What is Hilbert’s 24th Problem?

[Ala14] Jesse Alama. The simplest axiom system for hyperbolic geometry revisited, again. Studia Logica, 102(3):609–615, 2014.10.1007/s11225-013-9509-0Search in Google Scholar

[Ara17] Andrew Arana. On the alleged simplicity of impure proof. In Roman Kossak and Philip Ording, editors, Simplicity: Ideals of Practice in Mathematics and the Arts, pages 205–226. Springer, 2017.10.1007/978-3-319-53385-8_16Search in Google Scholar

[AZ09] M. Aigner and G.M. Ziegler. Proofs from THE BOOK. Springer, 4th edition, 2009.10.1007/978-3-642-00856-6Search in Google Scholar

[Ber67] Paul Bernays. Hilbert, David. In Paul Edwards, editor, The Encyclopedia of Philosophy, pages 496–505. Macmillan, 1967.Search in Google Scholar

[GG00] Ivor Grattan-Guinness. A sideways look at Hilbert’s twenty-three problems of 1900. Notices of the AMS, 47(7):752–757, 2000.Search in Google Scholar

[Hil97] David Hilbert. Theorie der algebraischen Invarianten nebst Anwendungen auf Geometrie. 1897. lecture notes from Summer 1897 prepared by Sophus Marxsen, Library of the Mathematical Institute of the University of Göttingen; English translation Theory of Algebraic Invariants, R.C. Laubenbacher and B. Sturmfels (eds.) [using a different copy from the Mathematics Library of Cornell University], Cambridge University Press, Cambridge, 1993.Search in Google Scholar

[Hil01a] DavidHilbert. Mathematical problems. Bulletin of the American Mathematical Society, 8, 1901.10.1090/S0002-9904-1901-00860-9Search in Google Scholar

[Hil01b] David Hilbert. Mathematische Probleme. Archiv für Mathematik und Physik, 3. Reihe, 1:44–63, 213–237, 1901. Reprinted in [Hil35, p. 290–329].Search in Google Scholar

[Hil05] David Hilbert. Über die Grundlagen der Logik und der Arithmetik. In Adolf Krazer, editor, Verhandlungen des Dritten Internationalen Mathematiker-Kongresses in Heidelberg vom 8. bis 13. August 1904, pages 174–185. Leipzig, 1905.Search in Google Scholar

[Hil10] David Hilbert. The Foundations of Geometry. Open Court, 1910.Search in Google Scholar

[Hil18] David Hilbert. Axiomatisches Denken. Mathematische Annalen, 78(3/4):405–415, 1918. English translation: [Hil70].10.1007/BF01457115Search in Google Scholar

[Hil35] David Hilbert. Gesammelte Abhandlungen, Band III. Springer, 1935. Second edition 1970.10.1007/978-3-662-25726-5Search in Google Scholar

[Hil70] David Hilbert. Axiomatic thinking. Philosophia Mathematica, 1970.10.1093/philmat/s1-7.1-2.1Search in Google Scholar

[Hug06a] Dominic Hughes. Proofs without syntax. Annals of Mathematics, 143(3):1065–1076, 2006.10.4007/annals.2006.164.1065Search in Google Scholar

[Hug06b] Dominic Hughes. Towards Hilbert’s 24 problem: Combinatorial proof invariants: (preliminary version). Electr. Notes Theor. Comput. Sci., 165:37–63, 2006.10.1016/j.entcs.2006.05.036Search in Google Scholar

[KO17] Roman Kossak and Philip Ording, editors. Simplicity: Ideals of Practice in Mathematics and the Arts. Springer, 2017.10.1007/978-3-319-53385-8Search in Google Scholar

[Lan17] Marc Lange. Because Without Cause. Oxford Studies in Philosophy of Science. Oxford University Press, 2017.10.1093/oso/9780198777946.003.0002Search in Google Scholar

[Loo68] ElishaScott Loomis. The Pythagorean Proposition. Ann Arbor Michigan, 1968. Reprint of the 2nd edition from 1940. First published in 1927.Search in Google Scholar

[Mac34a] Saunders MacLane. Abbreviated proofs in logic calculus. Bulletin of the American Mathematical Society, 40(1):37–38, 1934. Abstract.Search in Google Scholar

[Mac34b] Saunders MacLane. Abgekürzte Beweise im Logikkalkul. PhD thesis, Georg August-Universität zu Göttingen, 1934.Search in Google Scholar

[Man01] Paolo Mancosu. Mathematical explanation: Problems and prospects. Topoi, 20:97–117, 2001.10.1023/A:1010621314372Search in Google Scholar

[Man08] Paolo Mancosu. Mathematical explanation: why it matters. In Paolo Mancosu, editor, The Philosophy of Mathematical Practice, pages 134–149. Oxford University Press, 2008.10.1093/acprof:oso/9780199296453.003.0006Search in Google Scholar

[NvP14] S. Negri and J. von Plato. Proof Analysis — A Contribution to Hilbert’s Last Problem. Cambridge University Press, 2014.Search in Google Scholar

[Pam88] Victor Pambuccian. Simplicity. Notre Dame Journal of Formal Logic, 29(3):396–411, 1988.10.1305/ndjfl/1093637936Search in Google Scholar

[Pam11] Victor Pambuccian. The simplest axiom system for plane hyperbolic geometry revisited. Studia Logica, 97(3):347–349, 2011.10.1007/s11225-011-9314-6Search in Google Scholar

[Str05] Lutz Straßburger. What is a logic, and what is a proof? In Jean-Yves Beziau, editor, Logica Universalis, pages 135–145. Birkhäuser, 2005.10.1007/3-7643-7304-0_8Search in Google Scholar

[Str06] Lutz Straßburger. Proof nets and the identity of proofs. CoRR, abs/cs/0610123, 2006.Search in Google Scholar

[Thi03] R. Thiele. Hilbert’s twenty-fourth problem. American Mathematical Monthly, 110(1):1–24, January 2003.10.1080/00029890.2003.11919933Search in Google Scholar

[TW02] R. Thiele and L. Wos. Hilbert’s twenty-fourth problem. Journal of Automated Reasoning, 29(1):67–89, 2002.10.1023/A:1020537107897Search in Google Scholar

[WP03] Larry Wos and GailW. Pieper. Automated Reasoning and the Discovery of Missing and Elegant Proofs. Rinton Press, 2003.Search in Google Scholar