Recent publications on infinitesimals

Links to recent publications on infinitesimals (and related subjects) by Jacques Bair, Tiziana Bascelli, Piotr Błaszczyk, Alexandre Borovik, Emanuele Bottazzi, Robert Ely, Valérie Henry, Frederik Herzberg, Renling Jin, Vladimir Kanovei, Karin Katz, Taras Kudryk, Semen Samsonovich Kutateladze, Eric Leichtnam, Thomas McGaffey, Thomas Mormann, Tahl Nowik, Luie Polev, Patrick Reeder, David Schaps, Mary Schaps, David Sherry, Steven Shnider, and David Tall can be found below.

A nice introduction to our program can be found in the following review by Guillaume: Guillaume's review in pdf

year '16

Błaszczyk, P.; Kanovei, V.; Katz, M.; Sherry, D. "Controversies in the foundations of analysis: Comments on Schubring's Conflicts." Foundations of Science. See and See also Reception

year '15

Kanovei, V.; Katz, K.; Katz, M.; Schaps, M. "Proofs and Retributions, Or: Why Sarah Can't Take Limits." Foundations of Science 20 (2015), no. 1, 1-25. See and

Kanovei, V.; Katz, K.; Katz, M.; Sherry, D. "Euler's lute and Edwards' oud." The Mathematical Intelligencer 37 (2015), 48-51. See and and see also Reception

Katz, M.; Kutateladze, S. "Edward Nelson (1932-2014)." The Review of Symbolic Logic 8 (2015), no. 3, 607-610. See and

Nowik, T; Katz, M. "Differential geometry via infinitesimal displacements." Journal of Logic and Analysis 7:5 (2015), 1-44. See and

year '14

Bascelli, T.; Bottazzi, E.; Herzberg, F.; Kanovei, V.; Katz, K.; Katz, M.; Nowik, T.; Sherry, D.; Shnider, S. "Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow." Notices of the American Mathematical Society 61 (2014), no. 8, 848-864. See and

Katz, K.; Katz, M.; Kudryk, T. "Toward a clarity of the extreme value theorem." Logica Universalis 8 (2014), no. 2, 193-214. See and and

Sherry, D.; Katz, M. "Infinitesimals, imaginaries, ideals, and fictions." Studia Leibnitiana 44 (2012), no. 2, 166-192. See (Article was published in 2014 even though the journal issue lists the year as 2012)

Tall, D.; Katz, M. "A cognitive analysis of Cauchy's conceptions of function, continuity, limit, and infinitesimal, with implications for teaching the calculus." Educational Studies in Mathematics 86 (2014), no. 1, 97-124. See and

year '13

Bair, J.; Błaszczyk, P.; Ely, R.; Henry, V.; Kanovei, V.; Katz, K.; Katz, M.; Kutateladze, S.; McGaffey, T.; Schaps, D.; Sherry, D.; Shnider, S. "Is mathematical history written by the victors?" Notices of the American Mathematical Society 60 (2013) no. 7, 886-904. Accessible here,,, and

Błaszczyk, P.; Katz, M.; Sherry, D. "Ten misconceptions from the history of analysis and their debunking." Foundations of Science 18 (2013), no. 1, 43-74. See,,, and Reception

Kanovei, V.; Katz, M.; Mormann, T. "Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics." Foundations of Science 18 (2013), no. 2, 259--296. See,, and

Katz, M.; Leichtnam, E. "Commuting and noncommuting infinitesimals." American Mathematical Monthly 120 (2013), no. 7, 631-641. See,, and

Katz, M.; Schaps, D.; Shnider, D. "Almost Equal: The Method of Adequality from Diophantus to Fermat and Beyond." Perspectives on Science 21 (2013), no. 3, 283-324. See,, and

Katz, M.; Sherry, D. "Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond." Erkenntnis 78 (2013), no. 3, 571-625. See,, and

Katz, M.; Tall, D. "A Cauchy-Dirac delta function." Foundations of Science, 18 (2013), no. 1, 107-123. See,, and

Mormann, T.; Katz, M. "Infinitesimals as an issue of neo-Kantian philosophy of science." HOPOS: The Journal of the International Society for the History of Philosophy of Science 3 (2013), no. 2, 236-280. See and

year '12

Borovik, A.; Jin, R.; Katz, M. "An Integer Construction of Infinitesimals: Toward a Theory of Eudoxus Hyperreals." Notre Dame Journal of Formal Logic 53 (2012), no. 4, 557-570. See,, and

Borovik, A.; Katz, M. "Who gave you the Cauchy--Weierstrass tale? The dual history of rigorous calculus." Foundations of Science 17 (2012), no. 3, 245-276. see,, and, as well as

Katz, K.; Katz, M. "Stevin numbers and reality." Foundations of Science 17 (2012), no. 2, 109-123. See and and

Katz, K.; Katz, M. "A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography." Foundations of Science 17 (2012), no. 1, 51-89. See,, and

Katz, M.; Sherry, D. "Leibniz's laws of continuity and homogeneity." Notices of the American Mathematical Society 59 (2012), no. 11, 1550-1558. See,,, and

Katz, M.; Tall, D. "Tension between Intuitive Infinitesimals and Formal Mathematical Analysis." Chapter in: 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, 2012, pp. 71-89. See

year '11

Katz, K.; Katz, M. "Meaning in Classical Mathematics: Is it at Odds with Intuitionism?" Intellectica 56 (2011), no. 2, 223-302. See

Katz, K.; Katz, M. "Cauchy's continuum." Perspectives on Science 19 (2011), no. 4, 426-452. See,, and

year '10

Ely, R. "Nonstandard student conceptions about infinitesimal and infinite numbers." Journal for Research in Mathematics Education 41 (2010), no. 2, 117-146. See and

Katz, K.; Katz, M. "Zooming in on infinitesimal 1-.9.. in a post-triumvirate era." Educational Studies in Mathematics 74 (2010), no. 3, 259-273. See

Katz, K.; Katz, M. "When is .999... less than 1?" The Montana Mathematics Enthusiast 7 (2010), No. 1, 3--30. See and

Arithmetic, Geometry, and Topology (AGT) Seminar: current schedule
Jim Holt "Infinitesimally yours"
Infinitesimal topics
Special session AMS/IMU on the history and philosophy of mathematics
Salvaging Leibniz
Teaching True Infinitesimal Calculus

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If, as Kurt Goedel said, Robinson's theory is the analysis of the future, then it should be called standard analysis, not nonstandard analysis. Hello?