Moritz Pasch

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Born: 8 Nov 1843 in Breslau, Germany (now Wroclaw, Poland)
Died: 20 Sept 1930 in Bad Homburg, Germany

Moritz 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 Pasch.