Category Theory 1.1: Motivation and Philosophy

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]: [VIDEO]

If you are coming from imperative land (more specifically C++) then nothing beats articles and videos by Dr. Bartosz Milewski: [LINK] [VIDEO] [LINK] [LINK]

That just means you are missing some foundation. If you are interested in understanding the theory I really recommend this: [VIDEO] [LINK]

I recently started going through Bartoz Milewski's Category Theory lectures [1]. I think they are a very nice place to start learning these things. [1] [VIDEO]

Those articles (and the videos [VIDEO] ) are great but one doesn't need to learn category theory to understand monads in Haskell. The Haskell Wikibook is an underrated resource: [LINK]

I can recomend the video series of Bartosz Milewski ( [VIDEO] ) I'm at the 4th video and it's the first time that i start to become an understanding of the howl thing. But expect it to take some time. (10 Videos, most are around 1h, i needed to pause several times and think or try something out)

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 [VIDEO]

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 [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.