Ten Misconceptions from the History of Analysis and Their Debunking

Foundations of Science

Volumn 18, Issue 1, 2013, Pages 43-74

  Błaszczyk, Piotr ^a   Katz, Mikhail G ^b   Sherry, David ^c  

^a PEDAGOGICAL UNIVERSITY   (Poland)

^b BAR ILAN UNIVERSITY   (Israel)

^c NORTHERN ARIZONA UNIVERSITY   (United States)

Author keywords

Abraham Robinson; Adequality; Archimedean continuum; Bernoullian continuum; Cantor; Cauchy; Cognitive bias; Completeness; Constructivism; Continuity; Continuum; du Bois Reymond; Epsilontics; Felix Klein; Fermat Robinson standard part; Infinitesimal; Leibniz o transfer principle; Limit; Mathematical rigor; Nominalism; Non Archimedean; Simon Stevin; Stolz; Sum theorem; Weierstrass

Indexed keywords

SOCIAL SCIENCES;

ADEQUALITY; ARCHIMEDEAN CONTINUUM; BERNOULLIAN CONTINUUM; CANTOR; CAUCHY; COGNITIVE BIAS; COMPLETENESS; CONSTRUCTIVISM; CONTINUITY; CONTINUUM; DU BOIS-REYMOND; EPSILONTICS; FELIX KLEIN; INFINITESIMAL; LIMIT; MATHEMATICAL RIGOR; NOMINALISM; NON-ARCHIMEDEAN; ROBINSON; SIMON STEVIN; STOLZ; SUM THEOREM; WEIERSTRASS;

NUMBERING SYSTEMS;

EID: 84874545257     PISSN: 12331821     EISSN: 15728471     Source Type: Journal    
DOI: 10.1007/s10699-012-9285-8     Document Type: Article

References (152)

