After decades of research, searching, and inspection, mathematicians have discovered a fresh instance of a singular integer known as a Dedekind number.
In a press release, researchers from Paderborn University and KU Leuven claimed that the so-called ninth Dedekind number, which has 42 digits, had solved a three-decade-old mathematical enigma.
Since 1991, experts have been looking for its value. Using the Noctua supercomputer that is stationed there, the Paderborn scientists were able to determine the precise sequence of numbers.
In Norway in September, the findings will be presented at the International Workshop on Boolean Functions and Their Applications (BFA).
Lennart Van Hirtum began working on this subject as his master’s thesis, and it has now become a major success. Lennart Van Hirtum is now a research associate at the University of Paderborn.
With their work, the scientists join a remarkable group. Mathematician Richard Dedekind first identified the problem in 1897, while later pioneers of early computer technology including Randolph Church and Morgan Ward discovered earlier numbers in the sequence.
According to Van Hirtum, “the calculation of D(9) was an open problem for 32 years, and it was doubtful whether this number could ever be calculated at all.”
Using a Cray 2, the most potent supercomputer available at the time, researchers discovered the 8th Dedekind number, the previous number in the Dedekind series, in 1991. Van Hirtum explains the inspiration behind the challenging endeavour, which he initially carried out in collaboration with the supervisors of his master’s thesis at KU Leuven, in his statement. “It therefore seemed conceivable to us that it should by now be possible to calculate the 9th number on a large supercomputer,” he adds.
According to the news release, the programme ran on the supercomputer for around five months following several years of development. The moment has finally arrived: on March 8, scientists discovered the ninth Dedekind number, which is 286386577668298411128469151667598498812366.