Date: 09/20/97 at 03:56:00 From: Noel A. Srefanek Subject: Need biography of mathematician I'm hoping you can help me on a project for school. Can you give me information on the following? 1. Picture or photo of Moritz Pasch 2. Family background of Moritz Pasch 3. What are the works Pasch made for Mathematics? 4. What were his contributions to Mathematics? 5. What happened in his later days? 6. Biography of Moritz Pasch These questions my teacher gave me are very hard for me. I have already read most of the books in school but they are incomplete. Please help me on this very hard reference. Thank you. Best regards, Kristeen Joan Stefanek
Date: 09/20/97 at 22:48:26 From: Doctor Jodi Subject: Re: Need biography of mathematician Hi Kristeen, Thanks for your question. I searched at the St. Andrew's math history site. Here's what I found (look under P: http://www-history.mcs.st-and.ac.uk/~history/BiogIndex.html There's a picture here, if you have Web access. Otherwise, see the paper references below. Pasch studied in Berlin and then taught in Giessen. He worked on the foundations of geometry. He found a number of assumptions in Euclid that nobody had noticed before. Pasch's Axiom is that if a line enters a triangle ABC through the side AB and does not pass through C then it must leave the triangle either between B and C or between C and A. Pasch argued in 1882 that geometers rely too heavily on physical intuition. In his view an argument in mathematics should not depend on the physical interpretation of the terms involved, but upon purely formal axioms. Pash claimed that the principle of duality contradicted physical intuition about points and lines; nobody believed that these terms were interchangeable. Hilbert was to be influenced by these ideas of Pash. Several references were also listed at http://www-history.mcs.st-and.ac.uk/~history/References/Pasch.html If you can get any of them, especially the Dictionary of Scientific Biography, you should be able to find the rest of the information that you need. References for Moritz Pasch 1. Biography in Dictionary of Scientific Biography (New York 1970- 1990). Articles: 2. W S Contro, Von Pasch zu Hilbert, Arch. History Exact Sci. 15 (3) (1975/76), 283-295. 3. M Dehn and F Engel, Moritz Pasch, Jahresberichte der Deutschen Mathematiker vereinigung 44 (1934), 120-142. 4. H C Kennedy, The origins of modern axiomatics: Pasch to Peano, Amer. Math. Monthly 79 (1972), 133-136. 5. G Pickert, Habilitation und Vorlesungstötigkeit von M Pasch, Mitt. Math. Sem. Giessen 146 (1980), 46-57. 6. G Pickert, Inzidenz, Anordnung und Kongruenz in Pasch's Grundlegung der Geometrie, Mitt. Math. Sem. Giessen 146 (1980), 58-81. Best luck with your project, -Doctor Jodi, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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