1. Albeverio S., Høegh-Krohn R., Fenstad J., Lindstrøm T. (1986) Nonstandard methods in stochastic analysis and mathematical physics. Pure and Applied Mathematics, 122. Academic Press, Inc, Orlando, FL.
2. Andersen K. (2011) One of Berkeley's arguments on compensating errors in the calculus. Historia Mathematica 38(2): 219-231.
3. Anderson R. (1976) A non-standard representation for Brownian motion and Itô integration. Israel Journal of Mathematics 25(1-2): 15-46.
4. Arkeryd L. (1981) Intermolecular forces of infinite range and the Boltzmann equation. Archive for Rational Mechanics and Analysis 77(1): 11-21.
5. Arkeryd L. (2005) Nonstandard analysis. American Mathematical Monthly 112(10): 926-928.
6. Bacon, F. (1620). Novum Organum.
7. Baltus C. (2004) D'Alembert's proof of the fundamental theorem of algebra. Historia Mathematica 31(4): 414-428.
8. Barany M. J. (2011) Revisiting the introduction to Cauchy's Cours d'analyse. Historia Mathematica 38(3): 368-388.
9. Bell E. T. (1945) The development of mathematics. McGraw-Hill Book Company, Inc, New York.
10. Bell J. L. (2008) A primer of infinitesimal analysis (2nd ed.). Cambridge University Press, Cambridge.
11. Bell, J. L. (2009a). Continuity and infinitesimals. Stanford Encyclopedia of Philosophy. Revised 20 July 2009.
12. Bell, J. L. (2009b). Le continu cohésif. Intellectica, 2009/1(51).
13. Benci V., Di Nasso M. (2003) Alpha-theory: An elementary axiomatics for nonstandard analysis. Expositiones Mathematicae 21(4): 355-386.
14. Berkeley, G. (1734). The analyst, a discourse addressed to an infidel Mathematician.
15. Błaszczyk, P. (2009). Nonstandard analysis from a philosophical point of view. In Non-classical mathematics 2009 (Hejnice, 18-22 June 2009), pp. 21-24.
16. Borel, E. (1902) Leçons sur les séries àtermes positifs, ed. Robert d'Adhemar, Paris (Gauthier-Villars).
17. Borovik, A., Jin, R., & Katz, M. (2012). An integer construction of infinitesimals: Toward a theory of Eudoxus hyperreals. Notre Dame Journal of Formal Logic, 53(4).
18. Borovik, A., & Katz, M. (2011). Who gave you the Cauchy-Weierstrass tale? The dual history of rigorous calculus. Foundations of Science, see http://dx. doi. org/10. 1007/s10699-011-9235-x and http://arxiv. org/abs/1108. 2885.
19. Bos H. J. M. (1974) Differentials, higher-order differentials and the derivative in the Leibnizian calculus. Archive for History of Exact Sciences 14: 1-90.
20. Boyer C. (1949) The concepts of the calculus. Hafner Publishing Company, New York.
21. Bråting K. (2007) A new look at E. G. Björling and the Cauchy sum theorem. Archive for History of Exact Sciences 61(5): 519-535.
22. Cajori. (1993). A history of mathematical notations (Vol. 1-2). La Salle, IL: The Open Court Publishing Company, 1928/1929. Reprinted by Dover.
23. Cauchy A. L. (1821) Cours d'Analyse de L'Ecole Royale Polytechnique. Première Partie. Analyse algébrique. Imprimérie Royale, Paris.
24. Cauchy A. L. (1823) Résumé des Leçons données à l'Ecole Royale Polytechnique sur le Calcul Infinitésimal. Imprimérie Royale, Paris.
25. Cauchy A. L. (1815) Théorie de la propagation des ondes à la surface d'un fluide pesant d'une profondeur indéfinie (published 1827, with additional Notes). Oeuvres 1(1): 4-318.
26. Cauchy, A. L. (1829). Leçons sur le calcul différentiel. Paris: Debures. In Oeuvres complètes (Ser. 2, Vol. 4, pp. 263-609). Paris: Gauthier-Villars, 1899.
27. Cauchy, A. L. (1853). Note sur les séries convergentes dont les divers termes sont des fonctions continues d'une variable réelle ou imaginaire, entre des limites données. In Oeuvres complètes (Ser. 1, Vol. 12, pp. 30-36). Paris: Gauthier-Villars, 1900.
28. Connes A. (1995) Noncommutative geometry and reality. Journal of Mathematical Physics 36(11): 6194-6231.
29. Crossley J. (1987) The emergence of number (2nd ed.). World Scientific Publishing Co, Singapore.
