in broader narratives.

Teaching and mentorship

As a professor at Bar-Ilan University and as a mentor at the CUNY Graduate Center and City College of New York, Katz has supervised graduate theses interacting with research programs at Tel Aviv University, Hebrew University of Jerusalem, Technion – Israel Institute of Technology, and North American institutions including Columbia University and New York University. His pedagogical interests have led to collaborations with educators from MIT, Stanford University, UC Berkeley, and the University of Oxford on curricular initiatives addressing the teaching of calculus grounded in historical perspectives from Leibniz and Newton.

Category:Mathematicians Category:Historians of mathematics Category:Bar-Ilan University faculty