Recent publications on infinitesimals



Provided below are links to 50 recent publications on infinitesimals and related subjects by Jacques Bair, Tiziana Bascelli, Piotr Błaszczyk, Alexandre Borovik, Emanuele Bottazzi, Robert Ely, Peter Fletcher, Valérie Henry, Frederik Herzberg, Karel Hrbacek, Renling Jin, Vladimir Kanovei, Karin Katz, Taras Kudryk, Semen Samsonovich Kutateladze, Eric Leichtnam, Claude Lobry, Thomas McGaffey, Thomas Mormann, Tahl Nowik, Luie Polev, Patrick Reeder, Sam Sanders, Jan Peter Schäfermeyer, David Sherry, and others.

A nice introduction to our program can be found in the MathSciNet review by M. Guillaume in pdf
To see where the papers have appeared click on List of periodicals
See also List of critics
See also Reappraisal of the procedures of the pioneers of infinitesimal analysis


year '18

18a. Bair, J.; Błaszczyk, P.; Heinig, P.; Katz, M.; Schäfermeyer, J.; Sherry, D. "Klein vs Mehrtens: restoring the reputation of a great modern." Mat. Stud. 48 (2017), no. 2, 189-219. See https://arxiv.org/abs/1803.02193 and http://dx.doi.org/10.15330/ms.48.2.189-219 and https://mathscinet.ams.org/mathscinet-getitem?mr=3819950

18b. TBA

18c. Bair, J.; Błaszczyk, P.; Katz, K.; Katz, M.; Kudryk, T.; Sherry, D. "Analyzing Benardete's comment on decimal notation." Philosophy of Mathematics Education Journal no. 33, january 2018. See at journal and https://arxiv.org/abs/1706.00191

18d. Bair, J.; Katz, M.; Sherry, D. "Fermat's dilemma: Why did he keep mum on infinitesimals? and the European theological context." Foundations of Science 23 (2018), no. 3, 559-595. See http://dx.doi.org/10.1007/s10699-017-9542-y and https://arxiv.org/abs/1801.00427 and https://mathscinet.ams.org/mathscinet-getitem?mr=3836239

18e. Bascelli, T.; Błaszczyk, P.; Borovik, A.; Kanovei, V.; Katz, K.; Katz, M.; Kutateladze, S.; McGaffey, T.; Schaps, D.; Sherry, D. "Cauchy's infinitesimals, his sum theorem, and foundational paradigms." Foundations of Science 23 (2018), no. 2, 267-296. See http://dx.doi.org/10.1007/s10699-017-9534-y and https://arxiv.org/abs/1704.07723 and https://mathscinet.ams.org/mathscinet-getitem?mr=3803893

18f. Bascelli, T.; Błaszczyk, P.; Kanovei, V.; Katz, K.; Katz, M.; Kutateladze, S.; Nowik, T.; Schaps, D.; Sherry, D. "Gregory's sixth operation." Foundations of Science 23 (2018), no. 1, 133-144. See http://dx.doi.org/10.1007/s10699-016-9512-9 and https://arxiv.org/abs/1612.05944 and https://mathscinet.ams.org/mathscinet-getitem?mr=3772065

18g. Błaszczyk, P.; Kanovei, V.; Katz, M.; Nowik, T. "Monotone subsequence via ultrapower." Open Mathematics 16 (2018), 149-153. See https://doi.org/10.1515/math-2018-0015 and https://arxiv.org/abs/1803.00312 and https://mathscinet.ams.org/mathscinet-getitem?mr=3772690

18h. Herzberg, F.; Kanovei, V.; Katz, M.; Lyubetsky, V. "Minimal axiomatic frameworks for definable hyperreals with transfer." Journal of Symbolic Logic 83 Issue 1, March 2018, pp. 385-391. See http://dx.doi.org/10.1017/jsl.2017.48 and https://arxiv.org/abs/1707.00202 and https://mathscinet.ams.org/mathscinet-getitem?mr=3796290

