Abstract
In the present chapter, interpretations of the mathematics of the past are problematized, based on examples such as archeological artifacts, as well as written sources from the ancient Egyptian, Babylonian, and Greek civilizations. The distinction between history and heritage is considered in relation to Euler’s function concept, Cauchy’s sum theorem, and the Unguru debate. Also, the distinction between the historical past and the practical past, as well as the distinction between the historical and the nonhistorical relations to the past, are made concrete based on Torricelli’s result on an infinitely long solid from the seventeenth century. Two complementary but different ways of analyzing the mathematics of the past are the synchronic and diachronic perspectives, which may be useful, for instance, regarding the history of school mathematics. Furthermore, recapitulation, or the belief that students’ conceptual development in mathematics is paralleled to the historical epistemology of mathematics, is problematized emphasizing the important role of culture.
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References
Abel NH (1826) Untersuchungen über die Reihen, u.s.w., Journal für die reine und angewandte Mathematik, 1:311–339
Björling EG (1853) Om oändliga serier, hvilkas termer äro continuerliga functioner a fen reel variable mellan ett par gränser, mellan hvilka serierna äro convergerande. Öfvers Kongl Vetens Akad Förh Stockholm 10:147–160
Bråting K (2007) A new look at E.G. Björling and the Cauchy sum theorem. Arch Hist Exact Sci 61(5):519–535
Bråting K, Pejlare J (2015) On the relations between historical epistemology and students’ conceptual developments in mathematics. Educ Stud Math 89(2):251–265
Bråting K, Pejlare J (2019) The role of Swedish school algebra in a historical perspective. Paper presented at Nordic educational research conference, NERA 2019, 6–8 Mar. Uppsala University
Butterfield H (1931) The Whig interpretation of history. G. Bell and Sons, London
Cauchy AL (1821) Cours d’analyse de l‘École royale polytechnique (Analyse AlgÉbrique)
Corry L (2013) Geometry and arithmetic in the medieval traditions of Euclid’s Elements: a view from book II. Arch Hist Exact Sci 67:637–705
De Heinzelin J (1962) Ishango. Sci Am 206(6):105–118
Euler L (1748) Introductio in analysin infinitorum [Introduction to the analysis of the infinite]. Lausanne: Marcum Michaelem Bousquet.
Fried MN (2001) Can mathematics education and history of mathematics coexist? Sci Educ 10(4):391–408
Fried MN (2007) Didactics and history of mathematics: knowledge and self-knowledge. Educ Stud Math 66:203–223
Fried MN (2018) Ways of relating to the mathematics of the past. J Humanist Math 8(1):3–23
Grattan-Guinness I (1986) The Cauchy-Stokes-Seidel story on uniform convergence: was there a fourth man? Bull Belg Soc Math 38:225–235
Grattan-Guinness I (2000) The search for mathematical roots 1870–1940: logics, set theories and the foundations of mathematics from Cantor through Russell to Gödel, Princeton University Press, Princeton, N.J.
Grattan-Guinness I (2004) The mathematics of the past: distinguishing its history from our heritage. Hist Math 31(3):163–185
Haeckel E (1912) The evolution of man. London: Watts & Co. (Original work published 1874)
Heath T (1956) The thirteen books of Euclid’s Elements, vol I, 2nd edn. Dover Publications, New York
Klein F (1926) Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, vol I. Julius Springer, Berlin
Kline M (1972) Mathematical thought from ancient to modern times. Oxford University Press, New York
Kline M (1983) Euler and infinite series. Math Mag 56(5):307–314
Lam LY (1994) Jiu zhang suanshu (nine chapters on the mathematical art): an overview. Arch Hist Exact Sci 47:1–51
l’Hospital GFA (1696) Analyse des infiniment petits pour l’intelligence des lignes courbes [Analysis of the infinitely small to understand curves]. Paris: (n.p.).
Mancosu P (1996) Philosophy of mathematics & mathematical practice in the seventeenth century. Oxford University Press, Oxford
Marshack A (1972) The roots of civilization: the cognitive beginnings of Man’s first art, symbol and notation. McGraw-Hill Book Company, New York
Oakeshott M (1933) Experience and its modes. Cambridge University Press, Cambridge
Pejlare J (2017) On the relationships between the geometric and the algebraic ideas in Duhre’s textbooks of mathematics, as reflected via Book II of Euclid’s Elements. In: Bjarnadóttir K, Furinghetti F, Menghini M, Prytz J, Schubring G (eds) Dig where you stand 4. Proceedings of the fourth international conference on the history of mathematics education. Edizioni Nuova Cultura, Rome, pp 263–273
Piaget J, Garcia R (1989) Psychogenesis and the history of science. Columbia University Press, New York
Pletser V, Huylebrouck D (1999) The Ishango artefact: the missing base 12 link. Forma 14:339–346
Poincaré H (1899) La logique et l’intuition dans la science mathématique et dans l’enseignement, [Logic and intuition in mathematical science and education]. L’Enseignement Matheématique 1:157–162
Radford L (1997) On psychology, historical epistemology, and the teaching of mathematics: towards a socio-cultural history of mathematics. Learn Math 17(1):26–33
Sørensen HK (2005) Exceptions and counterexamples: understanding Abel’s comment on Cauchy’s theorem. Hist Math 32(4):453–480
Spalt D (2002) Cauchys Kontinuum – eine historiografische Annäherung via Cauchys Summensatz. Arch Hist Exact Sci 56:285–338
Stedall J (2002) A discourse concerning algebra – English algebra to 1685. Oxford University Press, Oxford
Thomaidis Y, Tzanakis C (2007) The notion of historical parallelism revisited: historical evolution and students’ conception of the order relation on the number line. Educ Stud Math 66(2):165–183
Toeplitz O (1927) Das Problem der Universitätsvorlesungen über Infinitesimalrechnung und ihrer Abgrenzung gegenüber der Infinitesimalrechnung an der höheren Schulen. Jahresbericht der Deutschen Mathematiker-Vereinigung 36:88–100
Unguru S (1975) On the need to rewrite the history of Greek mathematics. Arch Hist Exact Sci 15:67–114
Wallis J (1685) A treatise of algebra, both historical and practical. London: printed by John Playford for Richard Davis
Weil A (1978) Who betrayed Euclid? Extract from a letter to the editor. Arch Hist Exact Sci 19:91–93
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Pejlare, J., Bråting, K. (2021). Writing the History of Mathematics: Interpretations of the Mathematics of the Past and Its Relation to the Mathematics of Today. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-57072-3_63
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