近年来，国外关于“无穷小”的研究是个“热点”，反观国内，菲氏微积分的徒子徒孙对此却“不感兴趣”，可悲也。
近年来，国外发表40多篇关于无穷小的研究论文，连接如下：
袁萌 5月18日
附：Recent publications oninfinitesimals
Provided beloware links to over 40 recent publications on infinitesimals and related subjectsby Jacques Bair, Tiziana Bascelli, Piotr B?aszczyk, Alexandre Borovik, EmanueleBottazzi, Robert Ely, Peter Fletcher, Valérie Henry, Frederik Herzberg, Karel Hrbacek,Renling Jin, Vladimir Kanovei, Karin Katz, Taras Kudryk, Semen SamsonovichKutateladze, Eric Leichtnam, Claude Lobry, Thomas McGaffey, Thomas Mormann,Tahl Nowik, Luie Polev, Patrick Reeder, Sam Sanders, David Sherry, and others.
A niceintroduction 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 ofperiodicals. See also List of critics and Reappraisal of the procedures of thepioneers of infinitesimal analysis.
year '18
18a. Bair, J.; B?aszczyk, P.; Heinig, P.; Katz, M.; Sch?fermeyer, J.;Sherry, D. "Klein vs Mehrtens: restoring the reputation of a greatmodern." Mat. Stud. 48 (2017), no. 2. See https://arxiv.org/abs/1803.02193
18b. TBA
18c. Bair, J.; B?aszczyk, P.; Katz, K.; Katz, M.; Kudryk, T.; Sherry,D. "Analyzing Benardete's comment on decimal notation." Philosophy ofMathematics Education Journal no. 33, january 2018. See at journal andhttps://arxiv.org/abs/1706.00191
18d. Bair, J.; Katz, M.; Sherry, D. "Fermat's dilemma: Why did hekeep mum on infinitesimals? and the European theological context."Foundations of Science. 23 (2018). Seehttp://dx.doi.org/10.1007/s10699-017-9542-y andhttps://arxiv.org/abs/1801.00427
18e. Bascelli, T.; B?aszczyk, P.; Borovik, A.; Kanovei, V.; Katz, K.;Katz, M.; Kutateladze, S.; McGaffey, T.; Schaps, D.; Sherry, D. "Cauchy'sinfinitesimals, his sum theorem, and foundational paradigms." Foundationsof Science 23 (2018), no. 2. See http://dx.doi.org/10.1007/s10699-017-9534-yand https://arxiv.org/abs/1704.07723
18f. Bascelli, T.; B?aszczyk, P.; Kanovei, V.; Katz, K.; Katz, M.;Kutateladze, S.; Nowik, T.; Schaps, D.; Sherry, D. "Gregory's sixthoperation." Foundations of Science 23 (2018), no. 1, 133-144. Seehttp://dx.doi.org/10.1007/s10699-016-9512-9 andhttps://arxiv.org/abs/1612.05944 andhttps://mathscinet.ams.org/mathscinet-getitem?mr=3772065
18g. B?aszczyk, P.; Kanovei, V.; Katz, M.; Nowik, T. "Monotonesubsequence via ultrapower." Open Mathematics 16 (2018), 149-153. See https://doi.org/10.1515/math-2018-0015and https://arxiv.org/abs/1803.00312 andhttps://mathscinet.ams.org/mathscinet-getitem?mr=3772690
18h. Herzberg, F.; Kanovei, V.; Katz, M.; Lyubetsky, V. "Minimalaxiomatic frameworks for definable hyperreals with transfer." Journal ofSymbolic Logic 83 Issue 1, March 2018, pp. 385-391. Seehttp://dx.doi.org/10.1017/jsl.2017.48 and https://arxiv.org/abs/1707.00202 andhttps://mathscinet.ams.org/mathscinet-getitem?mr=3796290
18i. Kanovei, V.; Katz, K.; Katz, M.; Mormann, T. "What makes atheory of infinitesimals useful? A view by Klein and Fraenkel." Journal ofHumanistic Mathematics 8 (2018), no. 1, 108-119. Seehttp://scholarship.claremont.edu/jhm/vol8/iss1/7 andhttps://arxiv.org/abs/1802.01972 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 incontemporary mathematics." Historia Mathematica 45 (2018), no. 2, 176-181.See https://doi.org/10.1016/j.hm.2018.03.002 andhttps://arxiv.org/abs/1804.02645 and https://mathscinet.ams.org/mathscinet-getitem?mr=3802555A portrait of Errett Bishop as a young... chicken.
