Abstract
Thus far we have reviewed the progression of the science of numbers in the Old World from prehistoric times to approximately 1000 b.c. We have seen the concept of number expand from the natural numbers to include the unit fractions (with form 1/n) of the Egyptians and the sexagesimal fractions (with form n/60) of the Babylonians, plus the negative numbers of the Chinese. It is now time to look at the contributions of the ancient Greeks. It has been claimed that the Greeks defined science, philosophy, and mathematics, and created standards for these disciplines that were maintained for two thousand years. Others, however, claim that we give too much credit to the Greeks, ignoring other societies’ contributions.
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End Notes
Chambers et al., p. 40.
Menninger, p. 272.
Ibid., p. 299.
Kline, p. 28.
David Eugene Smith, p. 64.
The two different positions are illustrated by Smith, p. 71; and Boyer, p. 52.
Michael Moffatt, The Ages of Mathematics: Vol.1, The Origins (New York: Doubleday and Company, 1977), p. 96.
Boyer, p. 60.
Bunt et al., p. 83.
Aristotle, The Basic Works of Aristotle, trans. J. Annas (Richard McKeon, ed.) (New York: Random House, 1941); The Metaphysics, 986a, lines 1–3 and 15–18, Oxford University Press.
Ibid., 1090a, lines 20–25.
Two different visual proofs come from Stuart Hollingdale, Makers of Mathematics (London: Penguin Books, 1989), p. 39; and Eric Temple Bell, Mathematics: Queen and Servant of Science (New York: McGraw-Hill, 1951), p. 190.
Kline, p. 33.
Moffatt, p. 92.
Bunt et al., p. 86.
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© 1994 Calvin C. Clawson
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Clawson, C.C. (1994). Problems in Paradise. In: The Mathematical Traveler. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-6014-6_7
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