Remarks on Simple Proofs
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.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
- 3.Dieudonné, Jean. Linear Algebra and Geometry. Boston: Houghton Mifflin Co.,1969.Google Scholar
- 5.Detlefsen, Michael and Andrew Arana. “Purity of Methods. ” Philosophers’ Imprint 11, no. 2 (2011): 1–20.Google Scholar
- 6.van der Corput, Johannes Gaultherus. Démonstration élémentaire du théorème sur la distribution des nombres premiers. Amsterdam: Mathematisch Centrum, 1948.Google Scholar
- 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