Abstract
Everybody knows what a mathematical proof is. A proof of a mathematical theorem is a sequence of steps which leads to the desired conclusion. The rules to be followed in this sequence of steps were made explicit when logic was formalized early in this century and they have not changed since. These rules can be used to disprove a putative proof by spotting logical errors; they cannot, however, be used to find the missing proof of a mathematical conjecture.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
End Notes
Ronald L. Graham, Bruce L. Rothschild, Joel H. Spencer, Ramsey Theory, Wiley, New York, 1990.
Bertram Kostant, The principle of Triality and a distinguished unitary representation of SO (4, 4), Geometric Methods in Theoretical Physics, K. Bleuler and M. Werner (eds.), Kluwer Academic Publishers, 1988, 65-108; The Coxeter Element and the Structure of the Exceptional Lie groups, Colloquium Lectures of the AMS, Notes available from the AMS.
Andrew Wiles, Modular Elliptic Curves and Fermat’s Last Theorem, Annals of Mathematics, Vol. CXLII, 1995, 443–551.
H. F. Baker, Principles of Geometry. Vol. I, Foundations, Cambridge University Press, Cambridge, 1922.
G. D. Birkhoff, Proof of the Ergodic Theorem, Proceedings of the National Academy of Sciences, Vol. XVII, 1931, 656–660.
Adriano M. Garsia, A Simple Proof of E. Hopf’s Maximal Ergodic Theorem, Journal of Mathematics and Mechanics, Vol. XIV 1965, pp. 381–382.
Hans Lewy, On the local character of the solutions of an atypical differential equation in three variables and a related problem for regular functions of two complex variables, Annals of Mathematics, Vol. LXIV, 1956, pp. 514-22.
von Staudt, Geometrie der Lage, 1847.
Garrett Birkhoff, Lattice Theory, American Mathematical Society, 1948.
Emil Artin, Coordinates in Affine Geometry, Reports of Mathematical Colloquium, Notre Dame, 1940.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Rota, GC. (1997). The Phenomenology of Mathematical Proof. In: Palombi, F. (eds) Indiscrete Thoughts. Modern Birkhäuser Classics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4781-0_11
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4781-0_11
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4780-3
Online ISBN: 978-0-8176-4781-0
eBook Packages: Springer Book Archive