One of them is Catalan’s constant, a number that originated from nineteenth-century Belgian mathematician Eugène Catalan’s studies.
Kaminer’s team has experimented with a range of algorithms for finding continued fractions, and applied them to various conceptually important numbers. These express a number as an infinite sequence of fractions nested in each other’s denominators. The Ramanujan Machine currently has limited applications: so far, the algorithms can generate only formulae of a particular type, called continued fractions. “The novelty is to combine them in a unified framework.” Continued fractions The techniques in the Ramanujan Machine’s algorithms existed before, says mathematician Doron Zeilberger at Rutgers University in Piscataway, New Jersey. His work has continued to inspire new research long after he died, aged 32, in 1920. Instead, he filled entire notebooks with formulae that he believed came from a goddess who appeared in his dreams. Ramanujan rarely wrote the types of proof that appear in conventional maths papers. The project - described 1 in Nature on 3 February - is named after Srinivasa Ramanujan, an Indian mathematician who was active in the early twentieth century. The automated creation of conjectures could point mathematicians towards connections between branches of maths that people did not know existed, he adds. “The last result, the most exciting one, no one knows how to prove,” says physicist Ido Kaminer, who leads the project at the Technion - Israel Institute of Technology in Haifa. But some remain open questions, including one on Apery’s constant, a number that has important applications in physics. The team began to make the conjectures public on the project’s website in 2019, and researchers have since proved several of them correct. Machine learning leads mathematicians to unsolvable problem The process produces a good guess called a conjecture - it is then up to human mathematicians to prove that the formula can correctly calculate the whole number. From those, the algorithm tries to predict a new formula that does the same calculation just as well. The AI starts with well-known formulae to calculate the digits - the first few thousand digits of π, for example. The Ramanujan Machine is designed to generate new ways of calculating the digits of important mathematical constants, such as π or e, many of which are irrational, meaning they have an infinite number of non-repeating decimals. Researchers have built an artificial intelligence (AI) that can generate new mathematical formulae - including some as-yet unsolved problems that continue to challenge mathematicians.
Srinivasa Ramanujan made important contributions to mathematics in the early twentieth century.
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