The Most Powerful Pi Counter We Know

In December 2025, a Dell PowerEdge server computed pi to 314 trillion digits — a new world record. The shocking part: the algorithm behind it isn't new. It was published in 1989 by two brothers working out of a cramped Manhattan apartment on a homemade supercomputer.

This is the Chudnovsky algorithm. Every pi record since 1989 has used it, and after nearly forty years, no one has been able to beat it.

This video explains exactly how it works — from the formula's strange constant 640320 (which traces back to a Heegner number from algebraic number theory), to why it adds about 14.18 correct digits of pi per term, to why combining it with binary splitting and FFT-based multiplication makes it so absurdly fast that it still defines the state of the art four decades later.

It's a story about how a one-line equation, a 1965 algorithm, a 1976 trick, and a homemade computer in an apartment ended up powering every modern pi record on million-dollar enterprise hardware.

Chapters:
0:00 The Record
1:04 How Fast Is Fast
2:31 The Brothers
3:57 The Formula
5:55 Why 640320
8:13 The Catch
9:25 Binary Splitting
11:00 FFT Multiplication
12:38 Why It's Still Unbeaten
14:15 The Punchline

Music:
"Origami" — Scott Buckley (https://www.scottbuckley.com.au)
"Incredulity" — Scott Buckley (https://www.scottbuckley.com.au)
Used under Creative Commons BY 4.0 license.

Sources:
Chudnovsky, David V. and Gregory V. Chudnovsky. "The Computation of Classical Constants." Proceedings of the National Academy of Sciences 86, no. 21 (1989): 8178–8182.
Borwein, Jonathan M. and Peter B. Borwein. "Ramanujan, modular equations, and approximations to pi." American Mathematical Monthly 96, no. 3 (1989): 201–219.
Bailey, David H. "The Computation of π to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm." Mathematics of Computation 50, no. 181 (1988): 283–296.
Heegner, Kurt. "Diophantische Analysis und Modulfunktionen." Mathematische Zeitschrift 56 (1952): 227–253.
StorageReview / Dell. "Pi Computed to 314 Trillion Digits — A New World Record." December 2025.
y-cruncher — A Multi-Threaded Pi Program by Alexander J. Yee (numberworld.org).

#mathematics #pi #chudnovsky #algorithm #manim #problemsvisualized

Видео The Most Powerful Pi Counter We Know канала Euclidea