Audio recording of a lecture given by Jesse Wolfson on November 8, 2024 as part of the Dean's Lecture & Concert Series. The Dean's Office has provided this description of the event: "One hundred and seventy years ago, the German mathematician Bernhard Riemann submitted a short, 12 page note for his habilitation called 'On the hypotheses which lie at the bases of geometry.' Where Euclid began by considering constructions at arbitrary scales, Riemann asked what an observer could measure in nearby regions. With this seemingly small shift, Riemann initiated a radical expansion in our conceptions of space, one that set the stage for Einstein's theory of general relativity and all that comes after, and one which continues to lead mathematicians into strange and unfamiliar new worlds. In this talk, using thought experiments, visualizations, and Riemann's original writing, I will try to lead the audience through the doors Riemann opened and into some of these new worlds that mathematicians are still actively exploring and seeking to understand."
