Studium Generale | Johann Bernoulli Lecture | What is Curvature?

Curvature originally referred to how much a curve or surface bends, like how you would describe the shape of a bent road or a hill. In the 19th century, mathematicians Gauss and Riemann developed this idea further, showing that curvature could describe the shape of objects in space, not just flat surfaces. This concept later played a major role in Einstein's theory of relativity and in quantum physics. In recent research, mathematician Jürgen Jost and his group have discovered connections between curvature and techniques in data analysis, which could lead to new ways of applying it in machine learning.