I felt like we were rediscovering math from square-1 when watching this video

Tromp diagrams are the sort of thing you'd expect aliens to write their ancient inscriptions in.

I saw the screen fade to "SUCC" in big bold letters and I absolutely lost it.

They joke that the more advanced the math gets the less numbers it has... In Lambda-calculus there are actually no numbers, just abstract representations of numbers. This topic is both really interesting and good to fall asleep to thanks to the soothing ethereal music. Thanks

i love how this channel started off as a simple Connect 4 channel and quickly pivoted into delving into the deep underbelly of mathematics

Before watching this, I thought I didn't know math. Now I believe that while I may not know math, it probably knows me.

Beautiful video and a really clear explanation for such a tricky topic!

dude the sound design is literally insane like+sub immediately

I have to turn in my PhD dissertation to my committee tonight. The topic is a novel mathematical theory of the syntax of the lambda calculus using category theory. (If you've heard of Haskell and monads, the syntax is kind of like a free monad, except it forms a monoid in a category of very special endofunctors.) The beta reduction function you define at about 6:00 minutes in is actually EXTREMELY subtle and famously difficult to define correctly, which is one of the reasons people have invented so many different ways of representing the syntax. It's also the reason I spent the last several years working on this stuff. I haven't finished this video yet but it's extremely well done, it's incredible the stuff creators are producing these days.

1:29 I would have NOT guessed what this video was about from looking at it before this point, good job concealing it before the reveal.

I have a Ph.D. in the theory of programming languages, but I still watched this whole thing just to see your animations. I had always wondered if there was a way to make visually intuitive diagrams of lambda terms. I couldn't find anything this slick a decade ago when I was getting my Ph.D., and obviously your work on animating them really helped to show off their power.

I'm a linguist who uses a version of typed lambda calculus for studying natural language semantics. I've come to a working understanding of it in my field, but I always felt I had a hard time making the jump to understanding its use in mathematics and computing... But your video just made it make such clear intuitive sense to me! Amazingly well made video

22:44 this is so f***ing inefficient, I love it

I don't know maths. However, I now understand the eldritch horror genre. I have glimpsed unknown universes and the knowledge I now know I lack weights on my soul.

2:30 In particular, the word "calculus" as we use it today is actually a shorthand for "infinitesimal calculus" (which is then split up into differential and integral calculus respectively), where that "calculus" is being used the same way as with things such as lambda calculus or propositional calculus.

those animations are so cool and well made what

I like how each chapter shows the Church Numeral for the chapter number behind it! This way of representing functions really helped me understand what makes the Lambda Calculus so amazing, the complex behaviour emerging from simple rules.

When i clicked on this video i expected a video about another obscure conlang for ccc4. Now when i watched, i can say i got what i expected

Crazy youtube pull. A 6 hour old video with only 9k views about the most bizarre mathematical concept I ever heard of and it already has a comment by carykh and codeparade.

This feels like some kind of Necronomicon for mathematicians. Open this book, and the math becomes unraveled. You can calculate whatever you want with whichever subjects you like, and uncover the mysteries of mathematics... But then on the flipside you can get stuck in hell for eternity trying to evaluate a factorial of 3.