Mathematicians did the miracle! After 32 years of searching they found the 9th Dedekind number – What is it

After 32 years of searching, mathematicians have identified, with the help of a supercomputer, the value of a large number, D(9), previously thought impossible to find due to the complex calculation process required.

“For 32 years, calculating D(9) has been an open challenge, and it was doubtful that it would ever be possible to calculate this number,” computer scientist Lennart Van Hirtum, of the University of Paderborn in Germany, said in June. when the number was announced.

Dedekind numbers were first described by the German mathematician Richard Dedekind in the 19th century. The numbers are related to logic problems known as “monotone binary functions” (MBFs).

Boolean functions are a type of logic that can take as input only one of two values ​​- 0 (false) and 1 (true) – and distinguish between only those two values.

It is the 10th number in the sequence

The newly identified number, known as the “ninth Dedekind number” or D(9), is actually the 10th number in the mathematical sequence. Each Dedekind number represents the number of possible configurations of a particular kind of logical operation of the form true-false, in different spatial dimensions.

The first number in the sequence is D(0), which represents zero dimensions. That is why D(9), which represents nine dimensions, is the 10th number in the sequence.

Dedekind numbers get larger and larger for each new dimension, making them increasingly difficult to determine, according to Sciencealert.

The eighth Dedekind number, which follows the same rules for eight dimensions, was calculated in 1991. But because of the leap in computing power required to calculate the ninth, some mathematicians thought it impossible to calculate its exact value.

Understanding the concept of a Dedekind number is difficult for non-mathematicians, let alone processing it. Moreover, the calculations involved are so complicated and involve such huge numbers that it was not certain that D(9) would ever be discovered.

A specific supercomputer was required for the achievement

To be able to finally find the number and realize this scientific achievement, a supercomputer with the necessary FPGA cards was needed. FPGA or Field Programmable Gate Array is a type of general-purpose programmable integrated circuit that has a very large number of standard gates and other digital functions such as counters, memory registers, PLL generators, etc.

So the right computer was the Noctua 2 at the Paderborn Center for Parallel Computing (PC2) of the German University of Paderborn, which has one of the most powerful FPGA systems in the world. After several years of development, the program ran on the supercomputer for about five months and finally calculated the 9th Dedekind number, which is 286386577668298411128469151667598498812366…