18i. Kanovei, V.; Katz, K.; Katz, M.; Mormann, T. "What makes a theory of infinitesimals useful? A view by Klein and Fraenkel." Journal of Humanistic Mathematics 8 (2018), no. 1, 108-119. See http://scholarship.claremont.edu/jhm/vol8/iss1/7 and https://arxiv.org/abs/1802.01972 and https://mathscinet.ams.org/mathscinet-getitem?mr=3762866 and coming soon at http://dx.doi.org/10.5642/jhummath.201801.07

18j. Katz, B.; Katz, M; Sanders, S. "A footnote to The crisis in contemporary mathematics." Historia Mathematica 45 (2018), no. 2, 176-181. See https://doi.org/10.1016/j.hm.2018.03.002 and https://arxiv.org/abs/1804.02645 and https://mathscinet.ams.org/mathscinet-getitem?mr=3802555 A portrait of Errett Bishop as a young... chicken.

18k. Sherry, D. "The jesuits and the method of indivisibles." Foundations of Science 23 (2018), no. 2, 367-392. See http://dx.doi.org/10.1007/s10699-017-9525-z and https://mathscinet.ams.org/mathscinet-getitem?mr=3803897

18l. Sanders, S. "To be or not to be constructive, that is not the question." Indag. Math. (N.S.) 29 (2018), no. 1, 313-381. https://doi.org/10.1016/j.indag.2017.05.005 and https://mathscinet.ams.org/mathscinet-getitem?mr=3739620


year '17

17a. Bair, J.; Błaszczyk, P.; Ely, R.; Henry, V.; Kanovei, V.; Katz, K.; Katz, M.; Kudryk, T.; Kutateladze, S.; McGaffey, T.; Mormann, T.; Schaps, D.; Sherry, D. "Cauchy, infinitesimals and ghosts of departed quantifiers." Mat. Stud. 47 (2017), no. 2, 115-144. See https://arxiv.org/abs/1712.00226 and http://matstud.org.ua/texts/2017/47_2/115-144.pdf and http://dx.doi.org/10.15330/ms.47.2.115-144 and https://mathscinet.ams.org/mathscinet-getitem?mr=3733080

17b. Bair, J.; Błaszczyk, P.; Ely, R.; Henry, V.; Kanovei, V.; Katz, K.; Katz, M.; Kutateladze, S.; McGaffey, T.; Reeder, P.; Schaps, D.; Sherry, D.; Shnider, S. "Interpreting the infinitesimal mathematics of Leibniz and Euler." Journal for General Philosophy of Science 48 (2017), no. 2, 195-238. See http://dx.doi.org/10.1007/s10838-016-9334-z and https://arxiv.org/abs/1605.00455 and http://www.ams.org/mathscinet-getitem?mr=3663035 Here we analyze Euler's approach to infinitesimal analysis and his proof of the infinite product decomposition for the sine function. We also examine Giovanni Ferraro's flawed historical scholarship and propose a sounder alternative.

17c. Błaszczyk, P.; Kanovei, V.; Katz, K.; Katz, M.; Kudryk, T.; Mormann, T.; Sherry, D. "Is Leibnizian calculus embeddable in first order logic?" Foundations of Science 22 (2017), no. 4, 717-731. See http://dx.doi.org/10.1007/s10699-016-9495-6 and https://arxiv.org/abs/1605.03501 and https://mathscinet.ams.org/mathscinet-getitem?mr=3720412

17d. Błaszczyk, P.; Kanovei, V.; Katz, K.; Katz, M.; Kutateladze, S.; Sherry, D. "Toward a history of mathematics focused on procedures." Foundations of Science 22 (2017), no. 4, 763-783. See http://dx.doi.org/10.1007/s10699-016-9498-3 and https://arxiv.org/abs/1609.04531 and https://mathscinet.ams.org/mathscinet-getitem?mr=3720415 Here we propose an approach to the history of mathematics that focuses on the procedures of the historical masters rather than set-theoretic ontology of the entities they use. We also examine Jeremy Gray's flawed historical scholarship and propose a sounder alternative.

