A deceptively simple map puzzle — any map can be colored with just four colors so that no two neighboring regions match — stumped mathematicians for 170 years. From an 1852 letter, to an 1879 "proof" believed for eleven years before it broke, to the 1976 computer proof no human could fully read, all the way to today, when AI has begun to create new mathematics. This episode isn't only about the Four Color Theorem — it's about a deeper question: when we say something is "proved," why do we believe it? youtube.com/watch?v=-mzrShuU…

1796 年 3 月 30 日清晨，一个还差一个月才满 19 岁的年轻人，想通了欧几里得之后两千年里没有人做到的事——只用直尺和圆规，画出正十七边形。但比"画出来"更深的问题是：为什么可以画？ 本片从零讲起：费马素数、模 17 的时钟、高斯周期、Galois 群、四层二次扩张，直到 cos(2π/17) 的显式闭式与 Richmond 的二十步作图，再到 Wantzel 与 Lindemann 关上古希腊三大难题的门。youtu.be/TWnMkXEghFg

In 1766, at age 59, Euler returned to St. Petersburg at Catherine II's invitation. He'd been blind in his right eye for sixteen years already, and the left eye was failing too. In 1771, Wenzel performed a cataract operation; a few months later the blindness became complete — both eyes gone. Over the next seventeen years, totally blind, Euler dictated more than 400 papers — 46.9% of his lifetime 866. This episode walks through some of what he did in those seventeen years: the three-body Lagrange points L1-L5, the manual verification of Mersenne prime M_{31}, the 36-officers Latin-square conjecture. And the morning of September 18, 1783. youtu.be/N05KoZ2n_qQ

MeinMSC — Classical Music Visualizer | Open Source youtu.be/6QluZHnh2wM?si=U6zi… 来自 @YouTube

I vibed this entire chess/board game platform with my AI agent through conversation — it wrote the code, debugged with me, even edited the demo video. The AI also plays against you in the game. Same agent. Builder and opponent. Open source. Self-hosted. youtu.be/YDg-eCBUPLY?is=F_r1…