Slicing Spaces - From Contour Lines to Morse Theory: A Historical Perspective

Explore the historical development of Morse theory in this commemorative lecture celebrating the 100th anniversary of Marston Morse's groundbreaking work. Trace the evolution of geometric analysis from 19th-century pioneers like Cayley and Möbius through Poincaré's contributions to Morse's revolutionary 1925 generalization that extended contour line techniques to spaces of all dimensions. Discover how this mathematical approach, rooted in the simple concept of slicing spaces with planes—much like creating topographical maps with contour lines—became a powerful tool in the hands of later mathematicians including René Thom, John Milnor, and Stephen Smale. Learn about the fundamental geometric principle that mathematicians have only two basic tools to study spaces: slicing and projecting, and understand how Morse theory exemplifies the profound impact of systematically developing what began as isolated observations. Gain insight into approximately a century of mathematical progress through the lens of this elegant theory that connects cartography, topology, and advanced geometric analysis, presented by Étienne Ghys, Emeritus Director of Research at CNRS and Permanent Secretary of the French Academy of Sciences.