Abstract
Literature on History of Mathematics evolved in the last two centuries in two distinct directions. A group of scholars, whom we may call cultural historians, depicted a unified image of mathematics giving descriptive historical accounts of development of mathematical concepts over the ages, without making any analytical distinction between various branches of mathematics. The other other group of scholars, whom we may call mathematical historians, presented a pluralistic view of mathematics giving due emphasis to development of different branches of the subject. The purpose of this article is to take a glimpse into such divergent approahes in the evolution of history of mathematics and to examine their implications in the overall development of mathematical and humanistic cultures.
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References
William Aspray. John von Neumann and the Origins of Modern Computing. MIT Press, Cambridge, MA, 1990.
John L. Berggren. Episodes in the Mathematics of Medieval Islam. Springer-Verlag, New York, 1986.
J.D. Bond. The Development of Trignometric Methods down to the close of the Fifteenth Century. Isis, 4:295–323, 1921.
H.J.M. Bos. Differentials, higer-order differentials and the derivatives in the leibnizian calculus. Archives for History of Exact Sciences, 14:1–90, 1974.
Nicolas Bourbaki. Elements d’ Histoire des Mathematiques. Paris, Masou, 1984.
Joan Fisher Box. R.A. Fisher. The life of a Scientist. John Wiley & Sons, New York, 1978.
Carl B. Boyer. History of the Calculus and its Conceptual Development. Dover Publications, New York, 1947.
Carl B. Boyer. History of Analytic Geometry. New York, 1950.
Carl B. Boyer. A history of Mathematics. John Wiley and sons, New York, 1968.
Courtney Brown. Politics and the Environment, Nonlinear Instabilities Dominate. American Political Science Review, 88:292–303, 1994.
F.A. Cajori. A History of the Conception of Limits and Fluxions in Great Britain from Newton to Woodhouse. Chicago, 1931.
Moritz Cantor. Vorlesungen uber Geschichte der Mathematik, 4 Vols. Teubner, Leipzig, 1880–1908.
Caruccio. Matematica e logica nella storia e nel pensiero contemporaneo. Turin. English Translation: London 1964.
A. B. Chace, editor. The Rhind Mathematical Papyrus, 2 vols., Ohio, 1927–29.
Michael P. Closs, editor. Native American Mathematics. University of Texas Press, Austin, 1986.
T Dantzig. Number: The Language of Science. London, 1940.
Joseph Dauben. Georg Cantor: His Mathematics and Philosophy of the Infinite. Harvard University Press, Cambridge, Mass., 1979.
N.Z. Davis. Sixteenth century french arithmetic and the business life. J. Hist. Of Ideas, 21:18–48,1960.
L.E. Dickson. History of the theory of numbers, 3 Vols. Washington, 1919–27.
Jean Dieudonne. Abrege d’ Histoire des Mathematiques, 1700–1900, 2 Vols. Herman, Paris, 1978.
Jean Dieudonne. History of functional analysis. Amsterdam, 1981.
Thomas Drucker. Essay review of Gregory H.Moore, “Zermelo’s Axioms of Choice”. Historia Mathematica, 18:364–369, 1991.
B.B. Datta and A.N. Singh. History of Hindu Mathematics, 2 vols. Lahore, 1935–38. Reviewed by O. Neugebauer in Quellen und Studien 3B:; 263–271, 1936.
Hans Freudenthal. What is algebra and what has it been in history? Archive for History of Exact Sciences, 16:189–200, 1977.
R.J. Gillings. Mathematics in the time of Pharaohs. Cambridge, Mass., 1972.
H.H. Goldstine. A History of the Calculus of Variations from the 17th Through the 19th Century. New York, 1980.
J Gow. A Short History of Greek Mathematics. Cambridge University Press, 1884.
Jeremy Gray. Linear Differential Equations and Group theory from Riemann to Poincare. Birkhauser, Boston, 1986.
Ivor-Grattan Guinness. Does the history of science treat of the history of science? The case of Mathematics. History of Science, 28:149–173, 1990.
L.V. Gurjar. Ancient Indian Mathematics and Vedha. Poona, 1947. See also Math. Rev. 9: 73, 1948.
Ian Hacking. The Emergence of Probability. Cambridge University Press, Cambridge, 1975.
Anders Hald. A History of Probability and Statistics and their Applications before1750. John Wiley & Sons, New York, 1990.