17e. Błaszczyk, P.; Kanovei, V.; Katz, M.; Sherry, D. "Controversies in the foundations of analysis: Comments on Schubring's Conflicts." Foundations of Science 22 (2017), no. 1, 125-140. See http://dx.doi.org/10.1007/s10699-015-9473-4 and https://arxiv.org/abs/1601.00059 and http://www.ams.org/mathscinet-getitem?mr=3605125 See also Reception

17f. Fletcher, P.; Hrbacek, K.; Kanovei, V.; Katz, M.; Lobry, C.; Sanders, S. "Approaches to analysis with infinitesimals following Robinson, Nelson, and others." Real Analysis Exchange 42 (2017), no. 2, 193-252. See https://arxiv.org/abs/1703.00425 and http://msupress.org/journals/issue/?id=50-21D-61F and https://mathscinet.ams.org/mathscinet-getitem?mr=3721800 and eventually http://dx.doi.org/10.14321/realanalexch.41.1.0193

17g. Gutman, A.; Katz, M.; Kudryk, T.; Kutateladze, S. "The Mathematical Intelligencer Flunks the Olympics." Foundations of Science 22 (2017), no. 3, 539-555. See http://dx.doi.org/10.1007/s10699-016-9485-8 and https://arxiv.org/abs/1606.00160 and http://www.ams.org/mathscinet-getitem?mr=3696393 Here we examine Yaroslav Sergeyev's grossbit pathos.

17h. Katz, M.; Polev, L. "From Pythagoreans and Weierstrassians to true infinitesimal calculus." Journal of Humanistic Mathematics 7 (2017), no. 1, 87-104. See http://dx.doi.org/10.5642/jhummath.201701.07 and https://arxiv.org/abs/1701.05187

17i. Sanders, S. "Reverse Formalism 16." Synthese. See http://dx.doi.org/10.1007/s11229-017-1322-2 and https://arxiv.org/abs/1701.05066


year '16

16a. Bascelli, T.; Błaszczyk, P.; Kanovei, V.; Katz, K.; Katz, M.; Schaps, D.; Sherry, D. "Leibniz versus Ishiguro: Closing a Quarter Century of Syncategoremania." HOPOS: The Journal of the International Society for the History of Philosophy of Science 6 (2016), no. 1, 117-147. See http://dx.doi.org/10.1086/685645 and https://arxiv.org/abs/1603.07209

16b. Błaszczyk, P.; Borovik, A.; Kanovei, V.; Katz, M.; Kudryk, T.; Kutateladze, S.; Sherry, D. "A non-standard analysis of a cultural icon: The case of Paul Halmos." Logica Universalis 10 (2016), no. 4, 393-405. http://dx.doi.org/10.1007/s11787-016-0153-0 and https://arxiv.org/abs/1607.00149 and http://www.ams.org/mathscinet-getitem?mr=3566230

16c. Kanovei, V.; Katz, K.; Katz, M.; Nowik, T. "Small oscillations of the pendulum, Euler's method, and adequality." Quantum Studies: Mathematics and Foundations 3 (2016), no. 3, 231-236. See http://dx.doi.org/10.1007/s40509-016-0074-x and https://arxiv.org/abs/1604.06663 and http://www.ams.org/mathscinet-getitem?mr=3531864


year '15

15a. 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 http://dx.doi.org/10.1007/s10699-013-9340-0 and http://www.ams.org/mathscinet-getitem?mr=3312498 Here we examine Errett Bishop's criticisms of Robinson's framework

15b. Kanovei, V.; Katz, K.; Katz, M.; Sherry, D. "Euler's lute and Edwards' oud." The Mathematical Intelligencer 37 (2015), 48-51. See http://dx.doi.org/10.1007/s00283-015-9565-6 and https://arxiv.org/abs/1506.02586 and http://www.ams.org/mathscinet-getitem?mr=3435825 see also Reception

