Making History With 42 Digits: Scientists Solve Long-Known Problem In Mathematics

A novel instance of a unique integer known as a Dedekind number has been found by mathematicians after decades of study, searching, and examination.

According to a news release, making history with 42 digits, scientists at Paderborn University and KU Leuven have unlocked a three-decade-old mystery of mathematics with the so-called ninth Dedekind number.

Experts worldwide have been searching for its value since 1991. The Paderborn scientists arrived at the exact sequence of numbers with the help of the Noctua supercomputer located there.

The results will be presented in September at the International Workshop on Boolean Functions and Their Applications (BFA) in Norway.

This study, which started as a master's thesis project by Lennart Van Hirtum, has become a huge success. Lennart Van Hirtum is now a research associate at the University of Paderborn.

The scientists join an illustrious group with their work. Earlier numbers in the series were found by mathematician Richard Dedekind himself when he defined the problem in 1897, and later by greats of early computer science such as Randolph Church and Morgan Ward.

"For 32 years, the calculation of D(9) was an open challenge, and it was questionable whether it would ever be possible to calculate this number at all," Van Hirtum says.

The previous number in the Dedekind sequence, the 8th Dedekind number, was found in 1991 using a Cray 2, the most powerful supercomputer at the time. "It therefore seemed conceivable to us that it should be possible by now to calculate the 9th number on a large supercomputer," says Van Hirtum, describing the motivation for the ambitious project, which he initially implemented jointly with the supervisors of his master's thesis at KU Leuven.

The news release stated that, after several years of development, the program ran on the supercomputer for about five months. And then the time had come: on March 8, the scientists found the 9th Dedekind number: 286386577668298411128469151667598498812366.