Riemann hypothesis – Quanta Magazine

‘Sensational’ Proof Delivers New Insights Into Prime Numbers

Jordana Cepelewicz — Mon, 15 Jul 2024 13:55:18 +0000

Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the mathematical stakes are high, as with the Riemann hypothesis, whose solution comes with a $1 million reward from the Clay Mathematics Institute. Its proof would give mathematicians much deeper certainty about how prime numbers are distributed, while also implying a host...

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The Year in Math

Konstantin Kakaes — Sat, 23 Dec 2023 01:33:58 +0000

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing impulses that disrupt those patterns. That tension came up repeatedly in our coverage this past year. We covered breakthroughs in graph theory, combinatorics, number theory and geometry — areas where...

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How Do Mathematicians Know Their Proofs Are Correct?

Steven Strogatz — Wed, 13 Jul 2022 20:13:19 +0000

How can anyone speak with certainty about infinity? What can we really know about the mysterious prime numbers without knowing all of them? Just as scientists need data to assess their hypotheses, mathematicians need evidence to prove or disprove conjectures. But what counts as evidence in the intangible realm of number theory? In this episode, Steven Strogatz speaks with Melanie Matchett Wood...

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Mathematicians Clear Hurdle in Quest to Decode Primes

Kevin Hartnett — Thu, 13 Jan 2022 16:12:57 +0000

It’s been 162 years since Bernhard Riemann posed a seminal question about the distribution of prime numbers. Despite their best efforts, mathematicians have made very little progress on the Riemann hypothesis. But they have managed to make headway on simpler related problems. In a paper posted in September, Paul Nelson of the Institute for Advanced Study has solved a version of the subconvexity...

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How I Learned to Love and Fear the Riemann Hypothesis

Alex Kontorovich — Mon, 04 Jan 2021 18:20:20 +0000

I first heard of the Riemann hypothesis — arguably the most important and notorious unsolved problem in all of mathematics — from the late, great Eli Stein, a world-renowned mathematician at Princeton University. I was very fortunate that Professor Stein decided to reimagine the undergraduate analysis sequence during my sophomore year of college, in the spring of 2000. He did this by writing a...

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