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 conjectures, or mathematical conclusions that are likely to be true, but which have not been proven. Assumptions are the starting points of mathematical theorems, which are conclusions proved by a series of equations.
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The set of algorithms is named after the Indian mathematician Srinivasa Ramanujan. Ramanujan, born in 1887 as a shop assistant and a homemaker, was a 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 in London, and became the only Indian man admitted in 1841 to the marine engineer Ardaseer Cursetjee.
Ramanujan has an innate instinct for numbers and an eye for patterns that other people evade, said physicist Yaron Hadad, vice president of AI and computer science at medical equipment 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 set of potential equations, Hadad told WordsSideKick, making Ramanujan an appropriate namesake.
Mathematics by machine
Machine learning, in which an algorithm detects patterns in large amounts of data with minimal direction from programmers, has been used in a variety of applications to find patterns, from image recognition to drug discovery. Hadad and his colleagues from 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 is very, very basic, so we thought numbers and number theory were very, very basic,” Hadad told WordsSideKick. (Number theory is the study of integers, or numbers that can be written without fractions.)
Some researchers have already used machine learning to turn suspicions into statements – a process that proves automatic statement. The purpose of the Ramanujan machine is rather to identify promising suspicion in the first place. It used to be the domain of human mathematicians, who came up with famous proposals, such as Fermat’s last statement, which states that there are no three positive integers that can solve the equation an + bn = cn when n is greater than 2. ( The famous conjecture was scribbled on the side of a book by the mathematician Pierre de Fermat in 1637, but was only proven in 1994.)
To direct the Ramanujan machine, the researchers focused on fundamental constants, which are numbers that are fixed and fundamentally true in equations. The best known constant is perhaps the ratio between the circumference of a circle and the diameter, better known as PI. Regardless of the size of the circle, the ratio is always 3.14159265 … and on and on.
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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 matches and expand them to see if the patterns repeat further.
When a promising pattern appears, the suspicion is available for an attempt at proof. Hadad has so far generated more than a hundred interesting suspicions, and several dozen have already been proven.
The researchers reported their results in the journal on February 3 Nature. They also set up a website, RamanujanMachine.com, to share the suspicions that the algorithms generate and attempts to gather evidence from anyone who wants to sting to discover a new statement. Users can also download the code to perform their own search for suspicions, or let the machine use their own processing space on their own computers to view for themselves. Part of the goal, Hadad said, is to make lay people more involved in the world of mathematics.
The researchers also hope that the Ramanujan machine will help change the math. Hadad said that the algorithm could help to a better degree of irrationality for the constant of the Catalan, a number indicated by G containing at least 600,000 digits, but it is difficult to say whether an irrational number may or may not be . (‘A irrational number can not be written as a fraction; a rational number can.) The algorithm has not yet answered the question of whether or not Catalan’s constant is 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 only beginning to unfold,” he said in an email to WordsSideKick. “I believe that generalizing this concept to other areas of mathematics and physics (or even other disciplines) will enable researchers to get new computers from new research. Human scientists will therefore be able to choose better goals from a wider work. selection offered by computers, thereby enhancing their productivity and potential impact on human knowledge and future generations. ‘
Originally published on Live Science.