Tuesday, March 9, 2021

“Ramanujan machine”. AI reveals hidden patterns in numbers

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New “mathematical” software with artificial intelligence (AI), known as the Ramanujan Machine, manages to reveal hidden relationships between numbers.

According to LiveScience, the “machine” consists of algorithms that look for conjectures or mathematical conclusions that are probably true, more than have never been proven. Conjectures are the starting points of mathematical theorems, conclusions that have been proved by a series of equations.

This set of algorithms is named after the Indian mathematician Srinivasa Ramanujan. Born in 1887, the son of a clerk and a housewife, Ramanujan was a child prodigy who brought up many mathematical conjectures, proofs and solutions to equations never solved before. In 1918, two years before his early death from illness, he was elected Fellow gives The Royal Society London, becoming the second Indian man to be installed after the naval engineer Ardaseer Cursetjee in 1841.

Ramanujan had a innate sensitivity to numbers and an eye for patterns that eluded others, according to physicist Yaron Hadad, vice president of artificial intelligence (AI) and data science at the medical device company Medtronic and one of the creators of the new Ramanujan machine.

The new software is designed to extract promising mathematical patterns large sets of potential equations.

The machine, in which an algorithm detects patterns in large amounts of data with minimal programmer guidance, has been used in a variety of pattern locations, from image recognition to drug discovery.

Hadad and his colleagues at the Technion-Israel Institute of Technology wanted to see if they could use machine learning for something more fundamental. “We wanted to see if we could apply machine learning to something very, very basic, so we thought that numbers and number theory are very, very basic“, said.

Some researchers have already used machine learning to turn conjectures into theorems – a process called automated theorem proving. Instead, the objective of the Ramanujan Machine is, first, identify promising conjectures.

This has been the domain of human mathematicians, who came up with famous proposals like Fermat’s Last Theorem, which states that there are not three positive integers that can solve the equation an + bn = cn when n is greater than 2.

To make the Ramanujan machine, researchers focused on the fundamental constants, which are fixed and fundamentally true numbers in the equations.

The most famous constant may be the ratio of the circumference of a circle to its diameter, better known as pi. Regardless of the size of the circle, the proportion is always 3.14159265 (…).

The algorithms examine a large number of potential equations for patterns that can indicate the existence of formulas to express such a constant.

The programs first scan a limited number of digits, perhaps five or ten, and then record the matches and expand them to see if the patterns repeat even more. When a promising pattern appears, the conjecture is available for an attempt at proof.

The team created a website, RamanujanMachine.com, to share the conjectures that the algorithms generate and to gather attempts at proof from anyone who wants to try to discover a new theorem.

Users can also download the code to perform their own guesswork investigations or allow the machine to use the spare processing space on their own computers to search on their own.

According to Hadad, part of the objective is involve lay people more in the world of mathematics.

So far, more than 100 intriguing conjectures and several dozen have been proven. The algorithm helped to discover a better measure of irrationality for the Catalan constant, a number denoted by G that has at least 600 thousand digits, but may or may not be an irrational number.

The algorithm has not yet answered the question whether the Catalan constant is rational or not, but it has taken a step towards that goal.

Researchers hope the Ramanujan Machine will help change the way math is done. It is difficult to say how advances in number theory will translate into real-world applications.

The study was published this month in the scientific journal Nature.

Maria Campos Maria Campos, ZAP //

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