Recent publications on infinitesimals

Links to over 20 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, D. Schaps, M. Schaps, Sherry, Shnider, and Tall can be found below.

year '15

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. ?, ??-??. See

year '14

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

2. 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

3. 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

4. Sherry, D.; Katz, M. Infinitesimals, imaginaries, ideals, and fictions. Studia Leibnitiana 44 (2012), no. 2, 166-192. See

5. 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

3. 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

4. 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

5. 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

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

7. 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

8. 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

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

10. 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

11. 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

12. 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

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

14. 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

15. 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

16. 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

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

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

year '10

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

20. 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.

21. 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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