The Mathematical Intelligencer

, Volume 37, Issue 4, pp 48–51 | Cite as

Euler’s Lute and Edwards’s Oud

  • Vladimir Kanovei
  • Karin U. Katz
  • Mikhail G. Katz
  • David Sherry
Note

Notes

Acknowledgments

The work of Vladimir Kanovei was partially supported by the Russian Scientific Fund (project no. 14-50-00150) and RFBR grant 13-01-00006. M. Katz was partially funded by the Israel Science Foundation grant no. 1517/12. The influence of Hilton Kramer (1928–2012) is obvious.

References

  1. [Bascelli et al. 2014] 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, no. 8, 848–864.Google Scholar
  2. [Borovik & Katz 2012] Borovik, A., Katz, M. “Who Gave You the Cauchy—Weierstrass Tale? The Dual History of Rigorous Calculus.” Foundations of Science 17, no. 3, 245–276. See http:// dx.doi.org/10.1007/s10699-011-9235-x and http://arxiv.org/ abs/1108.2885.
  3. [Bos 1974] Bos, H. “Differentials, Higher-Order Differentials and the Derivative in the Leibnizian Calculus.” Archive for History of Exact Sciences 14, 1–90.Google Scholar
  4. [Edwards 1981] Edwards, H. “Read the Masters!” In Mathematics Tomorrow, Lynn Arthur Steen, ed., Springer-Verlag, New York-Berlin, pp. 105–110.Google Scholar
  5. [Edwards 2005] Edwards, H. Essays in Constructive Mathematics. Springer-Verlag, New York.Google Scholar
  6. [Edwards 2007a] Edwards, H. “A Normal Form for Elliptic Curves.” Bull. Amer. Math. Soc. (N.S.) 44, no. 3, 393–422.Google Scholar
  7. [Edwards 2007b] Edwards, H. “Euler’s Definition of the Derivative.” Bull. Amer. Math. Soc. (N.S.) 44, no. 4, 575–580.Google Scholar
  8. [Euler 1748] Euler, L. Introductio in Analysin Infinitorum, Tomus primus. SPb and Lausana.Google Scholar
  9. [Euler 1755] Euler, L. Institutiones Calculi Differentialis. SPb.Google Scholar
  10. [Euler 2000] Euler, L. Foundations of Differential Calculus. English translation of Chapters 1–9 of [Euler 1755] by J. Blanton, Springer, New York.Google Scholar
  11. [Grattan-Guinness 2000] Grattan-Guinness, I. “The Emergence of Mathematical Analysis and Its Foundational Progress, 1780–1880.” In From the Calculus to Set Theory, 1630–1910, pp. 94–148, Princeton Paperbacks, Princeton University Press, Princeton, New Jersey.Google Scholar
  12. [Kanovei et al. 2015] Kanovei, V., Katz, K., Katz, M., Schaps, M. “Proofs and Retributions, Or: Why Sarah Can’t Take Limits.” Foundations of Science 20, no. 1, 1–25. See http://dx.doi.org/ 10.1007/s10699-013-9340-0.
  13. [Katz et al. 2013] Katz, M., Schaps, D., Shnider, S. “Almost Equal: The Method of Adequality from Diophantus to Fermat and Beyond.” Perspectives on Science 21, no. 3, 283–324. See http://www. mitpressjournals.org/doi/abs/10.1162/POSC_a_00101 and http://arxiv.org/abs/1210.7750.
  14. [Katz & Sherry 2012] Katz, M., Sherry, D. “Leibniz’s Laws of Continuity and Homogeneity.” Notices of the American Mathematical Society 59, no. 11, 1550–1558. See http://www.ams.org/ notices/201211/rtx121101550p.pdf and http://arxiv.org/abs/ 1211.7188.
  15. [Katz & Sherry 2013] Katz, M., Sherry, D. “Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond.” Erkenntnis 78, no. 3, 571–625. See http://dx.doi.org/10.1007/s10670-012-9370-y and http://arxiv.org/abs/1205.0174.
  16. [Lagrange 1772] Lagrange, J. “Sur une nouvelle espece de calcul relatif a la différentiation et a l’integration des quantités variables.” Nouveaux Memoires de l’Academie royale des Sciences et Belles-Lettres de Berlin. (Oeuvres, Vol. III) pp. 441–478.Google Scholar
  17. [Lagrange 1811] Lagrange, J. Mécanique Analytique. Courcier. Reissued by Cambridge University Press, 2009.Google Scholar
  18. [Meschkowski 1965] Meschkowski, H. “Aus den Briefbüchern Georg Cantors.” Archive for History of Exact Sciences 2, 503–519.Google Scholar
  19. [Reeder 2013] Reeder, P. Internal Set Theory and Euler’s Introductio in Analysin Infinitorum. M.Sc. Thesis, Ohio State University.Google Scholar
  20. [Sherry & Katz 2014] Sherry, D., Katz, M. “Infinitesimals, Imaginaries, Ideals, and Fictions.” Studia Leibnitiana 44 (2012), no. 2, 166–192. See http://arxiv.org/abs/1304.2137 (Article was published in 2014 even though the journal issue lists the year as 2012).

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Vladimir Kanovei
    • 1
  • Karin U. Katz
    • 2
  • Mikhail G. Katz
    • 2
  • David Sherry
    • 3
  1. 1.IPPI, Moscow MIITMoscowRussia
  2. 2.Department of MathematicsBar Ilan UniversityRamat GanIsrael
  3. 3.Department of PhilosophyNorthern Arizona UniversityFlagstaffUSA

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