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Mathematicians Clear Hurdle in Quest to Decode Primes

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...

Symmetries Reveal Clues About the Holographic Universe

We’ve known about gravity since Newton’s apocryphal encounter with the apple, but we’re still struggling to make sense of it. While the other three forces of nature are all due to the activity of quantum fields, our best theory of gravity describes it as bent space-time. For decades, physicists have tried to use quantum field theories to describe gravity,...

Evolution ‘Landscapes’ Predict What’s Next for COVID Virus

In the fall of 2019, the world began one of the largest evolutionary biology experiments in modern history. Somewhere near the city of Wuhan in eastern China, a coronavirus acquired the ability to live inside humans rather than the bats and other mammals that had been its hosts. It adapted further to become efficient at spreading from one person to...

Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution

In 1779, the Swiss mathematician Leonhard Euler posed a puzzle that has since become famous: Six army regiments each have six officers of six different ranks. Can the 36 officers be arranged in a 6-by-6 square so that no row or column repeats a rank or regiment? The puzzle is easily solved when there are five ranks and five regiments, or seven ranks...

Qubits Can Be as Safe as Bits, Researchers Show

Over the centuries, we have learned to put information into increasingly durable and useful form, from stone tablets to paper to digital media. Beginning in the 1980s, researchers began theorizing about how to store the information inside a quantum computer, where it is subject to all sorts of atomic-scale errors. By the 1990s they had found a few methods,...

Flying Fish and Aquarium Pets Yield Secrets of Evolution

To escape predators beneath the waves, a flying fish can shoot out of the water and glide long distances because its paired pectoral and pelvic fins, longer and more rigid than those of other fish, act as airfoils. In a quirky triumph of evolution, creatures that were once strictly aquatic transformed into temporarily airborne ones through a few modifications...

An Injection of Chaos Solves Decades-Old Fluid Mystery

Fluids can be roughly divided into two categories: regular ones and weird ones. Regular ones, like water and alcohol, act more or less as expected when pumped through pipes or stirred with a spoon. Lurking among the weird ones — which include substances such as paint, honey, mucus, blood, ketchup and oobleck — are a vast variety of behavioral enigmas...

Mathematicians Outwit Hidden Number Conspiracy

A new proof has debunked a conspiracy that mathematicians feared might haunt the number line. In doing so, it has given them another set of tools for understanding arithmetic’s fundamental building blocks, the prime numbers. In a paper posted last March, Harald Helfgott of the University of Göttingen in Germany and Maksym Radziwiłł of the California...

The Year in Math and Computer Science

Mathematicians and computer scientists had an exciting year of breakthroughs in set theory, topology and artificial intelligence, in addition to preserving fading knowledge and revisiting old questions. They made new progress on fundamental questions in the field, celebrated connections spanning distant areas of mathematics, and saw the links between...

The Year in Physics

One of the first articles Quanta Magazine published in 2021 described a cosmic surprise: A long-puzzling smudge of X-ray light was not, as most believed, a nearby cloud of gas, the remnant of some long-ago stellar explosion. Instead, it was the edge of a truly enormous structure, a bubble that towered over our Milky Way galaxy. The revelation was the...

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