Bibliography for the history of induction in mathematics

Jordan Bell
January 15, 2015

Mathematical induction (=“complete induction”) often is worked out as a generalizable example (because once we have our hands on something fixed it is easier to do things), and the idea of a generalizable example is contained in the general idea of induction as used in philosophy.

In the Euler-Goldbach correspondence no. 85–86

Wallis [3, p. 474]

Euler used incomplete induction as an instrument of scientific research. Juškevič [13] writes the following: “It is frequently said that Euler saw no intrinsic impossibility in the deduction of mathematical laws from a very limited basis in observation; and naturally he employed methods of induction to make empirical use of the results he had arrived at through analysis of concrete numerical material. But he himself warned many times that an incomplete induction serves only as a heuristic device, and he never passed off as finally proved truths the suppositions arrived at by such methods”; also cf. Weil [21, Chapter II, §III] and Cajori [5].

Bernoulli [10, p. 29]

References

  • [1] F. Acerbi (2000) Plato: Parmenides 149a7-c3. A proof by complete induction?. Arch. Hist. Exact Sci. 55 (1), pp. 57–76.
  • [2] A. Baker (2007) Is there a problem of induction for mathematics?. In Mathematical Knowledge, M. Leng, A. Paseau, and M. Potter (Eds.), pp. 59–73.
  • [3] P. Beeley and C. J. Scriba (Eds.) (2014) Correspondence of John Wallis (1616–1703), volume IV (1672–April 1675). Oxford University Press. Cited by: Bibliography for the history of induction in mathematics.
  • [4] Kurt-R. Biermann (1958) Iteratorik bei Leonhard Euler. Enseign. Math. 4, pp. 19–24.
  • [5] F. Cajori (1918) Origin of the name “mathematical induction”. Amer. Math. Monthly 25 (5), pp. 197–201. Cited by: Bibliography for the history of induction in mathematics.
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  • [12] K. Hara (1962) Pascal et l’induction mathématique. Rev. Hist. Sci. 15 (3), pp. 287–302.
  • [13] A. P. Juškevič (1971) Euler, Leonhard. In Dictionary of Scientific Biography, volume IV: Richard Dedekind – Firmicus Maternus, C. C. Gillispie (Ed.), pp. 467–484. Cited by: Bibliography for the history of induction in mathematics.
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  • [20] M. Steiner (1978) Mathematical explanation. Philos. Stud. 34 (2), pp. 135–151.
  • [21] A. Weil (1984) Number theory: an approach through history from Hammurapi to Legendre. Birkhäuser. Cited by: Bibliography for the history of induction in mathematics.