Thomas Hankins. William Rowan Hamilton. John Hopkins University Press, Baltimore, 1973.
Sandra Harding. The Science Question in Feminism. Cornell University Press, Ithaca, 1986.
Thomas Hawkins. Non-euclidean geometry and Weierstrassian Mathematics: The background of Killing’s work on Lie Algebras. Historia Mathematica, 7:289–342, 1980.
Thomas Hawkins. Wilhelm Killing and the structure of Lie Algebras. Archive for History of Exact Sciences, 26:127–192, 1982.
Thomas Hawkins. Jacobi and the birth of Lie’s Theory of Groups. Archive for History of Exact Sciences, (42):187–278, 1991.
Thomas Hawkins. Line Geometry, Differential Equations and the birth of Lie’s Theory of Groups. Archive for History of Exact Sciences, 42:275–327, 1991. in David E. Rowe and John McCleary, eds., The History of Modern Mathematics, Vol. 1 (Boston, Academic Press, 1988).
T Hayashi. A Brief History of the Japanese Mathematics. In Nieuw Archief voor Wiskunde, volume 6 of series 2, pages 296–361, 1904–05.
Thomas L. Heath. The Thirteen Books of Euclid’s Elements, 3 vols. Dover Publications, New York, 1908.
Thomas L. Heath. A History of Greek Mathematics, 2 vols. Oxford: Clarendon Press, 1921.
Thomas L. Heath. A manual of Greek Mathematics. Oxford, 1931.
Andrew Hodges. Alan Turing: The Enigma. Simon and Schuster, New York, 1983.
L.C. Karpinski. The History of Arithmetic. Chicago, 1925.
G.R. Kaye. Indian Mathematics. Isis, 2:326–356, 1919.
Mathematics of the 19th century. In A.N Kolmogorov and A.P. Juskevic, editors, Mathematical logic, Theory of Numbers, Theory of Probability.(in Russian). Moscow, 1978.
Jacob Klein. Die griechische Logistik und Entstehung der Algebra, Part I. Quellen und Studien Zur Geschichte der Mathematik, Astrnomie und Physik, Abteilung B: Studien 3, fasc. l. Julius Springer, Berlin, 1934. Pages 1–105.
Jacob Klein. Die griechische Logistik und Entstehung der Algebra, Part IL Quellen und Studien Zur Geschichte der Mathematik, Astrnomie und Physik,Abteilung B: Studien 3, fasc.2. Julius Springer, Berlin, 1936. Pages 122–235.
Jacob Klein, (trans. Eva Braun) Greek Mathematical Thought and the Origin of Algebra. The MIT Press,Cambridge, MA, 1968.
Morris Kline. Mathematical Thought from Ancient to Modern Times. Oxford University Press, New York, 1991.
Ann Hubner Koblitz. A convergence of Lives: Sophia Kovalevskaya, Scientist, Writer, Revolutionary. Birkhauser, Boston, 1983.
B. Latour. A relativistic account of Einstein’s relativity. Social Studies of Sciences, 18:3–44,1988.
Jesper Lutzen and Walter Purkert. Conflicting tendencies in the historiography of mathematics, M. Cantor and H.G. Zeuthen. In Eberhard Knobloch and David E. Rowe, editors, The History of Modern Mathematics, 3, pages 1–42. Academic Press, Boston, 1994.
Jesper Lutzen. Joshep Liouville 1809–1882: Master of Pure and Applied Mathematics. Springer-Verlag, New York, 1990.
Donald Mackenzie. Statistics in Britain, 1865–1930 The Social Construction of Scientific Knowledge. Edinburgh University Press, Edinburgh, 1981.
Michael Mahoney. Babylonian Algebra: Form vs. Content. Studies in History and Philosophy of Science, 1:369–380, 1970.
Michael Mahoney. The Mathematical Career of Pierre de Fermat, 1601–1665. Princeton University Press, 1973.
K Manitius. Ptolemaus Handbuch der Astronomie, 2 Vols. Leipzig, 1912–13.
Pesi R. Masani. Norbert wiener 1894–1964. Vita Mathematics, 5, 1990.
Y. Mikami. The Development of Mathematics in China and Japan. Leipzig, 1931.
Gregory Moore. Zermelo’s Axiom of Choice: Its origin, Development and Influence. Springer-Verlag, 1982.
