Applied Compositional Thinking for Engineers
I always groan when I see posts on HN with grandiose claims about category theory, like this one.<p>I think it is actively harmful to propagate pseudo-mathematical claims like the those, for example, found in the 
slides of Guest Lecture 1:<p>&gt;&gt;&gt; It’s touched or greatly influenced all corners of mathematics.<p>&gt;&gt;&gt; It’s become a gateway to learning mathematics.<p>And from the audio of the lecture (paraphrasing):<p>&gt;&gt;&gt; Category theory is the stem cell that differentiates into and lies at the root of all pure mathematics. [&quot;All forms of pure math&quot; is also written on the slides.]<p>These statements are simply false. The vast majority of pure mathematics research done today does not involve category theory at all, and does not benefit from it. An even greater majority (like 99%+) of mathematics done in industry and in national labs does not involve category theory. Numerical analysis, probability, statistics, partial differential equations, dynamical systems, harmonic analysis, even lots of modern differential geometry – no category theory to be seen!<p>Want proof? Pick up any introductory graduate textbook, or any major journal in these fields.<p>Now, if you want to do research in number theory, or algebraic topology, or algebraic geometry – sure, you likely would benefit from categorical thinking. But those fields hardly have a monopoly on pure mathematics. Even in, for example, Hatcher&#x27;s introductory graduate text on algebraic topology (perhaps the most widely used), category theory is stuck in a small appendix and you can read the entire thing without it, with no real loss [1].<p>I don&#x27;t have the energy right now to explain why I find the lecture series misguided more generally, but I want to at least flag these <i>obviously incorrect statements</i> and urge caution.<p>[And before anyone grabs a PDE book and tells me the use of cohomology groups in certain places means PDE uses category theory, please note that e.g. homological algebraic and category theory are different things.]<p>[1] OK, I guess you need to know what e.g. a natural transformation is to read some parts of the last chapter, but no one does that in an introductory course anyway. A motivated teacher could easily present the material in such a way that this didn&#x27;t matter.