A new artificially intelligent “mathematician” known as the Ramanujan machine could potentially reveal hidden relationships between numbers.
The “machine” consists of algorithms that search for assumptions, or mathematical conclusions that are likely to be true, but which have not been proven. Assumptions are the starting point for mathematical theorems, which are conclusions that are proven by a series of equations.
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The set of algorithms is named after the Indian mathematician Srinivasa Ramanujan. Born in 1
Ramanujan had an innate sense of numbers and an eye for patterns that other people avoided, said physicist Yaron Hadad, vice president of AI and computer 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 WordsSideKick.com, making Ramanujan a suitable namesake.
Mathematics by machine
Machine learning, where an algorithm detects patterns in large amounts of data with minimal direction 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 basic.
“We wanted to see if we could use machine learning for something very, very basic, so we thought numbers and number theory were very, very basic,” Hadad told WordsSideKick.com. (Number theory is the study of integers, or numbers that can be written without fractions.)
Some researchers have already used machine learning to make assumptions into theorems – a process called automated theorem that proves. The goal of the Ramanujan machine is instead to identify promising assumptions in the first place. This has previously been the domain of human mathematicians, who have come up with well-known 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. written in the margins of a book by the mathematician Pierre de Fermat in 1637, but was not proven until 1994.)
To guide the Ramanujan machine, the researchers focused on basic constants, which are numbers that are fixed and fundamentally true across equations. The most famous constant may be the ratio of the circumference of the circle to the diameter, better known as pi. Regardless of the size of the circle, this ratio is always 3.14159265 … and on and off.
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The algorithms essentially scan 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 scan a limited number of digits, maybe five or ten, and then record any hits and expand them to see if the patterns repeat.
When a promising pattern emerges, the assumption is available for an attempt at proof. More than 100 exciting assumptions have been generated so far, Hadad said, and dozens have been proven.
The researchers reported the results on February 3 in the journal Nature. They have also created a website, RamanujanMachine.com, to share the assumptions the algorithms generate and gather attempts at evidence from anyone who wants to take a notch to discover a new theorem. Users can also download the code to run their own search for assumptions, or let the computer use its free processing space on its own computers to view alone. Part of the goal, Hadad said, is to get lay people more involved in the world mathematics.
The researchers also hope that the Ramanujan machine will help change the way mathematics 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 uncover a better measure of irrationality for Catalan constants, a number denoted by G that has at least 600,000 digits, but can or not be an irrational number. (An irrational number can not be written as a fraction; a rational number can.) The algorithm has not yet answered the question of whether the Catalan constant is or is not rational, but it has moved one step closer to the goal, Hadad said.
“We are still in the very early stages of this project, where the full potential is just beginning to unfold,” he told WordsSideKick.com in an email. “I believe that generalizing this concept to other areas of mathematics and physics (or even other fields of science) will enable researchers to lead new research from computers. So human scientists will be able to choose better goals to work with from a wider range of computers, thus improving productivity and the potential impact on human knowledge and future generations. “
Originally published on WordsSideKick.com.