15c. Katz, M.; Kutateladze, S. "Edward Nelson (1932-2014)." The Review of Symbolic Logic 8 (2015), no. 3, 607-610. See http://dx.doi.org/10.1017/S1755020315000015 and https://arxiv.org/abs/1506.01570

15d. Nowik, T; Katz, M. "Differential geometry via infinitesimal displacements." Journal of Logic and Analysis 7:5 (2015), 1-44. See http://www.logicandanalysis.com/index.php/jla/article/view/237 and http://u.math.biu.ac.il/~katzmik/dgnsa_arxiv.pdf and https://arxiv.org/abs/1405.0984 and http://www.ams.org/mathscinet-getitem?mr=3457545


year '14

14a. 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 http://www.ams.org/notices/201408/rnoti-p848.pdf and https://arxiv.org/abs/1407.0233

14b. Katz, K.; Katz, M.; Kudryk, T. "Toward a clarity of the extreme value theorem." Logica Universalis 8 (2014), no. 2, 193-214. See http://dx.doi.org/10.1007/s11787-014-0102-8 and https://arxiv.org/abs/1404.5658 and http://www.ams.org/mathscinet-getitem?mr=3210286

14c. Sherry, D.; Katz, M. "Infinitesimals, imaginaries, ideals, and fictions." Studia Leibnitiana 44 (2012), no. 2, 166-192. See http://www.jstor.org/stable/43695539 and https://arxiv.org/abs/1304.2137 (Article was published in 2014 even though the journal issue lists the year as 2012)

14d. 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 http://dx.doi.org/10.1007/s10649-014-9531-9 and https://arxiv.org/abs/1401.1468


year '13

13a. 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, http://www.ams.org/notices/201307/rnoti-p886.pdf, http://www.ams.org/mathscinet-getitem?mr=3086638, and https://arxiv.org/abs/1306.5973

13b. 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 http://dx.doi.org/10.1007/s10699-012-9285-8, http://www.ams.org/mathscinet-getitem?mr=3031794, https://arxiv.org/abs/1202.4153, and Reception

13c. 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 http://dx.doi.org/10.1007/s10699-012-9316-5, https://arxiv.org/abs/1211.0244, and http://www.ams.org/mathscinet-getitem?mr=3064607 Here we examine Alain Connes' criticisms of Robinson's framework

13d. Katz, M.; Leichtnam, E. "Commuting and noncommuting infinitesimals." American Mathematical Monthly 120 (2013), no. 7, 631-641. See http://dx.doi.org/10.4169/amer.math.monthly.120.07.631, http://www.ams.org/mathscinet-getitem?mr=3096469, and https://arxiv.org/abs/1304.0583 Here we examine Alain Connes' criticisms of Robinson's framework

13e. Katz, M.; Schaps, D.; Shnider, S. "Almost Equal: The Method of Adequality from Diophantus to Fermat and Beyond." Perspectives on Science 21 (2013), no. 3, 283-324. See http://dx.doi.org/10.1162/POSC_a_00101, https://arxiv.org/abs/1210.7750, and http://www.ams.org/mathscinet-getitem?mr=3114421. Here we refute Herbert Breger's interpretation of Fermat and propose a sounder alternative.

13f. 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 http://dx.doi.org/10.1007/s10670-012-9370-y, https://arxiv.org/abs/1205.0174, and http://www.ams.org/mathscinet-getitem?mr=3053644

13g. Katz, M.; Tall, D. "A Cauchy-Dirac delta function." Foundations of Science, 18 (2013), no. 1, 107-123. See http://dx.doi.org/10.1007/s10699-012-9289-4, https://arxiv.org/abs/1206.0119, and http://www.ams.org/mathscinet-getitem?mr=3031797

13h. 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 http://dx.doi.org/10.1086/671348 and https://arxiv.org/abs/1304.1027


year '12

12a. 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 https://arxiv.org/abs/1210.7475, http://dx.doi.org/10.1215/00294527-1722755, and http://www.ams.org/mathscinet-getitem?mr=2995420

12b. 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 http://dx.doi.org/10.1007/s10699-011-9235-x, https://arxiv.org/abs/1108.2885, and http://www.ams.org/mathscinet-getitem?mr=2950620, as well as http://u.math.biu.ac.il/~katzmik/straw.html Here we examine Judith Grabiner's flawed Cauchy scholarship and propose a sounder alternative.

