July 3, 2026
Math class or mind palace?
Applied Category Theory Course (2018)
A giant math course just dropped, and the comments are already fighting over whether it means anything
TLDR: John Baez’s 77-lecture course tries to make a notoriously abstract kind of math feel useful in areas like databases and design. The comments immediately turned it into a vibe war, with fans cheering and skeptics joking that “applied” and this kind of math don’t belong in the same sentence.
The big news is that physicist and math celebrity John Baez put together a full 2018 course based on Seven Sketches in Compositionality, turning a famously intimidating corner of math into a long, clickable lecture series. We’re talking 77 lectures covering everything from order and logic to databases, design, and even chemistry. In plain English: it’s an attempt to show that this super-abstract math can actually connect to real-world systems and problem-solving, not just blackboards and headaches.
But the real show is in the comments, where the audience instantly split into two camps: the cheer squad and the skeptics. One fan kept it simple with the extremely wholesome “Yay, John!”, while others went straight for the jugular. “Applied category theory” got roasted as if it were a reality-TV villain, with one commenter basically saying the phrase sounds as contradictory as “practical philosophy” or “organized chaos.” Ouch. The hottest mini-drama? Whether this stuff is useful genius or just abstract nonsense in a slightly nicer outfit.
Then came the relatable middle ground: one programmer admitted the book seems like a rare decent bridge between wild theory and things coders might actually use, while also confessing that it still feels hard to fully appreciate unless you’ve already been burned by these ideas before. That tension is the whole mood here: admiration, confusion, and low-key eye-rolling all packed into one thread. Math nerds see a treasure chest; everyone else sees a very elegant dare.
Key Points
- •The page presents a 2018 Applied Category Theory course taught by John Baez and based on *Seven Sketches in Compositionality* by Brendan Fong and David Spivak.
- •Simon Burton is credited with turning the course into webpages.
- •The course is organized into 77 lectures across four chapters: Ordered Sets, Resource Theories, Databases, and Collaborative Design.
- •Topics listed include preorders, Galois connections, adjoints, logic, monoidal preorders, enriched categories, Lawvere metric spaces, functors, natural transformations, Kan extensions, and enriched profunctors.
- •The final chapter covers collaborative design topics including feasibility relations, feedback, monoidal categories, string diagrams, and compact closed categories.