A new “mathematician” with artificial intelligence, known as the Ramanujan Machine, can reveal hidden relationships between numbers.
The “machine” consists of algorithms that seek conjectures or mathematical conclusions that are probably true, but have not been proven. Conjectures are the starting points of mathematical theorems, which are conclusions that have been proved by a series of equations.
Related: The most massive numbers that exist
The set of algorithms is named after the Indian mathematician Srinivasa Ramanujan. Born in 1887, the son of a clerk and housewife, Ramanujan was a child prodigy who came up with many mathematical conjectures, proofs and solutions to equations never solved before. In 1918, two years before his premature death from illness, he was elected a Fellow of The Royal Society London, becoming only the second Indian man to be sworn in after the naval engineer Ardaseer Cursetjee in 1841.
Ramanujan had an innate sensitivity to numbers and an eye for patterns that eluded others, said physicist Yaron Hadad, vice president of AI and data science at medical device company Medtronic and one of the developers of the new Ramanujan machine. The new AI mathematician is designed to extract promising mathematical patterns from large sets of potential equations, Hadad told Live Science, making Ramanujan a suitable namesake.
Mathematics by machine
Machine learning, in which an algorithm detects patterns in large amounts of data with minimal guidance from programmers, has been used in a variety of pattern-finding applications, from image recognition to drug discovery. Hadad and his colleagues at the Technion-Israel Institute of Technology in Haifa 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 think that numbers and number theory are very, very basic,” Hadad told Live Science. (Number theory is the study of integers, or numbers that can be written without fractions.)
Some researchers have already used machine learning to turn conjectures into theorems – a process called automated theorem proving. The purpose of the Ramanujan Machine, instead, is to identify promising conjectures in the first place. This has previously 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. (This famous conjecture was scrawled in the margins of a book by mathematician Pierre de Fermat in 1637, but was not proved until 1994.)
To drive the Ramanujan machine, the researchers focused on fundamental constants, which are fixed numbers and are fundamentally true in the equations. The most famous constant may be the ratio between the circumference of a circle and its diameter, better known as pi. Regardless of the size of the circle, this ratio is always 3.14159265 … and so on.
Related: 9 numbers that are nicer than pi
The algorithms essentially examine a large number of potential equations in search of patterns that may indicate the existence of formulas to express such a constant. The programs first examine a limited number of digits, perhaps five or 10, and then record any matches and expand them to see if the patterns repeat even more.
When a promising pattern appears, the conjecture is then available for a trial attempt. More than 100 intriguing conjectures have been generated so far, Hadad said, and several dozen have been proven.
The researchers reported their results on February 3 in the newspaper Nature. They also created a website, RamanujanMachine.com, to share the conjectures that the algorithms generate and to collect attempts at proof from anyone who would like to try to discover a new theorem. Users can also download the code to perform their own conjecture searches or allow the machine to use its spare processing space on their own computers to search on their own. Part of the objective, said Hadad, is to make laypeople more involved in the world of math.
The researchers also hope that 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, Hadad said, but so far, the algorithm has helped to discover a better measure of irrationality for the Catalan constant, a number denoted by G that has at least 600,000 digits, but it may or may not be an irrational number. (THE Irrational number it cannot be written as a fraction; a rational number can.) The algorithm has not yet answered the question of whether or not the Catalan constant is rational, but it has taken a step closer to that goal, Hadad said.
“We are still in the early stages of this project, where the full potential is just beginning to develop,” he told Live Science by email. “I believe that generalizing this concept to other areas of mathematics and physics (or even to other fields of science) will allow researchers to obtain clues for new computer research. Thus, human scientists will be able to choose the best goals to work with. from a wider context selection offered by computers, and thus improve their productivity and potential impact on human knowledge and future generations. “
Originally published on Live Science.