30. Crowe, M. (1988). Ten misconceptions about mathematics and its history. History and philosophy of modern mathematics (Minneapolis, MN, pp. 260-277, 1985). Minnesota studies in philosophical science, XI. Minneapolis, MN: University of Minnesota Press.
31. Cutland N., Kessler C., Kopp E., Ross D. (1988) On Cauchy's notion of infinitesimal. The British Journal for the Philosophy of Science 39(3): 375-378.
32. D'Alembert, J. (1754). Differentiel. In Encyclopédie, 4.
33. Dauben J. (1995) Abraham Robinson. The creation of nonstandard analysis. A personal and mathematical odyssey. With a foreword by Benoit B. Mandelbrot. Princeton University Press, Princeton.
34. Dauben, J. (1996). Arguments, logic and proof: Mathematics, logic and the infinite. History of mathematics and education: Ideas and experiences (Essen, 1992; Vol. 11, pp. 113-148), Stud. Wiss. Soz. Bildungsgesch. Mathematics. Göttingen: Vandenhoeck & Ruprecht.
35. Davis, M. (1977). Applied nonstandard analysis. Pure and Applied Mathematics. Wiley-Interscience: New York. Reprinted: Dover, NY, 2005, see http://store. doverpublications. com/0486442292. html.
36. Dedekind R. (1872) Stetigkeit und irrationale Zahlen, Freid. Vieweg & Sohn, Braunschweig.
37. Dedekind R. (1963) Essays on the theory of numbers. I: Continuity and irrational numbers. II: The nature and meaning of numbers. Authorized translation by Wooster Woodruff Beman Dover Publications, Inc, New York.
38. Dehn M. (1900) Die Legendre'schen Sätze über die Winkelsumme im Dreieck. Mathematische Annalen 53(3): 404-439.
39. Dossena R., Magnani L. (2007) Mathematics through diagrams: Microscopes in non-standard and smooth analysis. Studies in Computational Intelligence (SCI) 64: 193-213.
40. Ehrlich, P. (2005). Continuity. In D. M. Borchert (Ed.), Encyclopedia of philosophy (2nd ed., pp. 489-517). Farmington Hills, MI: Macmillan Reference USA (The online version contains some slight improvements).
41. Ehrlich P. (2006) The rise of non-Archimedean mathematics and the roots of a misconception. I. The emergence of non-Archimedean systems of magnitudes. Archive for History of Exact Sciences 60(1): 1-121.
42. Ehrlich P. (2012) The absolute arithmetic continuum and the unification of all numbers great and small. Bulletin of Symbolic Logic 18(1): 1-45.
43. Ely R. (2010) Nonstandard student conceptions about infinitesimals. Journal for Research in Mathematics Education 41(2): 117-146.
44. Euclid. (2007). Euclid's elements of geometry. Edited, and provided with a modern English translation, by Richard Fitzpatrick, http://farside. ph. utexas. edu/euclid. html.
45. Euler, L. (1770). Elements of algebra (3rd English edition). English translated by John Hewlett and Francis Horner. Orme Longman, 1822.
46. Faltin F., Metropolis N., Ross B., Rota G.-C. (1975) The real numbers as a wreath product. Advances in Mathematics 16: 278-304.
47. Fearnley-Sander D. (1979) Hermann Grassmann and the creation of linear algebra. The American Mathematical Monthly 86(10): 809-817.
48. Feferman, S. (2009). Conceptions of the continuum [Le continu mathématique. Nouvelles conceptions, nouveaux enjeux]. Intellectica, 51, 169-189. See also http://math. stanford. edu/~feferman/papers/ConceptContin. pdf.
49. Felscher W. (1979) Naive Mengen und abstrakte Zahlen. III. [Naive sets and abstract numbers. III] Transfinite Methoden. With an erratum to Vol. II. Bibliographisches Institut, Mannheim.
50. Felscher W. (2000) Bolzano, Cauchy, epsilon, delta. American Mathematical Monthly 107(9): 844-862.
51. Fisher G. (1979) Cauchy's variables and orders of the infinitely small. The British Journal for the Philosophy of Science 30(3): 261-265.
52. Fourier, J. (1822). Théorie analytique de la chaleur.
