Bartosz Milewski
11 HN recommenders · recommended in 16 months, 2016–2026
46:46 · 394K views · Aug 25, 2016
The first lecture in Bartosz Milewski's category theory series for programmers. It covers the motivation and philosophy behind category theory and why composition matters for handling complexity.
HN commenters repeatedly name it as the friendliest entry point to category theory for working programmers.
19 comments from Hacker News
This reminds me of a great talk by Bartosz Milewski [1] about the motivation and philosophy behind category theory. He makes the observation that our "monkey brains" are not good at dealing with complexity at all and we only really have one good strategy for dealing with it, that being to chop up complex problems into smaller, simpler problems which we can solve in isolation and then combine the results back together to approximate a solution to the larger problem. His point is that we do this everywhere and therefore it's no wonder that category theory is able to describe so many disparate areas of mathematics - because it's really describing just this mechanism, not some deep truth about the universe itself. Like - what if we as humans are so "register bound" that we can't solve any problems which can't be chopped up and put back together like this - such as those in the social sciences. His presentation style is wonderful - i recommend the whole talk but this part starts at 37:20. [1]: this video
If you are coming from imperative land (more specifically C++) then nothing beats articles and videos by Dr. Bartosz Milewski: [LINK] this video [LINK] [LINK]
I suggest a combination of theory (videos/books/papers) and practice. For practice; I highly recommend learning Haskell. If you are new to functional programming then learning Haskell is challenging and frustrating but as with any new topic the key is to not give up but keep probing. A good recent development is lot of mainstream languages are beginning to include functional paradigms such as lambda, closures etc., For example Java introduced lambda expressions, Javascript has had them for a while now. But from a first-principles stand point Haskell is as good as it gets so please do learn and code in Haskell if not at work then at least side projects. For theory I've found following material super useful. 0. This[0] is an incredibly awesome lecture where Phil Wadler takes us on a whirlwind tour of computer science. He talks us through different foundational structures on which almost everything (hardware and software) about computer science is built. I watch this lecture once every few months :-). It helps you build up context and ground various topics. 1. The one and only SICP. Book[1] and lectures[2]. 2. Automata theory[3]. This isn't an easy course but gets to the heart of the matter i.e., the meaning of "function" and what how can it be mechanically "computed". 3. Category Theory is where lot of active research is happening in CS theory. This is a very good lecture series[4]. The pace may seem a bit meandering but don't be put off. Bartosz is a gifted teacher and works i
John Baez (physicist / category theorist / smort dude) has a list of books to learn math and physics. Is an interesting source to crib from. [LINK] Gerhard t'Hooft has a page on how to become of a good physicist. [LINK] Not math though. I'm not necessarily suggesting that a mountain of books is the best way to go about it. I think I respond best to video lectures. I'm not sure where you're starting from or how applied/pure you want. Here's a quick mind dump some of my favorites and some that I haven't watched. Roughly in order of how much I liked them. Gilbert Strang's Computational Methods for engineers was life changing for me. It is a two part MIT opencourse. [LINK] A Stanford course on the Fourier transform [LINK] Bartosz Milewski's Category theory for programmer's this video Stephen Boyd's courses are online. [LINK] Linear Systems, convex optimization. Useful stuff. Francis Su's Real Analysis is very good [LINK] Indian universities have an astounding collection of videos [LINK] I have a tough time with the accents, which is a bummer. UCCS MathOnline has quite a haul [LINK] I've been enjoying this Visual Group Theory course lately [LINK] Math Doctor Bob [LINK] Wildberger has some interesting takes on elementary and non elementary topics [LINK] [LINK] Perimeter scholars lectures. Physics not math. Good stuff. Federico Ardila has a number of combinatorics courses. [LINK] Nonlinear algebra course [LINK] Also of course there is Coursera and edX stuff. Godspeed.
This is a fun read (fair warning: you should have some understanding of monoids and monads before reading) and further validates my hypothesis that understanding category theory would make me a more effective engineer. If you've had the joy of constructing useful shell pipelines, and part of it is in the ease of knowing how it will behave. this is a nice formal statement that the underlying reasons WHY it just “feels right” are because of category theory--which means if I can just learn category theory, I’ll have a new tool for approaching and factoring problems that will be, technically speaking, hella useful. I suppose I should start (re)working my way through this video