SSP-100 (037) The Non-Euclidean Revolution

Mark Huibregtse, Professor of Mathematics

Can human beings know anything with absolute certainty? How about Euclidean geometry? The theorems of geometry are proven using clear, rigorous logical reasoning, starting from a small number of obvious axioms. If Euclidean geometry were in doubt, then the very possibility of certain knowledge of anything might well be in doubt as well. Indeed, the discovery (in the early 1800s) that Euclidean geometry might not be a perfect description of physical space led to deep reappraisal of the relationships among mathematics, natural science, and physical reality, and changed the way we view the world—no less profoundly than did the Darwinian revolution in biology or the Copernican revolution in astronomy. We will study the Non-Euclidian Revolution from mathematical, philosophical, and historical perspectives, and thereby explore the nature of, and the human search for, truth.