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+--- Thread: Scientists invent a machine that generates mathematics we've never seen before (/thread-9793.html)
Scientists invent a machine that generates mathematics we've never seen before - C C - Feb 9, 2021
https://www.sciencealert.com/scientists-invented-a-machine-that-generates-mathematics-we-ve-never-seen-before
INTRO: His name was Srinivasa Ramanujan, and he had a unique gift for dreaming up mathematics of a kind few, if any, had ever contemplated. Attributing his skills to a divine goddess, the Indian mathematician introduced thousands of mathematical ideas and equations to the world, and was especially known for devising conjectures: mathematical propositions not yet proven to be true (in which case they become classified as theorems).
Such an ability – crafting mathematical statements that are both informed and yet uncertain – is rare, and relatively few mathematicians make their name on the basis of such output, let alone theorists with little in the way of formal training.
But now, a new algorithmic invention developed by researchers in Israel could help us automate the discovery of mathematical conjectures like those Ramanujan once pioneered. Named after Ramanujan – who died in India at the age of 32 – the 'Ramanujan Machine' is a computerised system capable of self-generating conjectures involving mathematical constants: strange numbers like π and e that seem to crop up all over the place, even if entirely by coincidence.
"Fundamental mathematical constants such as e and π are ubiquitous in diverse fields of science, from abstract mathematics and geometry to physics, biology and chemistry," researchers from Technion – Israel Institute of Technology explain in a newly published study detailing the system. "Nevertheless, for centuries new mathematical formulas relating fundamental constants have been scarce and usually discovered sporadically."
The Ramanujan Machine might speed things up a little on that front. A system of algorithms powered by a community of cloud-connected computers, it's capable of producing conjectures and discovering mathematical formulas for fundamental constants that stand to reveal the underlying structure of the constants... (MORE)