53. Fowler D. H. (1992) Dedekind's theorem: √2×√3=√6. American Mathematical Monthly 99(8): 725-733.
54. Fraenkel A. (1967) Lebenskreise. Aus den Erinnerungen eines jüdischen Mathematikers. Deutsche Verlags-Anstalt, Stuttgart.
55. Freudenthal H. (1971) Did Cauchy plagiarise Bolzano?. Archive for History of Exact Sciences 7: 375-392.
56. Gerhardt, C. I. (ed.) (1850-1863). Leibnizens mathematische Schriften. Berlin and Halle: Eidmann.
57. Gilain, C. (1989). Cauchy et le cours d'analyse de l'Ecole polytechnique. With an editorial preface by Emmanuel Grison. Bulletin Society des amis de la Bibliothèque, Ecole Polytechnique, Vol. 5.
58. Giordano P. (2010) Infinitesimals without logic. Russian Journal of Mathematical Physics 17(2): 159-191.
59. Giordano P. (2010) The ring of Fermat reals. Advances in Mathematics 225(4): 2050-2075.
60. Giordano, P., & Katz, M. (2011). Two ways of obtaining infinitesimals by refining Cantor's completion of the reals. See http://arxiv. org/abs/1109. 3553.
61. Gordon, E. I., Kusraev, A. G., & Kutateladze, S. S. (2002). Infinitesimal analysis. Updated and revised translation of the 2001 Russian original. Translated by Kutateladze. Mathematics and its applications (Vol. 544). Dordrecht: Kluwer.
62. Grabiner J. (1983) Who gave you the epsilon? Cauchy and the origins of rigorous calculus. American Mathematics Monthly 90(3): 185-194.
63. Grattan-Guinness I. (2004) The mathematics of the past: Distinguishing its history from our heritage. Historia Mathematica 31: 163-185.
64. Gray J. (2008) Plato's ghost. The modernist transformation of mathematics. Princeton University Press, Princeton, NJ.
65. Guicciardini, N. (2011). Private communication, 27 november.
66. Hawking, S., (Ed.) (2007). The mathematical breakthroughs that changed history. Philadelphia, PA: Running Press (originally published 2005).
67. Hewitt E. (1948) Rings of real-valued continuous functions. I. Transactions of the American Mathematical Society 64: 45-99.
68. Hoborski, A. (1923). Aus der theoretischen Arithmetik (German). Opusc. math. Kraków, 2 11-12 (1938).
69. Hrbáček K. (1978) Axiomatic foundations for nonstandard analysis. Fundamenta Mathematicae 98(1): 1-19.
70. Hrbacek K. (2007) Stratified analysis? The strength of nonstandard analysis. Springer, Vienna, pp 47-63.
71. Hrbacek K., Lessmann O., O'Donovan R. (2010) Analysis with ultrasmall numbers. American Mathematics Monthly 117(9): 801-816.
72. R., R. (1940) OEuvres complètes. Martinus Nijhoff, La Haye.
73. Katz, K., & Katz, M. (2010a). Zooming in on infinitesimal 1-. 9. in a post-triumvirate era. Educational Studies in Mathematics, 74 (3), 259-273. See http://arxiv. org/abs/arXiv: 1003. 1501.
74. Katz K., Katz M. (2010) When is 0. 999...less than 1?. The Montana Mathematics Enthusiast 7(1): 3-30.
75. Katz, K., & Katz, M. (2011a). Cauchy's continuum. Perspectives on Science, 19(4), 426-452. See http://www. mitpressjournals. org/toc/posc/19/4 and http://arxiv. org/abs/1108. 4201.
76. Katz, K., & Katz, M. (2011b). Stevin numbers and reality. Foundations of Science. See http://dx. doi. org/10. 1007/s10699-011-9228-9 and http://arxiv. org/abs/1107. 3688.
77. Katz, K., & Katz, M. (2011c) Meaning in classical mathematics: Is it at odds with Intuitionism? Intellectica, 56(2), 223-302. See http://arxiv. org/abs/1110. 5456.
78. Katz, K., & Katz, M. (2012). A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography. Foundations of Science, 17(1), 51-89. See http://dx. doi. org/10. 1007/s10699-011-9223-1 and http://arxiv. org/abs/1104. 0375.
79. Katz, K., & Sherry, D. (2012). Leibniz's infinitesimals: Their fictionality, their modern implementations, and their foes from Berkeley to Russell and beyond. Erkenntnis (to appear).
