John Carlos Baez

Here’s a great, simple article on applied category theory! I’m glad that it explains a bit about ‘green mathematics’ and my struggle to do mathematics that will help the world.

Natalie Wolchover interviewed me twice for this, and it also features Matteo Capucci, Brendan Fong, Bob Coecke, David Spivak, Amar Hadzihasanovic, Nathaniel Osgood and Tom Leinster.

https://www.quantamagazine.org/can-the-most-abstract-math-make-the-world-a-better-place-20260304/

Can the Most Abstract Math Make the World a Better Place? | Quanta Magazine

Columnist Natalie Wolchover explores whether applied category theory can be “green” math.

Quanta Magazine
Mar 5 at 9:30pmWeb
Show threadCadenMar 6

@johncarlosbaez very interesting!

I've had to brush up on category theory recently as the work I'm doing right now has become very intertwined with it: the research team I'm on is developing a tool that makes functional programming more convenient (especially for beginners) by automatically coercing values to the right types (even when the coercions are nontrivial). This would essentially allow you to define a function to operate on values of some type T, and then automatically be able to apply that same function to any data structure containing values of type T with just a regular function call (among other things).

In order to do such a thing soundly, we're finding category theory to be a nice way to attack it, although we're still ironing out the specifics.

Show threadJohn Carlos BaezMar 6
@tarix29 - great! Indeed, when type theory gets sufficiently subtle it tends to be good to bring in category theory. I'm not at all an expert on type theory, but I've listened to lots of conversations where I can't tell whether people are doing category theory or type theory, because the borderline is so fuzzy.
Show threadAditya KhannaMar 6
@johncarlosbaez I like the article for sure. I didn't know about your family connection with Joan Baez! I'm glad to know that now. Also, the article provides such a broad view that I'm starved for details. How's the application of category theory, per se, any better than our current choice of using flowcharts and functions? Is there a place where I can read about category theoretic concepts being applied to model, say, a toy real-world problem?
Show threadJohn Carlos BaezMar 6

@adityakhanna - in my blog I often talk about my work on applied category theory. Here's a blog article with a link to a more detailed article on how we're applying category theory to public health:

https://johncarlosbaez.wordpress.com/2025/09/11/categories-for-public-health-modeling/

Other people would give you very different examples, but this is my favorite.

Categories for Public Health Modeling

How, exactly, can category theory help modeling in public health? I wrote a paper about this with two people who helped run Canada’s COVID modeling, together with a software engineer and a ma…

Azimuth
Show threadAditya KhannaMar 6
@johncarlosbaez oop there doesn't seem to be a link
Show threadJohn Carlos BaezMar 6
@adityakhanna - there should be a link now. There are difficulties with posting links to Azimuth: Mastodon claims the owner of the blog needs to give permission, and though the owner is me I don't know how that works. Luckily there is a workaround.