Subject: Re: [HM] Hilbert's Foundations of Geometry
From: Elena Marchisotto (vcmth01c@csun.edu)
Date: Tue Jan 04 2000 - 12:49:22 EST
Hello Sam,
Here are some possible resources for reviews of Hilbert.
Toepell, M. On the origin of David Hilbert's "Grundlagen der Geometrie"
in Archive for History of Exact Sciences, Springer-Verlag, Berlin, 1986.
This is a synopsis of the author's doctoral dissertation, and a book was
later published which I believe was reviewed by Jeremy Gray in HM.
The article has a bibliography you may find useful.
Review of the Grundlagen by Poincare, H. in Bulle. des Sciences Math. (2)
vol. 26, September, 1902. Also found translated by E.V. Huntington in
the Bulletin of the Amer. Math. Monthly, volume 10, 1903, pages 1-23.
Review of the Grundlagen by Sommer, J. in Bull. of the Amer. Math>
Society, vol. 6, April, 1900, pages 287-299
Weyl, H. David Hilbert and his mathematical work in the Bulletin of the
Amer. Math. Society. Volume 50, 1944, pages 612-654
Abrusci, V. Michele (ed.) Ricerche sui fondamenti della matematica,
Bibliopolis, Naples, 1985. -- attempts to give a picture of the
development and articulation of Hilbert's investigations in foundations.
Contro, W. Von Pasch zu Hilbert. in the Archive for the History of Exact
Sciences, vol. 15.
There may be something in Hilbert - Towards a Philosophy of Modern
Mathematics by J. Fang, Paieda Press, New York, 1970.
Halsted, G. The Betweenness Assumptions in the American Mathematical
Monthly, volume 9, April 1902, pages 98 to 101.
Nagel, E. 1939. The formation of modern conceptions of formal logic in
the development of geometry in Osiris, volume 7, 1939, pages 142-223.
Cassini, Ugo. Critica dei principi della matematica e questioni di
logica, Edizioni Cremonese, Rome, 1961. See chapter 22.
Also, I seem to recall a review by Hans Freudenthal in 1957, but I don't
know where.
It won't surprise you that I prefer Mario Pieri's 1899 axiomatization of
elementary geometry "Della geometria elementare come sistema ipotetico
deduttivo" based on point and motion, and his 1908 axiomatization "La
geometria elementare istituita sulle nozioni di punto e sfera" based on
point and sphere to Hilbert's.
Regards,
Elena
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