Machines Are Inventing New Math We've Never Seen
A good conjecture has something like a magnetic pull for the mind of a mathematician. At its best, a mathematical conjecture states something extremely profound in an extremely precise and succinct way, crying out for proof or disproof.
But posing a good conjecture is difficult. It must be deep enough to provoke curiosity and investigation, but not so obscure as to be impossible to glimpse in the first place. Many of the most famous problems in mathematics are conjectures, and not solutions, such as Fermat’s last theorem.
Now, a group of researchers from the Technion in Israel and Google in Tel Aviv presented an automated conjecturing system that they call the Ramanujan Machine, named after the mathematician Srinivasa Ramanujan, who developed thousands of innovative formulas in number theory with almost no formal training. The software system has already conjectured several original and important formulas for universal constants that show up in mathematics. The work was published last week in Nature.
One of the formulas created by the Machine can be used to compute the value of a universal constant called Catalan’s number more efficiently than any previous human-discovered formulas. But the Ramanujan Machine is imagined not to take over mathematics, so much as provide a sort of feeding line for existing mathematicians.
As the researchers explain in the paper, the entire discipline of mathematics can be broken down into two processes, crudely speaking: conjecturing things and proving things. Given more conjectures, there is more grist for the mill of the mathematical mind, more for mathematicians to prove and explain.
That’s not to say their system is unambitious. As the researchers put it, the Ramanujan Machine is “trying to replace the mathematical intuition of great mathematicians and providing leads to further mathematical research.”
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