Moritz Pasch
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Moritz Pasch was a German mathematician known for his work on the foundations of geometry. In 1882, he published Vorlesungen über neuere Geometrie (Lectures on the New Geometry), where he identified the need for undefined concepts, axioms, and more rigorous logic in geometry. Pasch argued that mathematical arguments should rely on formal criteria rather than physical intuition. His ideas influenced David Hilbert and contributed to the development of the axiomatic method in mathematics. This approach, which involves building systems from basic propositions (axioms) through logical deduction, has been applied to various fields, including logic and science.123
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mathematicsThe foundations of geometry…successfully was the German mathematician Moritz Pasch, who argued in 1882 that the mistake had been to rely too heavily on physical intuition. In his view an argument in mathematics should depend for its validity not on the physical interpretation of the terms involved but upon purely formal criteria. Indeed,…
Read More…successfully was the German mathematician Moritz Pasch, who argued in 1882 that the mistake had been to rely too heavily on physical intuition. In his view an argument in mathematics should depend for its validity not on the physical interpretation of the terms involved but upon purely formal criteria. Indeed,…
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geometryA grand synthesisThe German mathematician Moritz Pasch (1843–1930), in his Vorlesungen über neuere Geometrie (1882; “Lectures on the New Geometry”), identified what was wanting: undefined concepts, axioms about those concepts, and more rigorous logic based on those axioms. The choice of undefined concepts and axioms is free, apart from the…
Read MoreThe German mathematician Moritz Pasch (1843–1930), in his Vorlesungen über neuere Geometrie (1882; “Lectures on the New Geometry”), identified what was wanting: undefined concepts, axioms about those concepts, and more rigorous logic based on those axioms. The choice of undefined concepts and axioms is free, apart from the…
Read More