Experimental mathematics, computers and the a priori

Synthese 190 (3):397-412 (2013)
  Copy   BIBTEX

Abstract

In recent decades, experimental mathematics has emerged as a new branch of mathematics. This new branch is defined less by its subject matter, and more by its use of computer assisted reasoning. Experimental mathematics uses a variety of computer assisted approaches to verify or prove mathematical hypotheses. For example, there is “number crunching” such as searching for very large Mersenne primes, and showing that the Goldbach conjecture holds for all even numbers less than 2 × 1018. There are “verifications” of hypotheses which, while not definitive proofs, provide strong support for those hypotheses, and there are proofs involving an enormous amount of computer hours, which cannot be surveyed by any one mathematician in a lifetime. There have been several attempts to argue that one or another aspect of experimental mathematics shows that mathematics now accepts empirical or inductive methods, and hence shows mathematical apriorism to be false. Assessing this argument is complicated by the fact that there is no agreed definition of what precisely experimental mathematics is. However, I argue that on any plausible account of ’experiment’ these arguments do not succeed.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,419

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The epistemological status of computer-assisted proofs.Mark McEvoy - 2008 - Philosophia Mathematica 16 (3):374-387.
Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan.
Apriority and applied mathematics.Robert A. Holland - 1992 - Synthese 92 (3):349 - 370.
Proofs and arguments: The special case of mathematics.Jean Paul Van Bendegem - 2005 - Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.
Medium AI and experimental science.Andre Kukla - 1994 - Philosophical Psychology 7 (4):493-5012.
Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos (ed.) - 1976 - Cambridge and London: Cambridge University Press.

Analytics

Added to PP
2011-10-20

Downloads
101 (#124,542)

6 months
8 (#105,788)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Mark McEvoy
Hofstra University

Citations of this work

Non-deductive methods in mathematics.Alan Baker - 2010 - Stanford Encyclopedia of Philosophy.
Computers as a Source of A Posteriori Knowledge in Mathematics.Mikkel Willum Johansen & Morten Misfeldt - 2016 - International Studies in the Philosophy of Science 30 (2):111-127.

Add more citations

References found in this work

Naming and Necessity.S. Kripke - 1972 - Tijdschrift Voor Filosofie 45 (4):665-666.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford, England: Oxford University Press.
Mathematics as a Science of Patterns.Michael David Resnik - 1997 - Oxford, England: New York ;Oxford University Press.
What is Mathematical Truth?Hilary Putnam - 1975 - In Mathematics, Matter and Method. Cambridge University Press. pp. 60--78.

View all 21 references / Add more references