On March 18, 2019, two mathematicians, David Harvey, an employee of the University of New South Wales in Sydney, and his French colleague Joris van der Hoeven discovered the most efficient algorithm for multiplying large numbers and posted their work on the Internet for viewing and checking by others.

In the history of the Earth, there were three key discoveries of new methods of multiplication in mathematics. They resonate with the theme of three Ananke: blind matter, laws, dogmas (consequence, process, cause).

“Most everyone learns to multiply the same way. We stack two numbers, multiply every digit in the bottom number by every digit in the top number, and do addition at the end.” The larger the dimension of the numbers, the more multiplication operations must be performed. If the dimension is n, the number of operations is n². The number of operations becomes huge for large numbers and, accordingly, the counting time is also long.

People have been using this method for four millennia without trying to change it. Around 1956, the famous Soviet mathematician Andrey Kolmogorov suggested in his lecture that this is the best possible method to multiply two numbers together. It turned out that there were other ways, just no one thought about it. About seventy years ago, the hypothesis arose that there is a faster way than the traditional way of multiplying in a column. And since then, scientists have tried to solve this issue.

The Practical Application of Operations with Big Numbers

“Every time you engage in encrypted communication on the internet — for example, access your banking website or perform a web search — your device performs a head-spinning number of multiplications, involving numbers with hundreds or even thousands of digits.”

Rapid multiplication in our material world is of great interest in the field of public key cryptography. Public key cryptographic systems are now widely used in various network protocols TLS, SSL, SSH.