Tag: Quantum Stuff

Similarly, 7! + 4 is divisible by 4, 7! + 5 by 5, 7! + 6 by 6, and 7! + 7  by 7, which makes 7! + 2, 7! + 3, 7! + 4, 7! + 5, 7! + 6, 7! + 7 a sequence of six consecutive composite numbers. We have a prime… Continue reading How Can Infinitely Many Primes Be Infinitely Far Apart?

As soon as President Biden unveiled the first image from the James Webb Space Telescope (JWST) on July 11, Massimo Pascale and his team sprang into action. Coordinating over Slack, Pascale, an astrophysicist at the University of California, Berkeley, and 14 collaborators divvied up tasks. The image showed thousands of galaxies in a pinprick-size portion… Continue reading Two Weeks In, the Webb Space Telescope Is Reshaping Astronomy

The Kakeya conjecture sounds like a brain teaser. Place a needle flat on a table. How much area do you need in order to be able to turn it so that it points in all possible directions? The most obvious possible answer is a circle whose diameter is the length of the needle. But this… Continue reading New Number Systems Point Geometry Problem Toward a Real Solution

One of the longest-standing questions in biology is how a living thing that starts as an embryonic blob of uniform cells morphs over time into an organism with diverse tissues, each with its own unique pattern and characteristics. The answer would explain how a leopard gets its spots, a zebra gets its stripes, trees get… Continue reading Embryo Cells Set Patterns for Growth by Pushing and Pulling

Conserved physical quantities should not vary, or appear to do so, based on how we choose to label things. That was the situation that Chen, Wang, Wang, and Yau hoped to rectify. Starting with their 2015 definition of quasilocal angular momentum, they computed the angular momentum contained within a region of finite radius. Then they… Continue reading Mass and Angular Momentum, Left Ambiguous by Einstein, Get Defined

In November 2020, the GOP tweeted a C-SPAN clip of Trump campaign lawyer Sidney Powell saying, “President Trump won by a landslide. We are going to prove it.” It was retweeted over 22,000 times and still hasn’t been deleted. Powell’s claim, of course, was not true. Biden officially won the election. Currently the Select Committee… Continue reading Don’t Give Up on Facts

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,… Continue reading How Do Mathematicians Know Their Proofs Are Correct?

In 1850, Thomas Penyngton Kirkman, a mathematician when he wasn’t fulfilling his main responsibility as a vicar in the Church of England, described his “schoolgirl problem”: “Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that no two shall walk twice… Continue reading Hypergraphs Reveal Solution to 50-Year-Old Problem

President Biden used his first State of the Union address to reset his administration after a year of inflation and crises at home and abroad that has left him with nearly record-low approval ratings. But Biden did little to restart his stalled climate agenda. He spoke only briefly about climate change—talking about it roughly as… Continue reading What Biden Said—and Didn’t Say—on Climate during the State of the Union

Explore A gulp of air, a kick of flippers, and the elephant seal dives. Sunlight slants through the Southern Ocean’s melting roof of sea-ice, its solid dome shattered by the arrival of Antarctic summer. The seal—Mirounga, we’ll call her—descends many times each day to snatch fish and squid in her toothy jaws; she spends 90… Continue reading What Oceanographers Can Learn From Their Animal Colleagues