It’s been a busy past few weeks. My podcast The Cartesian Cafe, previously only available on YouTube, is now available on Apple Podcasts and Spotify. Please leave a rating and review if you enjoy the show.

And just yesterday, my most recent episode with John Baez was just released. At 3 hours, it’s my longest recording to date, but full of great nuggets!

John Baez is a mathematical physicist, professor of mathematics at UC Riverside, a researcher at the Centre for Quantum Technologies in Singapore, and a researcher at the Topos Institute in Berkeley, CA. John has worked on an impressively wide range of topics, pure and applied, ranging from loop quantum gravity, applications of higher categories to physics, applied category theory, environmental issues and math related to engineering and biology, and most recently on applying network theory to scientific software.

Additionally, John is a prolific writer and blogger. This first began with John’s column This Week’s Finds in Mathematical Physics, which ran 300 issues between 1993 and 2010, which then continued in the form of his ongoing blog Azimuth. Last but not least, John is also a host and contributor of the popular blog The n-category Cafe.

In this episode, we dive into John Baez and John Huerta’s paper “The Algebra of Grand Unified Theories” which was awarded the Levi Conant Prize in 2013. The paper gives a crash course in the representation theory underlying the Standard Model of particle physics and its three most well known Grand Unified Theories (GUTs): the SU(5), SO(10) (aka Spin(10)), and Pati-Salam theories. The main result of Baez-Huerta is that the particle representations underlying the three GUTs can in fact be unified via a commutative diagram. We dive deep into the numerology of the standard model to see how the SU(5) theory naturally arises. We then make brief remarks about the SO(10) and Pati-Salam theories in order to state the Baez-Huerta theorem about their organization into a commutative square: a unification among grand unifications!

Ever wanted to learn about category theory? Did you know it can offer insights into language models of today’s AI rage? Now you can with my latest podcast guest, the wonderful Tai-Danae Bradley over at the Cartesian Cafe. We talk about the basic constructions and definitions of category theory, providing lots of definitions as well as analogies inspired by computer science. We then delve into the Yoneda Lemma, a fundamental result in category theory, and apply it to give insights into language models by clarifying the notions of syntax, word probabilities, and semantics.

I recently interviewed Marcus Du Sautoy for Talks at Google, who is the Professor for the Public Understanding of Science and a Professor of Mathematics at Oxford University. It was tremendous fun talking as mathematicians about AI and creativity: an eclectic mix of Hardy’s apology, automated theorem proving, counterpoints between mental shortcuts and the self-imposed struggles of games, and more. You can find more about these topics in Marcus’s books The Creativity Code and Thinking Better as well as his forthcoming book Around the World in 80 Games. Finally, during the Q&A, we also briefly discuss Eric Weinstein and his Geometric Unity theory, a topic which Marcus and I are both intimately familiar with.