A new artificially intelligent “mathematician” known as the Ramanujan machine may be able to reveal hidden relationships between numbers.
The “machine” consists of algorithms that seek conjecture or mathematical conclusions that are likely to be true but not proven. Guesses are the premises of mathematical theorems, which are conclusions proven by a series of equations.
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The set of algorithms is named after the Indian mathematician Srinivasa Ramanujan. Born in 1887 as the son of a shop assistant and housewife, Ramanujan was a child prodigy who came up with many mathematical conjectures, proofs, and solutions to equations that had never been solved before. In 1918, two years before his early death from illness, he was elected a Fellow of The Royal Society London, becoming only the second Indian man to be inducted after naval engineer Ardaseer Cursetjee in 1841.
Ramanujan had an innate sense of numbers and an eye for patterns that elude other people, said physicist Yaron Hadad, vice president of AI and data science at Medtronic, a medical device company and one of the developers of the new Ramanujan machine. The new AI mathematician is designed to pull promising math patterns from large sets of potential equations, Hadad told Live Science, making Ramanujan a fitting namesake.
Mathematics by machine
Machine learning, in which an algorithm detects patterns in large amounts of data with minimal cues from programmers, is used in a variety of pattern discovery 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 that’s very, very basic, so we thought 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 guesses into theorems – a process that automated theorems prove. The purpose of the Ramanujan machine is primarily to identify promising conjectures. This has previously been the domain of human mathematicians, who have come up with famous proposals, such as Fermat’s Last Theorem, which claims that there are no three positive integers that can solve the equation an + bn = cn when n is greater than 2. (That famous conjecture was scribbled on the sidelines of a book by mathematician Pierre de Fermat in 1637, but was not proven until 1994.)
To steer the Ramanujan machine, the researchers focused on fundamental constants, which are numbers that are fixed and fundamentally true in equations. Perhaps the best known constant is the ratio of a circle’s circumference to its diameter, more commonly known as piRegardless of the size of the circle, that ratio is always 3.14159265… and so and so.
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The algorithms essentially scan large numbers of potential equations looking for patterns that might indicate the existence of formulas to express such a constant. The programs first scan a limited number of digits, maybe five or ten, and then record and expand any matches to see if the patterns repeat further.
If a promising pattern emerges, the conjecture is available for attempted evidence. So far, more than 100 intriguing conjectures have been generated, Hadad said, and several dozen have been proven.
The researchers reported their results Feb. 3 in the journal NatureThey also set up a website, RamanujanMachine.com, to share the assumptions generated by the algorithms and to collect evidence attempts from anyone who would attempt to discover a new theorem. Users can also download the code to run their own suspicion searches, or let the machine use the free processing space on their own computers to look at it independently. Part of the goal, Hadad said, is to get lay people more involved in the world of math
The researchers also hope that the Ramanujan machine will help change the way math is done. It’s hard to say how advancements in number theory will translate into real-world applications, Hadad said, but so far the algorithm has helped uncover a better measure of irrationality for the Catalan constant, a number denoted by G that has at least 600,000 digits may or may not be an irrational number. (A irrational number cannot be written as a fraction; a rational number does.) The algorithm has not yet answered whether or not Catalan’s constant is rational, but it has moved one step closer to that goal, Hadad said.
“We are still in the very early stages of this project, where its full potential is only beginning to unfold,” he told Live Science in an email. “I believe that generalizing this concept to other areas of mathematics and physics (or even other fields of science) will allow researchers to get leads for new research from computers. So human scientists will be able to choose better targets to work on. from a broader perspective. selection offered by computers, thus improving their productivity and potential impact on human knowledge and future generations. “
Originally published on Live Science.