Mathematicians Find ‘Seemingly Impossible’ Number

Mathematicians, equipped with powerful supercomputers, have achieved a significant breakthrough by determining the value of an immensely large number that was once considered impossible to calculate.

This particular number is referred to as the “ninth Dedekind number” or D(9), and it holds the position of being the tenth number in a specific sequence.

Each Dedekind number in this sequence represents the various configurations of a specific type of true-false logical operation in different spatial dimensions.

To clarify, the first number in the sequence, D(0), corresponds to zero dimensions. So, D(9) symbolizes nine dimensions, thus making it the tenth number in the sequence, as explained by Live Science.

As the number of dimensions increases, Dedekind numbers become progressively larger, making them increasingly challenging to determine. Mathematicians successfully calculated the eighth Dedekind number back in 1991, adhering to the rules for eight dimensions.

The first eight Dedekind numbers have been known to us, but the ninth one has remained elusive until now. KU Leuven and Paderborn University scientists have solved a decades-old mathematics problem by computing the ninth Dedekind number. pic.twitter.com/OK31hf3gSM

— Mundus 2035 (@Mundus2035) June 29, 2023

However, when it came to the ninth Dedekind number, the task proved to be incredibly demanding due to the substantial increase in computing power required. So, certain mathematicians regarded it as an impossible task to calculate the precise value of this number.

D(9) value found by two separate studies using supercomputers

In a remarkable turn of events, two distinct research groups have independently conducted unrelated studies that have achieved the unimaginable.

The first study, submitted to the preprint server arXiv on April 5, was followed by the second study, submitted to the same server on April 6.

What makes this discovery truly astounding is that both studies used supercomputers, although running different programs, yet they arrived at the exact same numerical result.

While it is important to note that the results have not undergone the peer-review process, the fact that both studies arrived at an identical conclusion gives a high level of confidence in the accuracy of the deciphered number.

Lennart Van Hirtum, the lead author of the second paper and a mathematician at Paderborn University in Germany, expressed his certainty by stating that the number has been deciphered “100% certain,” as reported to Live Science.

To further support their findings, Van Hirtum and his colleagues presented and defended their work during a lecture held at Paderborn University on June 27.

A basic program could take 100 years to complete calculations

For over three years, Van Hirtum has dedicated his efforts to the task of determining the value of D(9). To accomplish this task, he developed a novel computer program specifically designed to process the data in a precise manner.

Van Hirtum emphasized that had he opted for a more basic program, even with a high-performance supercomputer, the calculations could have taken as long as 100 years to complete.