year '17
17a. Bair, J.; B?aszczyk, 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 departedquantifiers." Mat. Stud. 47 (2017), no. 2, 115-144. Seehttps://arxiv.org/abs/1712.00226 andhttp://matstud.org.ua/texts/2017/47_2/115-144.pdf andhttp://dx.doi.org/10.15330/ms.47.2.115-144 and https://mathscinet.ams.org/mathscinet-getitem?mr=3733080
17b. Bair, J.; B?aszczyk, 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 andEuler." Journal for General Philosophy of Science 48 (2017), no. 2,195-238. See http://dx.doi.org/10.1007/s10838-016-9334-z andhttps://arxiv.org/abs/1605.00455 andhttp://www.ams.org/mathscinet-getitem?mr=3663035 Here we analyze Euler's approachto infinitesimal analysis and his proof of the infinite product decompositionfor the sine function. We also examine Giovanni Ferraro's flawed historicalscholarship and propose a sounder alternative.
17c. B?aszczyk, P.; Kanovei, V.; Katz, K.; Katz, M.; Kudryk, T.;Mormann, T.; Sherry, D. "Is Leibnizian calculus embeddable in first orderlogic?" Foundations of Science 22 (2017), no. 4, 717-731. Seehttp://dx.doi.org/10.1007/s10699-016-9495-6 andhttps://arxiv.org/abs/1605.03501 and https://mathscinet.ams.org/mathscinet-getitem?mr=3720412
17d. B?aszczyk, 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. Seehttp://dx.doi.org/10.1007/s10699-016-9498-3 andhttps://arxiv.org/abs/1609.04531 andhttps://mathscinet.ams.org/mathscinet-getitem?mr=3720415 Here we propose anapproach to the history of mathematics that focuses on the procedures of thehistorical masters rather than set-theoretic ontology of the entities they use.We also examine Jeremy Gray's flawed historical scholarship and propose asounder alternative.
17e. B?aszczyk, P.; Kanovei, V.; Katz, M.; Sherry, D."Controversies in the foundations of analysis: Comments on Schubring'sConflicts." Foundations of Science 22 (2017), no. 1, 125-140. Seehttp://dx.doi.org/10.1007/s10699-015-9473-4 andhttps://arxiv.org/abs/1601.00059 andhttp://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 followingRobinson, Nelson, and others." Real Analysis Exchange 42 (2017), no. 2,193-252. See https://arxiv.org/abs/1703.00425 andhttp://msupress.org/journals/issue/?id=50-21D-61F andhttps://mathscinet.ams.org/mathscinet-getitem?mr=3721800 and eventuallyhttp://dx.doi.org/10.14321/realanalexch.41.1.0193
17g. Gutman, A.; Katz, M.; Kudryk, T.; Kutateladze, S. "TheMathematical Intelligencer Flunks the Olympics." Foundations of Science 22(2017), no. 3, 539-555. See http://dx.doi.org/10.1007/s10699-016-9485-8 andhttps://arxiv.org/abs/1606.00160 andhttp://www.ams.org/mathscinet-getitem?mr=3696393 Here we examine YaroslavSergeyev's grossbit pathos.
