Remarks on Simple Proofs

  • Rosalie IemhoffEmail author
Part of the Mathematics, Culture, and the Arts book series (MACUAR)


This note consists of a collection of observations on the notion of simplicity in the setting of proofs. It discusses its properties under formalization and its relation to the length of proofs, showing that in certain settings simplicity and brevity exclude each other. It is argued that when simplicity is interpreted as purity of method, different foundational standpoints may affect which proofs are considered to be simple and which are not.



Support by the Netherlands Organization for Scientific Research under grant 639.032.918 is gratefully acknowledged. I thank an anonymous referee for useful remarks on an earlier draft of this paper.


  1. 1.
    Bohr, Harold. “Address of Professor Harold Bohr.” In Proceedings of the International Congres Mathematicians: Cambridge, Massachusetts, U.S.A., August 30-September 6, 1950 vol. 1, 127–134. Providence, RI: American Mathematical Society, 1952.Google Scholar
  2. 2.
    Buss, Samuel. “Polynomial size proofs of the propositional pigeonhole principle.” Journal of Symbolic Logic 5, no. 2 (1987): 916–927.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dieudonné, Jean. Linear Algebra and Geometry. Boston: Houghton Mifflin Co.,1969.Google Scholar
  4. 4.
    Detlefsen, Michael. “Purity as an Ideal of Proof.” In The Philosophy of Mathematical Practice, edited by Paolo Mancosu, 179–197. Oxford, NY: Oxford University Press, 2008.CrossRefGoogle Scholar
  5. 5.
    Detlefsen, Michael and Andrew Arana. “Purity of Methods. ” Philosophers’ Imprint 11, no. 2 (2011): 1–20.Google Scholar
  6. 6.
    van der Corput, Johannes Gaultherus. Démonstration élémentaire du théorème sur la distribution des nombres premiers. Amsterdam: Mathematisch Centrum, 1948.Google Scholar
  7. 7.
    Hadamard, Jacques. “Sur la distribution des zéros de la fonction zeta(s) et ses conséquences arithmétiques.” Bulletin de la Société Mathématique de France 24 (1896): 199–220.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Goldfeld, Dorian. “The Elementary Proof of the Prime Number Theorem: An Historical Perspective.” In Number Theory, edited by David Chudnovsky, Gregory Chudnovsky, and Melvyn B. Nathanson, 179–192. New York: Springer, 2004.CrossRefGoogle Scholar
  9. 9.
    Selberg, Atle. “An Elementary Proof of the Prime Number Theorem.” Annals of Mathematics 50 (1949): 305–313.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    de la Vallée Poussin, Charles Jean. “Recherches analytiques la théorie des nombres premiers.” Annales de la Société Scientifique de Bruxelles 20 (1896): 183–256.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of PhilosophyUtrecht UniversityUtrechtThe Netherlands

Personalised recommendations