The “Ramanujan machine”, the device that generates …

Thanks to artificial intelligence (AI) and computer automation, Technion researchers have developed a “conjecture generator “for the development of mathematical theorems.

The study, published in the Nature magazine, was carried out by students from different faculties under the supervision of the assistant professor Ido fireplaces from Teknion College of Electrical Engineering, short for Israel Institute of Technology.

The project deals with one of the most fundamental elements of mathematics: mathematical constants. A mathematical constant is a number with a fixed value that naturally results from different mathematical calculations and mathematical structures in different fields.

Many mathematical constants are of great importance in mathematics, but also in external disciplines, such as biology, physics and ecology. Examples of these fundamental constants are the golden ratio and the Euler number.

The best known constant is pi, which was studied in ancient times against the background of the circumference of a circle. Today, pi appears in many forms in all branches of science, with many competing math buffs to see who can remember the largest number of digits after the decimal point: 3.1415926535897932384626433832795028841971693993751058209749445923078 16406286208998628034825342117067280898234258258998628034825342117067230898234258258998628034825342117067230898

Technion researchers proposed and examined a new idea: the use of computer algorithms to automatically generate mathematical assumptions that appear in the form of formulas for mathematical constants.

A conjecture is a mathematical conclusion or proposition that has not been proven; once the conjecture is proven, it becomes a theorem. The discovery of a mathematical conjecture about fundamental constants is relatively rare, and its source often lies in mathematical genius and exceptional human intuition. Examples of such genius are Newton, Riemann, Goldbach, Gauss, Euler and Ramanujan, and the new approach presented in the article is precisely named after the latter, Srinivasa Ramanujan.

The man who inspired the machine

Ramanujan is an Indian mathematician born in 1887, who grew up in a poor family, but managed to reach Cambridge at the age of 26 on the initiative of British mathematicians Godfrey Hardy and John Littlewood. Within a few years he fell ill and returned to India, where he died at the age of 32.

During his short life he achieved great achievements in the world of mathematics. One of Ramanujan’s rare abilities was the intuitive formulation of unproven mathematical formulas. So, The Technion research team decided to call their algorithm “the Ramanujan machine” because it generates guesses without testing it, by “mimicking” intuition using AI and computer automation. considerable.

How it works

According to Professor Kaminer, “the results are impressive because the computer doesn’t care whether testing the formula is easy or difficult, and does not base the new results on previous mathematical knowledge, but only on the numbers of the mathematical constants. “

He added: “To a large extent, these algorithms work the same as Ramanujan himself, who presented results without evidence. It is important to note that the algorithm itself is unable to test the guesses it has found; at this point, the task remains to be solved, to be solved by human mathematicians. “

The assumptions generated by the Technion’s Ramanujan machine gave new formulas for the mathematical constants known as pi, the Euler number (e), the Apery constant (which is related to the Riemann zeta function) and the Catalan constant. Surprisingly, the algorithms developed by Technion researchers succeeded not only in creating known formulas for these famous constants, but also in uncovering various previously unknown conjectures.

The researchers believe that this algorithm will be able to significantly speed up the generation of mathematical assumptions about fundamental constants and help identify new relationships between these constants.

Hours in which Gauss took a life

As mentioned, until now these guesses were based on rare genius. This is why in hundreds of years of research, only a few dozen formulas have been found.

It only took a few hours for the Technion Ramanujan Machine to discover all the pi formulas discovered by Gauss, the “Prince of Mathematics”, during a lifetime of work., as well as dozens of new formulas that Gauss was unaware of.

According to the researchers, “similar ideas could in the future lead to the development of mathematical conjectures in all areas of mathematics and thus provide a significant tool for mathematical research.”

The research team has launched a website, RamanujanMachine.com, which aims to engage the public more in the advancement of mathematical research by providing algorithmic tools that will be made available to mathematicians and the public.