Rikai Funo · Track 1 · opener
Ode to ∞-Category Theory
The mathematics of the mathematics of mathematics. Where ordinary categories track objects and morphisms, infinity-categories track morphisms between morphisms between morphisms — all the way up, infinitely. The cutting edge of algebraic topology and modern physics, where Jacob Lurie's thousand-page tomes define structures most mathematicians will never fully master. An ode to the infinite tower of abstraction, and the audacity of the people who climb it anyway.
Lyrics
[Intro] A book on the desk. No, a tower. A landmark. [Verse 1] Nine hundred and forty-four pages. A spine of white and blue. Princeton University Press, 2009. Written by one person. Jacob Lurie, were you there, in the Science Center lecture halls? Sixty-eight degrees, year-round. Or were you back in the MIT common rooms, 2003, with the ozone smell from the monitors and the hum of fluorescent tubes at three in the morning? Dreaming in diagrams. [Chorus] It's an arrow that points to an arrow. A path between the paths. A reason to draw a third line between those two. And a fourth between the third. All the way up. The tower with no final floor. The language for the language that describes the world. [Verse 2] They say you built it from your own TeX macros. A private script for a private universe, born while you were still a student. Not just 'Higher Topos Theory'. No. 'Higher Algebra' came first. Almost a thousand pages to clear your throat before you truly began to speak. And no co-authors credited on the text. Just you. [Chorus] It's an arrow that points to an arrow. A path between the paths. A reason to draw a third line between those two. And a fourth between the third. All the way up. The tower with no final floor. The language for the language that describes the world. [Bridge] And who can climb it? Who can even see the top from down here? We just trace the first few levels. It's a structure built for its own sake. A beautiful, impossible proof of... what? The audacity. Just the simple, quiet audacity to begin the climb alone. [Outro] An arrow. To an arrow. To an arrow. It never stops. It just goes up.