12c. Katz, K.; Katz, M. "Stevin numbers and reality." Foundations of Science 17 (2012), no. 2, 109-123. See http://dx.doi.org/10.1007/s10699-011-9228-9 and https://arxiv.org/abs/1107.3688 and http://www.ams.org/mathscinet-getitem?mr=2935194

12d. 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 http://dx.doi.org/10.1007/s10699-011-9223-1, https://arxiv.org/abs/1104.0375, and http://www.ams.org/mathscinet-getitem?mr=2896999

12e. Katz, M.; Sherry, D. "Leibniz's laws of continuity and homogeneity." Notices of the American Mathematical Society 59 (2012), no. 11, 1550-1558. See http://www.ams.org/notices/201211/rtx121101550p.pdf, https://arxiv.org/abs/1211.7188, http://www.ams.org/mathscinet-getitem?mr=3027109, and http://u.math.biu.ac.il/~katzmik/straw2.html

12f. 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 https://arxiv.org/abs/1110.5747


year '11

11a. Katz, K.; Katz, M. "Meaning in Classical Mathematics: Is it at Odds with Intuitionism?" Intellectica 56 (2011), no. 2, 223-302. See https://arxiv.org/abs/1110.5456 Here we examine Errett Bishop's criticisms of Robinson's framework

11b. Katz, K.; Katz, M. "Cauchy's continuum." Perspectives on Science 19 (2011), no. 4, 426-452. See http://dx.doi.org/10.1162/POSC_a_00047, https://arxiv.org/abs/1108.4201, and http://www.ams.org/mathscinet-getitem?mr=2884218


year '10

10a. Ely, R. "Nonstandard student conceptions about infinitesimal and infinite numbers." Journal for Research in Mathematics Education 41 (2010), no. 2, 117-146. See http://www.nctm.org/publications/article.aspx?id=26196 and http://u.math.biu.ac.il/~katzmik/ely10.pdf

10b. 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 http://dx.doi.org/10.1007/s10649-010-9239-4 and https://arxiv.org/abs/arXiv:1003.1501

10c. Katz, K.; Katz, M. "When is .999... less than 1?" The Montana Mathematics Enthusiast 7 (2010), No. 1, 3-30. See http://scholarworks.umt.edu/tme/vol7/iss1/11 and https://arxiv.org/abs/arXiv:1007.3018



List of periodicals where the articles have appeared, in alphabetical order:

American Mathematical Monthly 13d
Erkenntnis 13f
Foundations of Science 18d, 18e, 18f, 17c, 17d, 17e, 17g, 15a, 13b, 13c, 13g, 12b, 12c, 12d
Historia Mathematica 18j
HOPOS (Journal of the International Society for the History of Philosophy of Science) 13h, 16a
Intellectica 11a
Journal for General Philosophy of Science 17b
Journal of Humanistic Mathematics 17h
Journal of Logic and Analysis 15d
Journal of Symbolic Logic 18h
Logica Universalis 14b, 16b
Mat. Stud. 17a, 18a
Mathematical Intelligencer 15b
Notices of the American Mathematical Society 12e, 13a, 14a
Notre Dame Journal of Formal Logic 12a
Perspectives on Science 11b, 13e
Quantum Studies: Mathematics and Foundations 16c
Real Analysis Exchange 17f
Review of Symbolic Logic 15c
Studia Leibnitiana 14c
Synthese 17i



Reappraisal of the procedures of the pioneers of infinitesimal analysis from Stevin to Cauchy


