Reddit reviews How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics

It's a fair point; applied category theory is really in its infancy. For a long time, it was considered pretty inaccessible and obscure. I think that's starting to change, e.g. with some new pedagogically oriented books (Cheng, Fong-Spivak), new international conferences, new journal, etc. But it might take time.


The most successful application so far is certainly Haskell, OCAML, and other similar functional programming languages. These were built entirely on category-theoretic principles, and have become quite popular (Haskell is used at AT&T, Amgen, Apple, Bank of America, Facebook, Google, Verizon, etc.).


There are control theory researchers such as Paulo Tabuada, robotics researchers such as Aaron Ames and Andrea Censi, and others who have explicitly used category theory in their work. For-profit companies such as Kestrel, Statebox, R-Chain, Conexus, etc. all use category theory more or less explicitly.


Whether or not electrical engineers—or others of that sort—will use CT depends on whether there are enough interested parties who can drive it more deeply into that domain. So far, the work has been at a very surface level because category theorists have to "go to them" instead of them "coming to us". As category theorists, we don't know enough about the depths of these fields to make a direct and immediate impact without preparing the ground. It takes time and effort, and we need more people on the case.


But if we continue—and I think we will—my guess is that in the future, people will use category theory to learn lots of different fields and connect their knowledge from one to another. A major value proposition of category theory is its ability to transfer information and problem specification from one field to another. I think that will eventually be broadly useful.

I'm not so sure this is a fundamental difference, so much as a distinction in who is looking at each field. For the most part, category theory is studied by those who are looking to make advances in knowledge. Sure, the things researchers are looking at can be complex. But if you look at current research in abstract algebra, it's equally difficult to get up to speed and comprehend. The reason abstract algebra can be seen as simpler is that there is also introductory material, aimed at undergraduates, and even the general population.

Is it fundamentally impossible to produce such introductory material in category theory? Of course not! Several people have made serious and credible attempts. For example, here and here

For me, it was Conceptual Mathematics: A First Introduction to Categories. Today, I might suggest How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics or Category Theory in Context to start.

Eugenia Cheng wrote How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics, which was a fun read for both me as a first year math graduate school student and for my former colleague who didn't have any formal math background at all.

Dr. Cheng also has some wonderful videos on a Youtube channel called The Catsters. These videos really helped me to get started when I was first learning some category theory.

And last but not least, she's worth following on Twitter: @DrEugeniaCheng.