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Mathematicians report possible progress on proving the Riemann hypothesis

Added 05-24-19 12:16:02pm EST - “A new study advances one strategy in the quest to solve the notoriously difficult problem, which is still stumping researchers after 160 years.” - Sciencenews.org


Posted By TheNewsCommenter: From Sciencenews.org: “Mathematicians report possible progress on proving the Riemann hypothesis”. Below is an excerpt from the article.

In the May 11 & 25 SN: High-tech cricket farming, AI learns from Minecraft, looking for lithium, a new hominid species is named, signs of life in dead pig brains, Cherokee cave texts decoded, water molecules on the moon and more. 

STILL ELUSIVE  Researchers may have edged closer to a proof of the Riemann hypothesis — a statement about the Riemann zeta function, plotted here — which could help mathematicians understand the quirks of prime numbers.

Researchers have made what might be new headway toward a proof of the Riemann hypothesis, one of the most impenetrable problems in mathematics. The hypothesis, proposed 160 years ago, could help unravel the mysteries of prime numbers.

Mathematicians made the advance by tackling a related question about a group of expressions known as Jensen polynomials, they report May 21 in Proceedings of the National Academy of Sciences. But the conjecture is so difficult to verify that even this progress is not necessarily a sign that a solution is near (SN Online: 9/25/18).

At the heart of the Riemann hypothesis is an enigmatic mathematical entity known as the Riemann zeta function. It’s intimately connected to prime numbers — whole numbers that can’t be formed by multiplying two smaller numbers — and how they are distributed along the number line. The Riemann hypothesis suggests that the function’s value equals zero only at points that fall on a single line when the function is graphed, with the exception of certain obvious points. But, as the function has infinitely many of these “zeros,” this is not easy to confirm. The puzzle is considered so important and so difficult that there is a $1 million prize for a solution, offered up by the Clay Mathematics Institute.


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