Pioneer Journal where reappraisal appeared Link to article containing reappraisal
Simon Stevin Foundations of Science 12c
Pierre Fermat Perspectives on Science 13e
Pierre Fermat Foundations of Science 18d
James Gregory Foundations of Science 18f
Gottfried Leibniz Notices AMS 12e
Gottfried Leibniz Erkenntnis 13f
Gottfried Leibniz Studia Leibnitiana 14c
Gottfried Leibniz HOPOS (Journal of the International Society for the History of Philosophy of Science) 16a
Leonhard Euler Mathematical Intelligencer 15b
Leonhard Euler Journal for General Philosophy of Science 17b
A. L. Cauchy Perspectives on Science 11b
A. L. Cauchy Foundations of Science 12b
A. L. Cauchy Mat. Stud. 17a
A. L. Cauchy Foundations of Science 18e
A. L. Cauchy See this link: Misconceptions with regard to Cauchy and his infinitesimals


List of critics in alphabetical order:


Critic Venue where rebuttal appeared Link to article/venue containing rebuttal
Richard Arthur Erkenntnis 13f
Richard Arthur Foundations of Science 17d
Errett Bishop Foundations of Science 15a
Errett Bishop Intellectica 11a
Errett Bishop Historia Mathematica 18j
Errett Bishop New manuscripts New manuscripts
Bishop-Connes Synthese 17i
Umberto Bottazzini Math Overflow Q&A thread
Herbert Breger Perspectives on Science 13e
Herbert Breger Foundations of Science 18d
Alain Connes Foundations of Science 13c
Alain Connes American Mathematical Monthly 13d
Alain Connes Math Overflow Q&A thread
Alain Connes Dedicated page Dedicated page
John Earman Erkenntnis 13f
Kenny Easwaran Notices of the American Mathematical Society 14a
Harold M. Edwards Mathematical Intelligencer 15b
Harold M. Edwards Journal for General Philosophy of Science 17b, section 4.13
Giovanni Ferraro Journal for General Philosophy of Science 17b
Giovanni Ferraro Foundations of Science 18f
Craig Fraser Foundations of Science 18e
Craig Fraser Mat. Stud. 17a
Craig Fraser Math Overflow Q&A thread
Judith Grabiner Foundations of Science 12b
Judith Grabiner Foundations of Science 18e
Jeremy Gray Foundations of Science 17d
Jeremy Gray Stack Exchange Q&A thread
Paul Halmos Foundations of Science 16b
Hide Ishiguro Studia Leibnitiana 4c
Hide Ishiguro HOPOS (Journal of the International Society for the History of Philosophy of Science) 16a
Jesper Luetzen Mat. Stud. 17a, Section 3
Gert Schubring Foundations of Science 17e
Yaroslav Sergeyev Foundations of Science 17g
Yaroslav Sergeyev EMS Surveys in Mathematical Sciences "Both [EICs] have assumed responsibility for [the mistake of publishing Sergeyev's paper] and resigned from their position."
Yaroslav Sergeyev Retraction Watch Editors-in-chief of math journal resign over controversial paper
Yaroslav Sergeyev dedicated page Dedicated page
Yaroslav Sergeyev Zentralblatt Review by Louis Kauffman
Yaroslav Sergeyev Mathematical Reviews Review by Mikhail Katz
Detlef Spalt Perspectives on Science 11b


tallberkeley12



Other critics of infinitesimals and/or Robinson Journal where rebuttal appeared Link to article containing rebuttal
George Berkeley (1685-1753) Erkenntnis 13f
François-Napoléon-Marie Moigno (1804-1884) Erkenntnis 13f
Georg Cantor (1845-1918) Erkenntnis 13f
Bertrand Russell (1872-1970) Erkenntnis 13f, section 11.1
Henk Bos (1940- ) Erkenntnis 13f, section 11.3
Henk Bos (1940- ) Journal for General Philosophy of Science 17b, section 2.7



Kathleen Sullivan's '76 study of teaching calculus with infinitesimals based on Keisler's book
Amos Shalit: An analysis of Halmos's critique of nonstandard analysis
Borovik's blog Infinitesimals: Their Mathematics, Philosophy, History
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
Terry Tao on hyperreals
Terry Tao: there is more to mathematics than rigor and proofs
Cauchy's sum theorem

Return to home page

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