Mikhail Katz (born 1958, in Chișinău) is an Israeli mathematician, a professor of mathematics at Bar-Ilan University. His main interests are differential geometry and geometric topology; he is the author of a book about systolic geometry.
Katz earned a bachelor's degree in 1980 from Harvard University. He did his graduate studies at Columbia University, receiving his Ph.D. in 1984 under the joint supervision of Troels Jørgensen and Mikhael Gromov. He moved to Bar-Ilan University in 1999, after previously holding positions at the University of Maryland, College Park, Stony Brook University, Indiana University Bloomington, the Institut des Hautes Études Scientifiques, the University of Rennes 1, Henri Poincaré University, and Tel Aviv University.
Katz has performed research in systolic geometry in collaboration with Luigi Ambrosio, Victor Bangert, Mikhail Gromov, Steve Shnider, Shmuel Weinberger, and others. He has authored research publications appearing in journals including Communications on Pure and Applied Mathematics, Duke Mathematical Journal, Geometric and Functional Analysis, and Journal of Differential Geometry. Along with these papers, Katz was a contributor to the book "Metric Structures for Riemannian and Non-Riemannian Spaces". Marcel Berger in his article "What is... a Systole?" lists the book (Katz, 2007) as one of two books he cites in systolic geometry.
More recently Katz also contributed to the study of mathematics education including work that provides an alternative interpretation of the number 0.999....
Bair, Jacques; Błaszczyk, Piotr; Ely, Robert; Henry, Valérie; Kanovei, Vladimir; Katz, Karin; Katz, Mikhail; Kutateladze, Semen; McGaffey, Thomas; Schaps, David; Sherry, David; Shnider, Steve (2013), "Is mathematical history written by the victors?" (PDF), Notices of the American Mathematical Society, 60 (7): 886–904, arXiv:1306.5973 , doi:10.1090/noti1001 .
Katz, Mikhail G.; Sherry, David (2012), "Leibniz's laws of continuity and homogeneity", Notices of the American Mathematical Society, 59 (11): 1550–1558, doi:10.1090/noti921 .
Katz, Mikhail G.; Schaps, David; Shnider, Steve (2013), "Almost Equal: The Method of Adequality from Diophantus to Fermat and Beyond", Perspectives on Science, 21 (3), arXiv:1210.7750 .
Borovik, Alexandre; Jin, Renling; Katz, Mikhail G. (2012), "An Integer Construction of Infinitesimals: Toward a Theory of Eudoxus Hyperreals", Notre Dame Journal of Formal Logic, 53 (4): 557–570, arXiv:1210.7475 , doi:10.1215/00294527-1722755 .
Kanovei, Vladimir; Katz, Mikhail G.; Mormann, Thomas, "Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics", Foundations of Science, arXiv:1211.0244 , doi:10.1007/s10699-012-9316-5 .
Katz, Mikhail; Tall, David (2012), "A Cauchy-Dirac delta function", Foundations of Science, arXiv:1206.0119 , doi:10.1007/s10699-012-9289-4 .
Katz, Mikhail; Sherry, David (2012), "Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond", Erkenntnis, arXiv:1205.0174 , doi:10.1007/s10670-012-9370-y .
Błaszczyk, Piotr; Katz, Mikhail; Sherry, David (2012), "Ten misconceptions from the history of analysis and their debunking", Foundations of Science, arXiv:1202.4153 , doi:10.1007/s10699-012-9285-8 .
Katz, Mikhail; Tall, David (2012), Tension between Intuitive Infinitesimals and Formal Mathematical Analysis, Bharath Sriraman, Editor. Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast Monographs in Mathematics Education 12, Information Age Publishing, Inc., Charlotte, NC, pp. 71–89, arXiv:1110.5747 .
Katz, Karin Usadi; Katz, Mikhail G. (2011), "Meaning in Classical Mathematics: Is it at Odds with Intuitionism?", Intellectica, 56 (2): 223–302, arXiv:1110.5456 .
Borovik, Alexandre; Katz, Mikhail G. (2012), "Who gave you the Cauchy—Weierstrass tale? The dual history of rigorous calculus", Foundations of Science, 17 (3): 245–276, arXiv:1108.2885 , doi:10.1007/s10699-011-9235-x .
Katz, Karin Usadi; Katz, Mikhail G. (2011), "Cauchy's continuum", Perspectives on Science, 19 (4): 426–452, MR 2884218, doi:10.1162/POSC_a_00047 .
Katz, Karin Usadi; Katz, Mikhail G.; Sabourau, Stéphane; Shnider, Steven; Weinberger, Shmuel (2011), "Relative systoles of relative-essential 2-complexes", Algebraic & Geometric Topology, 11 (1): 197–217, MR 2764040, doi:10.2140/agt.2011.11.197 .
Katz, Karin Usadi; Katz, Mikhail G. (2012), "Stevin numbers and reality", Foundations of Science, 17 (2): 109–123, doi:10.1007/s10699-011-9228-9 .
Katz, Karin Usadi; Katz, Mikhail G. (2012), "A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography", Foundations of Science, 17 (1): 51–89, MR 2896999, arXiv:1104.0375 , doi:10.1007/s10699-011-9223-1 .
Katz, Mikhail G. (2007), Systolic geometry and topology, Mathematical Surveys and Monographs, 137, Providence, RI: American Mathematical Society, ISBN 978-0-8218-4177-8, MR 2292367 . With an appendix by J. Solomon.
Katz, Karin Usadi; Katz, Mikhail G. (2010), "When is .999... less than 1?", The Montana Mathematics Enthusiast, 7 (1): 3–30, arXiv:1007.3018 , archived from the original on 2011-07-20 .
Katz, Karin Usadi; Katz, Mikhail G. (2010), "Zooming in on infinitesimal 1–.9.. in a post-triumvirate era", Educational Studies in Mathematics, 74 (3): 259–273, arXiv:1003.1501 , doi:10.1007/s10649-010-9239-4 .
Bangert, Victor; Katz, Mikhail G. (2003), "Stable systolic inequalities and cohomology products", Communications on Pure and Applied Mathematics, 56 (7): 979–997, MR 1990484, doi:10.1002/cpa.10082 .
Katz, Mikhail G.; Rudyak, Yuli B. (2006), "Lusternik–Schnirelmann category and systolic category of low-dimensional manifolds", Communications on Pure and Applied Mathematics, 59 (10): 1433–1456, MR 2248895, doi:10.1002/cpa.20146 .
Bangert, Victor; Katz, Mikhail G.; Shnider, Steven; Weinberger, Shmuel (2009), "E7, Wirtinger inequalities, Cayley 4-form, and homotopy", Duke Mathematical Journal, 146 (1): 35–70, MR 2475399, arXiv:math.DG/0608006 , doi:10.1215/00127094-2008-061 .
Croke, Christopher B.; Katz, Mikhail G. (2003), "Universal volume bounds in Riemannian manifolds", in Yau, S. T., Surveys in Differential Geometry VIII, Lectures on Geometry and Topology held in honor of Calabi, Lawson, Siu, and Uhlenbeck at Harvard University, May 3–5, 2002, Int. Press, Somerville, MA, pp. 109–137, MR 2039987, arXiv:math.DG/0302248 .
Katz, Mikhail G. (1983), "The filling radius of two-point homogeneous spaces", Journal of Differential Geometry, 18 (3): 505–511, MR 723814 .