80. Katz, M., & Tall, D. (2011). The tension between intuitive infinitesimals and formal mathematical analysis. In B. Sriraman (Ed.), Crossroads in the history of mathematics and mathematics education. The Montana Mathematics Enthusiast Monographs in Mathematics Education (Vol. 12). Charlotte, NC: Information Age Publishing, Inc. See http://arxiv. org/abs/1110. 5747 and http://www. infoagepub. com/products/Crossroads-in-the-History-of-Mathematics.
81. Katz V. J. (1993) Using the history of calculus to teach calculus. Contributions from History, Philosophy and Sociology of Science and Education. Science & Education 2(3): 243-249.
82. Keisler H. J. (1986) Elementary calculus: An infinitesimal approach (2nd Ed.). Prindle, Weber & Schimidt, Boston.
83. Keisler, H. J. (1994). The hyperreal line. Real numbers, generalizations of the reals, and theories of continua, Synthese Lib. (Vol. 242, pp. 207-237). Dordrecht: Kluwer.
84. Keisler, H. J. (2008a). The ultraproduct construction. In Proceedings of the ultramath conference, Pisa, Italy.
85. Keisler, H. J. (2008b). Quantifiers in limits. Andrzej Mostowski and Foundational Studies (pp. 151-170). Amsterdam: IOS.
86. Klein, F. (1908). (Elementary Mathematics from an Advanced Standpoint. Vol. I. Arithmetic, Algebra, Analysis). Translation by E. R. Hedrick & C. A. Noble [Macmillan, New York, 1932] from the third German edition [Springer, Berlin, 1924]. Originally published as Elementarmathematik vom höheren Standpunkte aus (Leipzig, 1908).
87. Kleiner I., Movshovitz-Hadar N. (1994) The role of paradoxes in the evolution of mathematics. American Mathematical Monthly 101(10): 963-974.
88. Knobloch E. (2002) Leibniz's rigorous foundation of infinitesimal geometry by means of Riemannian sums. Foundations of the formal sciences, 1 (Berlin, 1999). Synthese 133(1-2): 59-73.
89. Koetsier T. (2009) Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity. In: Hanna G., Jahnke H., Pulte H. (eds) Explanation and proof in mathematics. Philosophical and Educational Perspectives. Springer, Berlin.
90. Lagrange, J.-L. (2009). (1811) Mécanique Analytique. Courcier. Reissued by Cambridge University Press.
91. Lakatos I. (1976) Proofs and refutations. The logic of mathematical discovery. Edited by John Worrall and Elie Zahar. Cambridge University Press, Cambridge.
92. Lakatos, I. (1978). Cauchy and the continuum: The significance of nonstandard analysis for the history and philosophy of mathematics. The Mathematical Intelligencer, 1(3), 151-161 (paper originally presented in 1966).
93. Laugwitz D. (1987) Infinitely small quantities in Cauchy's textbooks. Historia Mathematica 14(3): 258-274.
94. Laugwitz D. (1989) Definite values of infinite sums: Aspects of the foundations of infinitesimal analysis around 1820. Archive for History of Exact Sciences 39(3): 195-245.
95. Laugwitz D. (1992) Early delta functions and the use of infinitesimals in research. Revue d'histoire des sciences 45(1): 115-128.
96. Laugwitz D. (1997) On the historical developement of infinitesimal mathematics. Part II. The conceptual thinking of Cauchy. Translated from the German by Abe Shenitzer with the editorial assistance of Hardy Grant. American Mathematical Monthly 104(7): 654-663.
97. Lawvere F. W. (1980) Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body. Third Colloquium on Categories (Amiens, 1980), Part I. Cahiers Topologie Géom. Différentielle 21(4): 377-392.
98. Leibniz G. (2001) The Labyrinth of the continuum (Arthur, R., translator and editor). Yale University Press, New Haven.
99. Leibniz. (1701). Mémoire de M. G. G. Leibniz touchant son sentiment sur le calcul differéntiel. Mémoires de Trévoux, 1701(November), 270-272. Reprinted in (Gerhardt, 1850-1863, Vol. 5, p. 350).
100. Leibniz. (1710). GM V, pp. 381-2 (in Gerhardt (1850-1863)).
101. Levy S. H. (1991) Charles S. Peirce's Theory of Infinitesimals. International Philosophical Quarterly 31: 127-140.
