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Moritz Pasch

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:   

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 

Several references were also listed at   

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-


  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), 

Best luck with your project,

-Doctor Jodi,  The Math Forum
 Check out our web site!   
Associated Topics:
High School History/Biography

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