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Learn about the development of a higher-order differential calculus library within Lean's Mathlib mathematical library in this 26-minute conference presentation by Sébastien Gouëzel from CNRS - Rennes University. Explore how this formalization departs from standard textbook definitions to support broader applications by allowing arbitrary fields of scalars, working with functions defined on domains rather than full spaces, and integrating analytic functions within the broader framework of smooth functions. Discover the significant mathematical and formalization challenges these generalizations introduce and examine the solutions developed to address them. Gain insights into the intersection of formal mathematics, proof assistants, and differential calculus through this detailed exploration of smoothness classes and analytic functions within the Lean theorem prover ecosystem.
