Explore a fascinating lecture on the epistemic structure of mathematical proofs and their ability to generate certainty. Delve into a data science study examining proofs from Euclid's Geometry to modern computer-assisted theorems like Godel Incompleteness. Discover how the network structure of proofs enables explosive emergence of certainty, even in the face of skepticism about individual steps. Draw parallels between this phenomenon and phase transitions in material objects. Gain insights from practicing mathematicians that support the proposed model of mathematical belief formation. Presented by Simon DeDeo from Carnegie Mellon University and Santa Fe Institute, this talk challenges traditional views on the validity of mathematical arguments and offers a new perspective on the nature of mathematical certainty.