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What Simplicity Is Not

  • Maryanthe MalliarisEmail author
  • Assaf Peretz
Chapter
Part of the Mathematics, Culture, and the Arts book series (MACUAR)

Abstract

There is a duality in mathematics between proofs and counterexamples. To understand a mathematical question one investigates the limits. To investigate Hilbert’s 24th problem, and a mathematical concept of simplicity of a proof we deal here with both sides, focusing on what simplicity is not.

References

  1. 1.
    Benjamin, Walter. “The Image of Proust.” In Illuminations, translated by Harry Zohn. New York: Schocken Books, 1968.Google Scholar
  2. 2.
    Einstein, Albert. The Meaning of Relativity: Four Lectures Delivered at Princeton University, May, 1921. Translated by E. P. Adams. Project Gutenberg. May 29, 2011 [EBook #36276].Google Scholar
  3. 3.
    Einstein, Albert and Leopold Infeld. The Evolution of Physics. Cambridge, UK: Cambridge University Press, 1938.zbMATHGoogle Scholar
  4. 4.
    Fox, Jacob. “A new proof of the graph removal lemma.” Annals of Mathematics 174 (2011): 561–579.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Hilbert, David. “On the infinite.” (1925). In From Frege to Gödel, A Source Book in Mathematical Logic, 1879–1931, edited by Jean van Heijenoort. Cambridge, MA: Harvard University Press, 2002.Google Scholar
  6. 6.
    Hilbert, David. “Hilbert’s twenty-fourth problem” translated by Rüdiger Thiele. https://en.wikipedia.org/wiki/Hilbert’s_twenty-fourth_problem (2003).
  7. 7.
    Kleist, Heinrich von. “On the Marionette Theater.” 1810. Translation quoted from http://ada.evergreen.edu/~arunc/texts/literature/kleist/kleist.pdf.
  8. 8.
    M. Malliaris. “Independence, order, and the interaction of ultrafilters and theories.” Annals of Pure and Applied Logic 163 (11) (2012):1580–1595.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    A. Peretz. “Geometry of forking in simple theories.” Journal of Symbolic Logic 71 (1) (2006): 347–359.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Szemerédi, Endre. “On sets of integers containing no k elements in arithmetic progression.” Acta Arithmetica 27 (1975): 199–245.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.New YorkUSA

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