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Saturday, July 20, 2019


Context: Scientists from Technion — Israel Institute of Technology have developed a concept they have named the Ramanujan Machine, after the Indian mathematician.

What is it?
It is not really a machine but an algorithm, and performs a very unconventional function.

What it does?
The Ramanujan machine is more of a concept than an actual machine—it exists as a network of computers running algorithms dedicated to finding conjectures about fundamental constants in the form of continued fractions—these are defined as fractions of infinite length where the denominator is a certain quantity plus a fraction, where a latter fraction has a similar denominator, etc.)
The purpose of the machine is to come up with conjectures (in the form of mathematical formulas) that humans can analyze, and hopefully prove to be true mathematically.

Why Ramanujan?
The algorithm reflects the way Srinivasa Ramanujan worked during his brief life (1887-1920). With very little formal training, he engaged with the most celebrated mathematicians of the time, particularly during his stay in England (1914-19), where he eventually became a Fellow of the Royal Society and earned a research degree from Cambridge.
Throughout his life, Ramanujan came up with novel equations and identities —including equations leading to the value of pi — and it was usually left to formally trained mathematicians to prove these.

What’s the point?
Conjectures are a major step in the process of making new discoveries in any branch of science, particularly mathematics. Equations defining the fundamental mathematical constants, including pi, are invariably elegant. New conjectures in mathematics, however, have been scarce and sporadic, the researchers note in their paper, which is currently on a pre-print server. The idea is to enhance and accelerate the process of discovery.

How good is it?
The paper gives examples for previously unknown equations produced by the algorithm, including for values of the constants pi and e. The Ramanujan Machine proposed these conjecture formulas by matching numerical values, without providing proofs. It has to be remembered, however, that these are infinite series, and a human can only enter a finite number of terms to test the value of the series. The question is, therefore, whether the series will fail after a point. The researchers feel this is unlikely, because they tested hundreds of digits.
Until proven, it remains a conjecture. By the same token, until proven wrong, a conjecture remains one. It is quite possible that the algorithm will come up with conjectures that may take years to prove.

Sources: Indian Express.

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