A group of researchers from Israel have come up with a mechanism to generate new conjectures, which could subsequently be proved. They have named this machine ‘The Ramanujan Machine’ (who else can you name this after?).
Mathematicians are said to have a special type of intuition through which they see the world. It is almost like sixth sense with which they sense symmetry, rhythm, patterns, connections, relationships and beauty in the things around them. When it comes to Number Theory, the most simple and intriguing branch of Math, this is even more true.
Numbers are so basic when you consider just the natural or whole numbers. But when you consider special types of numbers and their distributions, then you start seeing interesting patterns. Then when you consider fractions, there is this whole alternate world that opens up with infinite number of small numbers hidden, but precisely placed, between the natural numbers. But the intrigue and mystery peaks when it comes to the so called irrational numbers, which are impossible to locate precisely, but have deeply interesting properties. An insightful Mathematician will be able to see these patterns and predict such properties easily.
Probably the most well known Mathematician with such insights into the world of numbers was Srinivasa Ramanujan. There are so many legends about how he could see remarkable patterns and hidden secrets behind numbers. He could not explain the process behind them and is known to have stated that a goddess revealed some of those patterns and formulae to him in his dreams.
The way Mathematicians have made advancements in the field of Numbers is by proposing certain formulae or ideas (technically called conjectures) based on their intuitions and then then collectively try to prove (or disprove) them. The first step of proposing these conjectures is still an elusive step as it needs great insights. Now a group of researchers from Technion — Israel Institute of Technology in Haifa, Israel, have come up with a mechanism (using Machine Learning, a special branch of Artificial Intelligence) to generate such new conjectures, which could subsequently be proved. They have named this machine ‘The Ramanujan Machine’ (who else can you name this after?). With the help of this machine, the team have apparently made some improvements in the calculation of a certain Mathematical constant (called the Catalan’s Constant) . The journal Nature has recently published an article on this.
It is remarkable that we are now able to emulate using machines the kind of intuitions once thought to be supernatural. But in Machine Learning today, the programs can ‘figure things out’, but cannot explain how they have figured them out. So our Ramanujan Machine may be able to propose new conjectures and theories, but we are not (yet) in a position to understand the working behind those intuitions.