Richard Borcherds is a mathematician and professor at University of California Berkeley known for his work on lattices, group theory, and infinite-dimensional algebras. His numerous accolades include being awarded the Fields Medal in 1998 and being elected a fellow of the American Mathematical Society and the National Academy of Sciences.Patreon (bonus materials + video chat): https://www.patreon.com/timothynguyenIn this episode, Richard and I give an overview of Richard's most famous result: his proof of the Monstrous Moonshine conjecture relating the monster group on the one hand and modular forms on the other. A remarkable feature of the proof is that it involves vertex algebras inspired from elements of string theory. Some familiarity with group theory and representation theory are assumed in our discussion.I. IntroductionII. Group TheoryIII. Modular FormsIV. Monstrous Moonshine Conjecture StatementV. Sketch of ProofVI. Epilogue Further reading: V Tatitschef. A short introduction to Monstrous Moonshine. https://arxiv.org/pdf/1902.03118.pdfTwitter: @iamtimnguyenWebpage: http://www.timothynguyen.org