After decades of study, search and investigation, mathematicians have found a new example of a unique integer known as the Dedekind number. Making history with 42 digits, scientists from the University of Paderborn and KU Leuven have unlocked a three-decade-old mathematical mystery with the so-called ninth Dedekind number, according to a press release.
Experts around the world have been searching for its value since 1991. The exact sequence of numbers was arrived at by Paderborn scientists using the Noctua supercomputer located there.
The results will be presented in September at the International Workshop on Boolean Functions and Applications (BFA) in Norway.
This study, which began as a thesis project of Lennart Van Hirtum, was a huge success. Lennart Van Hirtum is now a researcher at the University of Paderborn.
The scientists join the famous 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 early computer science greats 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,” says Van Hirtum.
The previous number in the Dedekind sequence, the 8th Dedekind number, was found in 1991 using the Cray 2, the most powerful supercomputer at the time. “It therefore seemed conceivable to us that it should already be possible to calculate the number 9 on a large supercomputer,” explains Van Hirtum of the motivation for the ambitious project, which he initially implemented together with the supervisors of his thesis at KU Leuven.
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