Videos:
Mikhail Gromov: What is a Manifold?
Ralph Abraham: The Early Years (including a great story on how Foundations of Mechanics came about), The place of UCSC in the History of Chaos Theory
Saunders Mac Lane: Mysteries and Marvels of Mathematics
BBC: Catastrophe Theory: with Zeeman, the riot controversy and more
Pablo Parrilo: Across the Watershed: Unifying Perspectives on Optimization
Brian D. O. Anderson: Extrema without Convexity
Any lecture by Frederic Schuller
Erik Demaine The Geometry of Origami
V.I. Arnold Continued fractions of quadratic irrationals
Karl Johan Åström The fascinating history and success of feedback control
Theo Jansen de jongensdroom (documentary)
L4DC 2019, 2020
Daniel Kuhn Data-driven and Distributionally Robust Optimization and Applications (including derivations), see also Data-driven distributionally robust optimization with MOSEK
Michael I. Jordan On Langevin Dynamics in Machine Learning
Zeyuan Allen-Zhu Natasha 2: Faster Non-convex Optimization Than SGD
Felix Otto Gradient Flow
Étienne Ghys Dynamics à la Dennis Sullivan, A guided tour of the seventh dimension
Dennis Sullivan Simplicity Is The Point
Jean-Pierre Serre How to write mathematics badly
Ferdinand Verhulst 2018 Tribute Lecture dedicated to Henri Poincare
James Isenberg Ricci Flow - Numberphile
Alessio Figalli and more 2020 Fields Medal Symposium: Public Opening
Vinay Prasad Old Fashioned Intelligence in Cancer Medicine
Any video from the Applied Algebraic Topology Network, in particular Konstantin Mischaikow interviewed by Tomas Gedeon
Katya Scheinberg: Recent advances in Derivative-Free Optimization and its connection to reinforcement learning
Christos Papadimitriou and Avi Wigderson on the Theory of Computing
Jessy Grizzle: Mathematics and Learning for Bipedal Locomotion
John Tsitsiklis: Tips on Writing Papers with Mathematical Content
Krishna Balasubramanian: Structured Stochastic Zeroth-order Optimization
Konstantin Mishchenko (OWOS): Regularized Newton Method with Global O(1/k^2) Convergence
Dimitri Bertsekas: Lessons from AlphaZero for Optimal, Model Predictive, and Adaptive Control
Any talk from the ETHZ Autonomy Talks
Artem Kirsanov: Neural manifolds - The Geometry of Behaviour
Rodolphe Sepulchre: Encounters between the local and the global
Andrej Bauer: Five Stages of Accepting Constructive Mathematics
Other: Alberto Padoan: inControl podcast