Discovery of the Ninth Dedekind Number: A Decades-Long Search and Computational Breakthrough

Date: 2023/11/20
Last Updated: 2024-08-16T15:42:43.993Z
Categories: News, Math
Tags: Dedekind number, Math, CS, Number Theory
Read Time: 1 minutes

After more than thirty years of searching, with the assistance of supercomputers, mathematicians have discovered the ninth Dedekind number. Dedekind numbers were defined by German mathematician Richard Dedekind in 1897 and are based on Boolean functions (values of false or true). These functions take $n$ Boolean variables as input and generate another Boolean variable as output. The first six Dedekind numbers are quite simple, with $D(1)$ being 2, followed by $3$, $6$, $20$, $168$, and $7581$, with subsequent numbers growing increasingly larger. In 1991, one of the most powerful supercomputers at the time, the Cray-2, took 200 hours to calculate $D(8)$. Thirty-two years later, mathematicians at the University of Paderborn in Germany used the Noctua 2 supercomputer and field-programmable gate arrays (FPGA) to calculate $D(9)$ as $286,386,577,668,298,411,128,469,151,667,598,498,812,366$ — a 42-digit number. Discovering $D(10)$ will undoubtedly take a considerable amount of time as well.