His name was Srinivasa Ramanujan and he had a unique gift for dreaming-up mathematics of a sort few, if any, had ever contemplated.
Attributing his skills to a divine goddess, Indian mathematician introduced thousands of mathematical ideas & equations to the world and was especially known for devising conjectures: mathematical propositions yet not proven to be true (in case, they become classified as theorems).
Such a ability, crafting mathematical statements that are both informed & yet uncertain is rare and relatively some mathematicians make their name on the basis of such output, let alone theorists with small in the way of formal training.
But now, a new algorithmic invention developed by the researchers in Israel could help-us automate the discovery of mathematical conjectures, just like those Ramanujan once pioneered.
Named after Ramanujan who died in India at the age of 32, the ‘Ramanujan Machine‘ is a computerized system that is capable of self-generating conjectures involving mathematical constants: strange numbers like π & e that seem to crop-up all over the place, even if entirely by coincidence.
“Fundamental mathematical constants like e & π are ubiquitous in diverse fields of science, from abstract mathematics & geometry to physics, biology & chemistry,” researchers from Technion Israel Institute of Technology explain in a newly-published study detailing the system.
“Nevertheless, for hundreds of years new mathematical formulas relating fundamental constants have been scarce & usually discovered sporadically.”
The Ramanujan Machine might speed things-up a small on that front. A system of algorithms powered-by a community of cloud-connected computers, it is capable of producing conjectures, and discovering mathematical formulas for fundamental constants that stand to-reveal the underlying structure of the constants.
So far, the algorithmic machine has generated conjectures that were easily provable, while discovering new fractional ways to-calculate constants such as π and also coming-up with conjectures that are yet to be proven.
“The computer does not care if proving the formula is easy or difficult and does not base the new results on any prior mathematical knowledge, but only on the numbers in mathematical constants,” explains senior author & physicist Ido Kaminer.
“It is important to point-out that the algorithm itself is incapable of proving the conjectures it found, at this point, the task is left-to be resolved by human mathematicians.”
The researchers observe that there are limitations to what the Ramanujan Machine can produce, notably, in some examples, what appear to be previously unknown conjectures generated-by the algorithms may be “merely mathematical coincidences that break-down once enough digits are calculated”.
So far, however, there are reasons to get excited about what these algorithms are enabling especially, the discovery of a new algebraic structure concealed within Catalan’s constant, which hints the machine could be capable of generating actual breakthroughs the mathematics world has never-seen before.
“We believe & hope that proofs of new computer-generated conjectures on fundamental constants will help to-create mathematical knowledge,” the researchers explain.
If you like the idea & want to get involved, there are several perks to unlock if you join the Ramanujan Machine’s community. Lend your computer’s processing power and you would possibly get a conjecture named after you.
Formulas & algorithms themselves also are up for naming rights, depending on your aptitude for mathematical proofs or developing code.
The findings are published in Nature.