This artificial intelligence generates new mathematical formulas

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Israeli researchers recently communicated about a computer system that is nothing more than a “generator” of mathematical conjectures. The artificial intelligence at the heart of this system has already generated several mathematical formulas unknown until today.

The Ramanujan machine

The mathematician of tomorrow is he a machine? For engineers the Israel Institute of Technology (Technion), there is little doubt. In a review published in the journal Nature on February 3, 2021, the researchers unveiled their “generator” of mathematical conjectures: The Ramanujan Machine. However, these conjectures – mathematical propositions requiring to be proved – are of potential bases of theorems. Let us recall that theorems occupy an important place in science, often making it possible to orient research over several decades.

According to engineers, their machine works with artificial intelligence and computer automation. This is based on constants which, unlike variables, are fixed values. Among the constants famous in the scientific world, we find the golden number (approximately 1.61803), the Euler number (approximately 2.71828) or the number Pi (approximately 3.14159).

The prowess of The Ramanujan Machine lies in its use of constants in the development of conjectures. However, with regard to the history of mathematics, it is rare that theorems have been generated from constants. Srinivasa Ramanujan (1887-1920) – who gave his name to the famous machine – is a relatively unknown Indian mathematician. This one, having learned mathematics in autodidact, had known a certain glory for having elaborated theorems from the constants of the number Pi and the number of Euler at the end of the 19th century.

Indian mathematician Srinivasa Ramanujan.
Credits: unknown author / Wikipedia

Several formulas already discovered

The secret lies in the mathematical intuition, which the researchers tried to recreate with their machine. The latter draws in correspondences between numeric values – that is to say the numbers within the constants themselves – in order to obtain conjectures. The goal ? Go into the deep structure of the constants. For Israeli scientists, the results are impressive, not least because the system does not care about the difficulties regarding the proof of the formula or even the knowledge acquired in mathematics.

Since its inception, The Ramanujan Machine has already found dozens of guesswork formulas. Some of them are unknown and related to the number Pi and the number of Euler. On the other hand, the fact is that the system generates conjectures, but does not provide any demonstration. Indeed, this task is that of human mathematicians. Some have already been proven quite easily and others have yet to be demonstrated, assuming the latter are true.





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