17h. Katz, M.; Polev, L. "From Pythagoreans and Weierstrassians totrue infinitesimal calculus." Journal of Humanistic Mathematics 7 (2017),no. 1, 87-104. See http://dx.doi.org/10.5642/jhummath.201701.07 andhttps://arxiv.org/abs/1701.05187
17i. Sanders, S. "Reverse Formalism 16." Synthese. Seehttp://dx.doi.org/10.1007/s11229-017-1322-2 andhttps://arxiv.org/abs/1701.05066
17j. Sherry, D. "The jesuits and the method of indivisibles."Foundations of Science (2017). See http://dx.doi.org/10.1007/s10699-017-9525-z
year '16
16a. Bascelli, T.; B?aszczyk, P.; Kanovei, V.; Katz, K.; Katz, M.;Schaps, D.; Sherry, D. "Leibniz versus Ishiguro: Closing a Quarter Centuryof Syncategoremania." HOPOS: The Journal of the International Society forthe History of Philosophy of Science 6 (2016), no. 1, 117-147. Seehttp://dx.doi.org/10.1086/685645 and https://arxiv.org/abs/1603.07209
16b. B?aszczyk, 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 andhttps://arxiv.org/abs/1607.00149 andhttp://www.ams.org/mathscinet-getitem?mr=3566230
16c. Kanovei, V.; Katz, K.; Katz, M.; Nowik, T. "Smalloscillations of the pendulum, Euler's method, and adequality." QuantumStudies: Mathematics and Foundations 3 (2016), no. 3, 231-236. Seehttp://dx.doi.org/10.1007/s40509-016-0074-x andhttps://arxiv.org/abs/1604.06663 andhttp://www.ams.org/mathscinet-getitem?mr=3531864
year '15
15a. Kanovei, V.; Katz, K.; Katz, M.; Schaps, M. "Proofs andRetributions, 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 andhttp://www.ams.org/mathscinet-getitem?mr=3312498 Here we examine ErrettBishop's criticisms of Robinson's framework
15b. Kanovei, V.; Katz, K.; Katz, M.; Sherry, D. "Euler's lute andEdwards' oud." The Mathematical Intelligencer 37 (2015), 48-51. Seehttp://dx.doi.org/10.1007/s00283-015-9565-6 andhttps://arxiv.org/abs/1506.02586 and http://www.ams.org/mathscinet-getitem?mr=3435825see also Reception
15c. Katz, M.; Kutateladze, S. "Edward Nelson (1932-2014)."The Review of Symbolic Logic 8 (2015), no. 3, 607-610. Seehttp://dx.doi.org/10.1017/S1755020315000015 andhttps://arxiv.org/abs/1506.01570
15d. Nowik, T; Katz, M. "Differential geometry via infinitesimaldisplacements." Journal of Logic and Analysis 7:5 (2015), 1-44. Seehttp://www.logicandanalysis.com/index.php/jla/article/view/237 andhttp://u.cs.biu.ac.il/~katzmik/dgnsa_arxiv.pdf andhttps://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, andthe gang: The true history of the concepts of limit and shadow." Noticesof the American Mathematical Society 61 (2014), no. 8, 848-864. Seehttp://www.ams.org/notices/201408/rnoti-p848.pdf andhttps://arxiv.org/abs/1407.0233
14b. Katz, K.; Katz, M.; Kudryk, T. "Toward a clarity of theextreme value theorem." Logica Universalis 8 (2014), no. 2, 193-214. Seehttp://dx.doi.org/10.1007/s11787-014-0102-8 and https://arxiv.org/abs/1404.5658and 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. Seehttp://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 as2012)
14d. Tall, D.; Katz, M. "A cognitive analysis of Cauchy'sconceptions of function, continuity, limit, and infinitesimal, withimplications for teaching the calculus." Educational Studies inMathematics 86 (2014), no. 1, 97-124. Seehttp://dx.doi.org/10.1007/s10649-014-9531-9 and https://arxiv.org/abs/1401.1468
year '13
13a. Bair, J.; B?aszczyk, 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 theAmerican 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, andhttps://arxiv.org/abs/1306.5973
13b. B?aszczyk, P.; Katz, M.; Sherry, D. "Ten misconceptions fromthe 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, andChimeras: Connes on the Role of Hyperreals in Mathematics." Foundations ofScience 18 (2013), no. 2, 259-296. Seehttp://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 AlainConnes' criticisms of Robinson's framework
13d. Katz, M.; Leichtnam, E. "Commuting and noncommutinginfinitesimals." 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, andhttps://arxiv.org/abs/1304.0583 Here we examine Alain Connes' criticisms ofRobinson's framework
13e. Katz, M.; Schaps, D.; Shnider, S. "Almost Equal: The Methodof Adequality from Diophantus to Fermat and Beyond." Perspectives onScience 21 (2013), no. 3, 283-324. See http://dx.doi.org/10.1162/POSC_a_00101,http://www.ams.org/mathscinet-getitem?mr=3114421, andhttps://arxiv.org/abs/1210.7750 Here we refute Herbert Breger's interpretationof Fermat and propose a sounder alternative.
