Abstract
A method of writing proofs is described that makes it harder to prove things that are not true. The method, based on hierarchical structuring, is simple and practical. The author’s twenty years of experience writing such proofs is discussed.
In addition to developing the students’ intuition about the beautiful concepts of analysis, it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions.
Michael Spivak, Calculus [7]
Similar content being viewed by others
References
Abadi M., Lamport L.: An old-fashioned recipe for real time. ACM Transactions on Programming Languages and Systems 16(5), 1543–1571 (1994)
J. L. Kelley, General Topology. The Univesity Series in Higher Mathematics, D. Van Nostrand Company, Princeton, NJ, 1995.
L. Lamport, TLA—temporal logic of actions. A web page, a link to which can be found at URL http://lamport.org. The page can also be found by searching the Web for the 21-letter string formed by concatenating uid and lamporttlahomepage.
L. Lamport, Useful LaTeX packages. http://research.microsoft.com/enus/um/people/lamport/latex/latex.html. The page can also be found by searching the Web for the 23-letter string formed by concatenating uid and lamportlatexpackages.
L. Lamport, How to write a proof. In: Global Analysis in Modern Mathematics, pp. 311–321. Publish or Perish, Houston, Texas, 1993. A symposium in honor of Richard Palais’ sixtieth birthday. Also published in Amer. Math. Monthly 102 (1995), no. 7, 600–608.
Microsoft Research-INRIA Joint Centre. Tools and methodologies for formal specifications and for proofs. http://www.msr-inria.inria.fr/Projects/tools-forformal-specs.
Spivak M.: Calculus. W. A. Benjamin, Inc., New York (1967)
Author information
Authors and Affiliations
Additional information
To D. Palais
Rights and permissions
About this article
Cite this article
Lamport, L. How to write a 21st century proof. J. Fixed Point Theory Appl. 11, 43–63 (2012). https://doi.org/10.1007/s11784-012-0071-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11784-012-0071-6