Recent publications on infinitesimals

Links to recent publications on infinitesimals (and related subjects) by Bair, Bascelli, Błaszczyk, Borovik, Bottazzi, Ely, Henry, Herzberg, Jin, Kanovei, Katz, Kudryk, Kutateladze, Leichtnam, T. McGaffey, Mormann, Nowik, Pat Reeder, D. Schaps, M. Schaps, Sherry, Shnider, and Tall can be found below.

year '15

Nowik, T; Katz, M. Differential geometry via infinitesimal displacements. See

Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Mary Schaps. Proofs and Retributions, Or: Why Sarah Can't Take Limits. Foundations of Science 20 (2015), no. 1, 1-25. See and

Mikhail G. Katz and Semen S. Kutateladze. EDWARD NELSON (1932-2014), The Review of Symbolic Logic. See

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

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 and google scholar.

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

Some interesting questions:
Was the early calculus inconsistent? (MO)
Can Euler's mathematics be reformulated in terms of modern theories?
Did Connes find a catch in the theory?
In what ways did Leibniz's philosophy anticipate modern mathematics?
A few questions on nonstandard analysis (SE)
Is mathematical history written by the victors? (SE)
What did Newton and Leibniz actually discover? (SE)
Who gave you the epsilon? (SE)

Infinitesimal topics

Special session AMS/IMU on the history and philosophy of mathematics
Salvaging Leibniz

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