13f. Katz, M.; Sherry, D. "Leibniz's Infinitesimals: TheirFictionality, Their Modern Implementations, And Their Foes From Berkeley ToRussell And Beyond." Erkenntnis 78 (2013), no. 3, 571-625. See http://dx.doi.org/10.1007/s10670-012-9370-y,http://www.ams.org/mathscinet-getitem?mr=3053644, andhttps://arxiv.org/abs/1205.0174
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,http://www.ams.org/mathscinet-getitem?mr=3031797, andhttps://arxiv.org/abs/1206.0119
13h. Mormann, T.; Katz, M. "Infinitesimals as an issue ofneo-Kantian philosophy of science." HOPOS: The Journal of theInternational Society for the History of Philosophy of Science 3 (2013), no. 2,236-280. See http://dx.doi.org/10.1086/671348 andhttps://arxiv.org/abs/1304.1027
year '12
12a. Borovik, A.; Jin, R.; Katz, M. "An Integer Construction ofInfinitesimals: Toward a Theory of Eudoxus Hyperreals." Notre Dame Journalof Formal Logic 53 (2012), no. 4, 557-570. See https://arxiv.org/abs/1210.7475,http://dx.doi.org/10.1215/00294527-1722755, andhttp://www.ams.org/mathscinet-getitem?mr=2995420
12b. Borovik, A.; Katz, M. "Who gave you the Cauchy-Weierstrasstale? 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, andhttp://www.ams.org/mathscinet-getitem?mr=2950620, as well ashttp://u.cs.biu.ac.il/~katzmik/straw.html Here we examine Judith Grabiner'sflawed 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/s10699-011-9228-9and https://arxiv.org/abs/1107.3688 andhttp://www.ams.org/mathscinet-getitem?mr=2935194
12d. Katz, K.; Katz, M. "A Burgessian Critique of NominalisticTendencies in Contemporary Mathematics and its Historiography." Foundationsof Science 17 (2012), no. 1, 51-89. Seehttp://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 andhomogeneity." 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, andhttp://u.cs.biu.ac.il/~katzmik/straw2.html
12f. Katz, M.; Tall, D. "Tension between Intuitive Infinitesimalsand Formal Mathematical Analysis." Chapter in: Bharath Sriraman, Editor.Crossroads in the History of Mathematics and Mathematics Education. The MontanaMathematics Enthusiast Monographs in Mathematics Education 12, Information AgePublishing, Inc., Charlotte, NC, 2012, pp. 71-89. Seehttps://arxiv.org/abs/1110.5747
year '11
11a. Katz, K.; Katz, M. "Meaning in Classical Mathematics: Is itat Odds with Intuitionism?" Intellectica 56 (2011), no. 2, 223-302. Seehttps://arxiv.org/abs/1110.5456 Here we examine Errett Bishop's criticisms ofRobinson's framework
11b. Katz, K.; Katz, M. "Cauchy's continuum." Perspectives onScience 19 (2011), no. 4, 426-452. See http://dx.doi.org/10.1162/POSC_a_00047,https://arxiv.org/abs/1108.4201, andhttp://www.ams.org/mathscinet-getitem?mr=2884218
year '10
10a. Ely, R. "Nonstandard student conceptions about infinitesimaland infinite numbers." Journal for Research in Mathematics Education 41(2010), no. 2, 117-146. Seehttp://www.nctm.org/publications/article.aspx?id=26196 andhttp://u.cs.biu.ac.il/~katzmik/ely10.pdf
10b. Katz, K.; Katz, M. "Zooming in on infinitesimal 1-.9.. in apost-triumvirate era." Educational Studies in Mathematics 74 (2010), no.3, 259-273. See http://dx.doi.org/10.1007/s10649-010-9239-4 andhttps://arxiv.org/abs/arXiv:1003.1501
10c. Katz, K.; Katz, M. "When is .999... less than 1?" TheMontana Mathematics Enthusiast 7 (2010), No. 1, 3-30. Seehttp://scholarworks.umt.edu/tme/vol7/iss1/11 andhttps://arxiv.org/abs/arXiv:1007.3018
List of periodicals where the articles have appeared, in alphabeticalorder:
American Mathematical Monthly 13d
Erkenntnis 13f
Foundations of Science 18f, 17c, 17d, 17e, 17g, 15a, ...
