Person: Pasch, Moritz
Moritz Pasch was a German mathematician who worked on the foundations of geometry. He found a number of assumptions in Euclid that nobody had noticed before.
Mathematical Profile (Excerpt):
- Pasch attended the Elisabeth Gymnasium in Breslau, graduating in 1860.
- Pasch was awarded his doctorate on 21 August 1865 for his thesis De duarum sectionem conicarum in circulos projectione Ⓣ(The two conic section in circular projection).
- His thesis advisor was Schröter and Pasch dedicated his thesis to him and to Kambly his mathematics teacher at the Gymnasium.
- In addition to remarkable research contributions which we mention below, Pasch was interested in the administration of the university and he devoted considerable effort as chairman of the committee responsible for the examination of prospective high school teachers.
- Drawing on the work of his predecessors, Pasch was the first to explicitly state all the basic concepts and axioms necessary for his construction of projective geometry.
- But no one before Pasch had laid a basis for dealing logically with such observations.
- Pasch's Axiom is that if a line enters a triangle ABCABCABC through the side ABABAB and does not pass through CCC then it must leave the triangle either between BBB and CCC or between CCC and AAA.
- Pasch argued in Vorlesungen über neuere Geometrie (1882) that geometers rely too heavily on physical intuition.
- Pasch 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.
- Pasch explains the axiomatic method in mathematics in great detail.
- According to Pasch, the mathematical language is often not clear, enough.
- Pasch received a number of honours for his outstanding contributions including honorary degrees from the University of Frankfurt and from the University of Freiburg to mark his eightieth birthday.
- After retiring in 1911 Pasch continued to live in Giessen.
- Pasch was taking a holiday in Bad Homburg when he died.
Born 8 November 1843, Breslau, Prussia (now Wrocław, Poland). Died 20 September 1930, Bad Homburg, Germany.
View full biography at MacTutor
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive