The Lambda Calculus is a tiny mathematical programming language that has the same computational power as any language you can dream of. In this video, we'll first explore this calculus before seeing how we can flesh it out into a functional programming language. After a brief tour of a simple type system, we'll see why the Lambda Calculus has some surprising applications in the field of mathematical logic, and how the implications of this relationship could alter the way that we study mathematics forever. ― Timestamps ― 0:00 - Intro 0:42 - Definition 5:30 - Multiple Inputs 8:10 - Booleans and Conditionals 13:11 - Simple Types 16:32 - Curry-Howard Correspondence 20:58 - Outro ― Credits ― All animation and voiceover created by Eyesomorphic. Lean4 proof of infinitude of primes taken from mathlib4 under Apache 2.0 license: %2Fdata%2Fnat% Background music: 'Reminisce', composed by Caleb Peppiatt. ― Further Reading ― Types and Programming Languages, by Benjamin C. Pierce (Book) Category Theory and Why We Care, by Eyesomorphic (Lecture series): ― Corrections ― At 4:35, the word 'comptuter' should obviously be 'computer', sorry about that! An entry to #SoMEPi