T Muir. The theory of determinants in the historical order of development, 4 vols. London, 1906–23.
J. Needham. Science and Civilisation in China. Cambridge, 1959.
Otto Neugebauer. Mathematische Keilschrift-Texte. I–III. Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abteilung A: Quellen, 3. Band, ersterdritter Teil. Springer-Verlag, Berlin, 1973). Printed earlier in: Berlin, Julius Springer, 1935–37.
Carol Parikh. The Unreal Life of Oscar Zariski. Academic Press, Boston, 1991.
T.E. Peet, editor. The Rhind Mathematical Papyrus, London, 1923.
D Pingree. History of mathematical astronomy in india. In Dictionary of Scientific Biography, volume 15, pages 533–633. 1978.
Theodore M. Porter. The Rise of Statistical Thinking, 1820–1900. Princeton University Press, Princeton, 1986.
James N. Rosenau. Turbulence in World Politics: A Theory of Change and Continuity. Princeton University Press, Princeton, 1990.
B.A. Rozenf’eld. History of Non-Euclidean Geometry. Springer-Verlag, New York, 1988.
A. Seidenburg. The Ritual origin of Geometry. Archive for History of Exact Sciences, Archive for History of Exact Sciences:488–527, 1962.
D.E. Smith and Y Mikami. History of Japanese Mathematics. Chicago, 1914.
D.E. Smith. Algebra of 4000 years ago. Scripta math., 4:111–125, 1936.
C.N. Srinivasiengar. The History of Ancient Indian Mathematics. Calcutta, 1967.
Stephen M. Stigler. The History of Statistics- The Measurement of Uncertainty before 1900. Harvard University Press, Cambridge, MA, 1986.
D.J. Struik. Outline of a history of differential geometry. Isis, 19:92–120, 1933.
D.J. Struik. Outline of a history of differential geometry. Isis, 20:161–191, 1933.
D.J. Struik. On ancient Chinese Mathematics. Mathematics Teacher, 56: 424–431,1963.
Arpad Szabo. Anfange der griechischen Mathematik. R. Oldenbourg, Munchen, 1969.
Paul Tannery. Memoires Scientifiques, Vols. 1–4. Gauthier-Villars, Paris, 1912–20.
Francois Thureau-Dangin. Texts Mathematiques babyloniens. Lei-den: Brill, 1938.
I. Thomas. Selections Illustrating the History of Greek Mathematics. Cambridge, 1939.
I. Todhunter. History of the Progress of the Calculus of Variations During the Nineteenth Century. New York, 1980.
Sabetai Unguru. On the need to Rewrite the History of Greek Mathematics. Archive for History of Exact Sciences, 15:67–114, 1975.
Sabetai Unguru. History of Ancient Mathematics: Some Reflections on the Sate of Art. Isis, 70:555–565, 1979.
B.L. van der Waerden. Defence of a Shocking Point of View. Archive for History of Exact Sciences, 15:199–210, 1976.
Andre Weil. Review of Michael S. Mahoney The Mathematical Career of Pierre de Fermat. Bulletin of American Mathematical Society, 79:1138–1149,1973.
Andre Weil. Who betrayed euclid? Archive for History of Exact sciences, 19:91–93, 1978.
Richard S. Wesfal. Never at Rest. A Biography of Isaac Newton. Cambridge University Press, 1980.
Derek T. Whiteside. The Mathematical Papers of Isaac Newton. 8 Vols. Cambridge University Press, Cambridge, 1967–1981.
T.R. Witmer. Trans, and ed. The Great Art or the Rules of Algebra by Girolamo Cardano. Cambridge, Mass., 1968.
Li Yan and Du Shiran, (trans. J. N. Crossley and A.W.-C. Lun) Chinese Mathematics: A Concise History. Oxford: Clarendon Press, 1987.
C. Zaslavsky. Africa Counts. Academic Press, 1973.
H.G. Zeuthen. Geschichte der Mathematik im Alterum und Mittelalter. Verlag von Andr. Fred. Host & Son, Copenhagen, 1908.
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Chaudhuri, K.S. (2004). Evolution of History of Mathematics: Some Trends. In: Grattan-Guinness, I., Yadav, B.S. (eds) History of the Mathematical Sciences. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-16-3_1
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