This artificial intelligence generates new mathematical formulas

Israeli researchers recently described a computer system that is nothing more than a “generator” of mathematical assumptions: The artificial intelligence underlying this system has already generated several mathematical formulas that were unknown until now.

Ramanujan machine

Is tomorrow’s mathematician a machine? Engineers at the Israel Institute of Technology (Technion) have no doubts. In a report published in the journal Nature on February 3, 2021, the researchers presented their “generator” of mathematical conjectures: the Ramanujan machine. However, these conjectures – mathematical propositions requiring proof – are the potential basis of theorems. Keep in mind that theorems occupy an important place in science, often allowing us to orient research for several decades.

According to engineers, their machine works with artificial intelligence and computer automation: It is based on constants, which, unlike variables, are fixed values. Among the constants known in the scientific world, we find the Golden Ratio (about 1.61803), Euler’s number (about 2.71828) or Pi number (about 3.14159).

The virtue of the Ramanujan machine is the use of constants in constructing hypotheses. However, rarely in the history of mathematics have theorems been derived from constants. Srinivasa Ramanujan (1887-1920), who gave his name to the famous machine, is a relatively unknown Indian mathematician. The latter, having studied mathematics on his own, became famous for having developed theorems on the constants of Pi and Euler’s number at the end of the 19th century.

The secret lies in the mathematical intuition that the researchers tried to recreate on their machine: The latter uses correspondences between numerical values, that is, numbers within the constants themselves, to make assumptions. The goal? Dive deep into the deep structure of the constants. For Israeli scientists, the results are impressive, not least because the system does not care about the difficulty of proving a formula or even the knowledge gained in mathematics.

Since its creation, the Ramanujan Machine has already found dozens of assumption formulas. Some of them are unknown and are related to the number of Pi and Euler’s number. On the other hand, the point is that the system generates assumptions, but does not give any proofs. Actually, this is the task of human mathematicians. Some of them are already quite easy to prove, and others have yet to be proven, assuming the latter are true.