In 2000, a draft note of David Hilbert was found in his Nachlass concerning a 24th problem he had consider to include in the his famous problem list of the talk at the International Congress of Mathematicians in 1900 in Paris. This problem concerns simplicity of proofs. In this paper we review the (very few) traces of this problem which one can find in the work of Hilbert and his school, as well as modern research started on it after its publication. We stress, in particular, the mathematical nature of the problem.1
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[GG00] Ivor Grattan-Guinness. A sideways look at Hilbert’s twenty-three problems of 1900. Notices of the AMS, 47(7):752–757, 2000.
[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.
[Hil01a] DavidHilbert. Mathematical problems. Bulletin of the American Mathematical Society, 8, 1901.
[Hil01b] David Hilbert. Mathematische Probleme. Archiv für Mathematik und Physik, 3. Reihe, 1:44–63, 213–237, 1901. Reprinted in [Hil35, p. 290–329].
[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.
[Hil10] David Hilbert. The Foundations of Geometry. Open Court, 1910.
[Hil18] David Hilbert. Axiomatisches Denken. Mathematische Annalen, 78(3/4):405–415, 1918. English translation: [Hil70].
[Hil35] David Hilbert. Gesammelte Abhandlungen, Band III. Springer, 1935. Second edition 1970.
[Hil70] David Hilbert. Axiomatic thinking. Philosophia Mathematica, 1970.
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