102. Lightstone A. H. (1972) Infinitesimals. American Mathematical Monthly 79: 242-251.
103. Łoś, J. (1955). Quelques remarques, théorèmes et problèmes sur les classes définissables d'algèbres. In Mathematical interpretation of formal systems (pp. 98-113). Amsterdam: North-Holland Publishing Co.
104. Lutz R., Albuquerque L. (2003) Modern infinitesimals as a tool to match intuitive and formal reasoning in analysis. Logic and mathematical reasoning (Mexico City, 1997). Synthese 134(1-2): 325-351.
105. Lützen J. (1982) The prehistory of the theory of distributions. Studies in the history of mathematics and physical sciences Vol. 7. Springer, New York.
106. Lützen, J. (2003). The foundation of analysis in the 19th century. A history of analysis. History of Mathematics (Vol. 24, pp. 155-195). Providence, RI: American Mathematical Society.
107. Luxemburg, W. (1964). Nonstandard analysis. Lectures on A. Robinson's Theory of infinitesimals and infinitely large numbers. Pasadena: Mathematics Department, California Institute of Technology' second corrected ed.
108. Madison E., Stroyan K. (1977) Reviews: Elementary calculus (Review of first edition of Keisler (1986)). American Mathematical Monthly 84(6): 496-500.
109. Magnani L., Dossena R. (2005) Perceiving the infinite and the infinitesimal world: Unveiling and optical diagrams in mathematics. Foundations of Science 10(1): 7-23.
110. Malet A. (2006) Renaissance notions of number and magnitude. Historia Mathematica 33(1): 63-81.
111. Mancosu P. (1996) Philosophy of mathematics and mathematical practice in the seventeenth century. The Clarendon Press/Oxford University Press, New York.
112. Mancosu, P. (eds) (2008) The philosophy of mathematical practice. Oxford University Press, Oxford.
113. Mancosu P. (2009) Measuring the size of infinite collections of natural numbers: Was Cantor's theory of infinite number inevitable?. The Review of Symbolic Logic 2(4): 612-646.
114. Mancosu, P., & Vailati, E. (1990). Detleff Clüver: An early opponent of the Leibnizian differential calculus. Centaurus, 33(4), 325-344.
115. Marsh, J. (1742). Decimal arithmetic made perfect. London.
116. McClenon R. B. (1923) A contribution of Leibniz to the history of complex numbers. American Mathematical Monthly 30(7): 369-374.
117. Mormann T. (2008) Idealization in Cassirer's philosophy of mathematics. Philosophia Mathematica (3) 16(2): 151-181.
118. Naets J. (2010) How to define a number? A general epistemological account of Simon Stevin's art of defining. Topoi 29(1): 77-86.
119. Nelson E. (1977) Internal set theory: A new approach to nonstandard analysis. Bulletin of American Mathematical Society 83(6): 1165-1198.
120. Newton, I. (1671). A treatise on the methods of series and fluxions. In Whiteside (1969) (Vol. III), pp. 33-35.
121. Newton, I. (1946). Sir Isaac Newton's mathematical principles of natural philosophy and his system of the world. A revision by F. Cajori of A. Motte's 1729 translation. Berkeley: University of California Press.
122. Newton, I. (1999). The principia: Mathematical principles of natural philosophy. Translated by I. B. Cohen & A. Whitman, preceded by A guide to Newton's Principia by I. B. Cohen. Berkeley: University of California Press.
123. Peirce, C. S. (1976). The new elements of mathematics, Vol. III/1. Mathematical miscellanea. Edited by Carolyn Eisele. Atlantic Highlands, NJ: Mouton Publishers/The Hague-Paris/Humanities Press.
124. Pourciau B. (2001) Newton and the notion of limit. Historia Mathematica 28(1): 18-30.
125. Putnam H. (1975) What is mathematical truth? Proceedings of the American Academy Workshop on the Evolution of Modern Mathematics (Boston, Mass., 1974). Historia Mathematica 2(4): 529-533.
126. Robinson A. (1966) Non-standard analysis. North-Holland Publishing Co, Amsterdam.