Historia Mathematica 18j
HOPOS (Journal of the International Society for the History ofPhilosophy 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 analysisfrom Stevin to Cauchy
Pioneer Journal wherereappraisal appeared Link to articlecontaining reappraisal
Simon Stevin Foundations ofScience 12c
Pierre Fermat Perspectives onScience 13e
Pierre Fermat Perspectives onScience 18d
James Gregory Foundations ofScience 18f
Gottfried Leibniz Notices AMS 12e
Gottfried Leibniz Erkenntnis 13f
Gottfried Leibniz StudiaLeibnitiana 14c
Gottfried Leibniz HOPOS(Journal of the International Society for the History of Philosophy of Science) 16a
Leonhard Euler MathematicalIntelligencer 15b
Leonhard Euler Journal forGeneral Philosophy of Science 17b
A. L. Cauchy Perspectives onScience 11b
A. L. Cauchy Foundations ofScience 12b
A. L. Cauchy Foundations ofScience 18e
A. L. Cauchy See this link:Misconceptions with regard to Cauchy and his infinitesimals
List of critics in alphabetical order:
Critic Venue where rebuttalappeared Link to article/venue containingrebuttal
Richard Arthur Erkenntnis 13f
Richard Arthur Foundations ofScience 17d
Errett Bishop Foundations of Science 15a
Errett Bishop Intellectica 11a
Errett Bishop HistoriaMathematica 18j
Errett Bishop New manuscripts New manuscripts
Bishop-Connes Synthese 17i
Umberto Bottazzini Math Overflow Q&A thread
Herbert Breger Perspectives onScience 13e
Herbert Breger Foundations ofScience 18d
Alain Connes Foundations ofScience 13c
Alain Connes AmericanMathematical Monthly 13d
Alain Connes Math Overflow Q&A thread
John Earman Erkenntnis 13f
Kenny Easwaran Notices ofthe American Mathematical Society 14a
Harold M. Edwards MathematicalIntelligencer 15b
Harold M. Edwards Journal forGeneral Philosophy of Science 17b,section 4.13
Giovanni Ferraro Journal forGeneral Philosophy of Science 17b
Giovanni Ferraro Foundationsof Science 18f
Craig Fraser Foundations ofScience 18e
Craig Fraser Mat. Stud. 17a
Craig Fraser Math Overflow Q&A thread
Judith Grabiner Foundationsof Science 12b
Judith Grabiner Foundationsof Science 18e
Jeremy Gray Foundations ofScience 17d
Jeremy Gray Stack Exchange Q&A thread
Paul Halmos Foundations ofScience 16b
Hide Ishiguro StudiaLeibnitiana 14c
Hide Ishiguro HOPOS (Journalof the International Society for the History of Philosophy of Science) 16a
Jasper Luetzen Mat. Stud. 17a
Gert Schubring Foundations ofScience 17e
Yaroslav Sergeyev Foundationsof Science 17g
Yaroslav Sergeyev MathOverflow Q&A thread
Yaroslav Sergeyev MathStackExchange Q&A thread 1 andQ&A thread 2
Yaroslav Sergeyev EMS Surveysin Mathematical Sciences "Both[EICs] have assumed responsibility for [the mistake of publishing Sergeyev'spaper] and resigned from their position."
Yaroslav Sergeyev RetractionWatch Editors-in-chief of mathjournal resign over controversial paper
Yaroslav Sergeyev dedicatedpage Of Pirahas, infinity, and Ayatollahs
Detlef Spalt Perspectiveson Science 11b
tallberkeley12
Other critics of infinitesimals and/or Robinson Journal where rebuttal appeared Linkto article containing rebuttal
George Berkeley (1685-1753) Erkenntnis 13f
Fran?ois-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- ) Journal forGeneral Philosophy of Science 17b,section 2.7
Kathleen Sullivan's '76 study of teaching calculus with infinitesimalsbased 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
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If, as Kurt Goedel said, Robinson's theory is the analysis of thefuture, then it should be called standard analysis (or infinitesimal analysis),not nonstandard analysis. Hello?