1843-1930

German mathematician who discovered many details of Euclid's work that had gone unnoticed for over 2000 years. Pasch also argued that geometers (those who study geometry) placed excessive reliance on intuition rather than formal mathematical proofs, claiming that the principle of duality contradicted physical intuition in some areas of geometry, such as the distinction between points and lines. These ideas had a significant influence on David Hilbert during his later work.