127. Roquette P. (2010) Numbers and models, standard and nonstandard. Math Semesterber 57: 185-199.
128. Russell B. (1903) The principles of mathematics. Routledge, London.
129. Rust H. (2005) Operational semantics for timed systems. Lecture Notes in Computer Science 3456: 23-29. doi: 10. 1007/978-3-540-32008-1_4.
130. Schubring G. (2005) Conflicts between generalization, rigor, and intuition. Number concepts underlying the development of analysis in 17-19th century France and Germany sources and studies in the history of mathematics and physical sciences. Springer, New York.
131. Sepkoski D. (2005) Nominalism and constructivism in seventeenth-century mathematical philosophy. Historia Mathematica 32(1): 33-59.
132. Sherry D. (1987) The wake of Berkeley's Analyst: Rigor mathematicae?. Studies in History and Philosophical Science 18(4): 455-480.
133. Sherry D. (1993) Don't take me half the way: On Berkeley on mathematical reasoning. Studies in History and Philosophical Science 24(2): 207-225.
134. Sinaceur H. (1973) Cauchy et Bolzano. Reviews of Histoire in Science and Applications 26((2): 97-112.
135. Skolem Th. (1934) Über die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ausschliesslich Zahlenvariablen. Fundamenta Mathematicae 23: 150-161.
136. Smale S. (1981) The fundamental theorem of algebra and complexity theory. Bulletin of the American Mathematical Society (N. S.) 4(1): 1-36.
137. Smith D. E. (1920) Source book in mathematics. Mc Grow-Hill, New York.
138. Stevin, S. (1585). L'Arithmetique. In A. Girard (Ed.), Les Oeuvres Mathematiques de Simon Stevin (Leyde, 1634), part I (pp. 1-101).
139. Stevin, S. L'Arithmetique. In A. Girard (Ed.), 1625, part II. Online at http://www. archive. org/stream/larithmetiqvedes00stev#page/353/mode/1up.
140. Stevin, S. (1958). The principal works of Simon Stevin (Vols. IIA, IIB). In D. J. Struik, C. V. Swets, & Zeitlinger (Eds.), Mathematics (Vols. IIA: v+pp. 1-455 (1 plate), IIB: 1958 iv+pp, pp. 459-976). Amsterdam.
141. Strømholm P. (1968) Fermat's methods of maxima and minima and of tangents. A reconstruction. Archive for History of Exact Sciences 5(1): 47-69.
142. Stroyan, K. (1972). Uniform continuity and rates of growth of meromorphic functions. Contributions to non-standard analysis (Sympos., Oberwolfach, 1970; Vol. 69, pp. 47-64). Studies in Logic and Foundations of Mathematics. Amsterdam: North-Holland.
143. Tall D. (1980) Looking at graphs through infinitesimal microscopes, windows and telescopes. The Mathematical Gazette 64: 22-49.
144. Tall D. (1991) The psychology of advanced mathematical thinking. In: Tall D. O. (eds) Advanced mathematical thinking mathematics education library, 11. Kluwer, Dordrecht.
145. Tall, D. (2009). Dynamic mathematics and the blending of knowledge structures in the calculus. In Transforming Mathematics Education through the use of Dynamic Mathematics. ZDM (pp. 1-11) (June 2009).
146. Tao T. (2010) An epsilon of room, II. Pages from year three of a mathematical blog. American Mathematical Society, Providence, RI.
147. Tarski A. (1930) Une contribution à la théorie de la mesure. Fundamenta Mathematicae 15: 42-50.
148. Urquhart, A. Mathematics and physics: Strategies of assimilation. In Mancosu (2008), pp. 417-440.
149. van der Waerden B. L. (1985) A history of algebra. From al-Khwarizmi to Emmy Noether. Springer, Berlin.
150. Weil A. (1973) Book review: The mathematical career of Pierre de Fermat. Bulletin of the American Mathematical Society 79(6): 1138-1149.
151. Weil A. (1984) Number theory. An approach through history. From Hammurapi to Legendre. Birkhäuser Boston, Inc, Boston.
152. Whiteside, D. T. (Ed.) (1969). The mathematical papers of Isaac Newton. In D. T. Whiteside with the assistance in publication of M. A. Hoskin and A. Prag (Eds.) (Vol. III, pp. 1670-1673). London: Cambridge University Press.