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]


  • [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.
  • [6] J. Cassinet (1988) The first arithmetic book of Francisco Maurolico, written in 1557 and printed in 1575: a step towards a theory of numbers. In Mathematics from Manuscript to Print. 1300–1600, C. Hay (Ed.), Oxford Science Publications, pp. 162–179.
  • [7] L. Euler (1767) Observationes analyticae. Novi Commentarii academiae scientiarum Petropolitanae 11, pp. 124–143. Note: Opera omnia I.15, pp. 50–69
  • [8] S. Feferman (1981) The logic of mathematical discovery vs. the logical structure of mathematics. In Proceedings of the 1978 Biennial Meeting of the Philosophy of Science Association, P. D. Asquith and I. Hacking (Eds.), pp. 309–327.
  • [9] U. Felgner (2012) Das Induktions-Prinzip. Jahresber. Dtsch. Math.-Ver. 114 (1), pp. 23–45.
  • [10] J. O. Fleckenstein, C. S. Roero, D. Speiser, and T. Viola (Eds.) (1989) Die Werke von Jakob Bernoulli, Band 2: Elementarmathematik. Birkhäuser. Cited by: Bibliography for the history of induction in mathematics.
  • [11] J. Franklin (1987) Non-deductive logic in mathematics. British Journal for the Philosophy of Science 38, pp. 1–18.
  • [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.
  • [14] J. R. Milton (1987) Induction before Hume. Brit. J. Phil. Sci. 38, pp. 49–74.
  • [15] N. L. Rabinovitch (1970) Rabbi Levi ben Gershon and the origins of mathematical induction. Arch. Hist. Exact Sci. 6 (3), pp. 237–248.
  • [16] R. Rashed (1972) L’induction mathématique: al-Karajī, as-Samaw’al. Arch. History Exact Sci. 9 (1), pp. 1–21.
  • [17] I. Schneider (1968) Der Mathematiker Abraham de Moivre (1667–1754). Arch. Hist. Exact Sci. 5 (3–4), pp. 177–317.
  • [18] I. Schneider (2006) Direct and indirect influences of Jakob Bernoulli’s Ars Conjectandi in 18th century Great Britain. J. Électron. Hist. Probab. Stat. 2 (1), pp. 1–17.
  • [19] J. A. Stedall (2004) The arithmetic of infinitesimals. John Wallis 1656. Sources and Studies in the History of Mathematics and Physical Sciences, Springer.
  • [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.