How Tadayuki Watanabe Disproved a Major Conjecture About Spheres | Quanta Magazine
In a burst of work, mathematicians have moved closer to understanding just how many ways there are of contorting a simple sphere so that, in the end, it still resembles itself. Much of the progress comes from results by Tadayuki Watanabe at Kyoto University. Over the last several years, he has figured out how to adapt a powerful technique for the broader purpose of studying spheres of any number o
Eternal Change for No Energy: A Time Crystal Finally Made Real | Quanta Magazine
In a preprint posted online Thursday night, researchers at Google in collaboration with physicists at Stanford, Princeton and other universities say that they have used Google’s quantum computer to demonstrate a genuine “time crystal.” In addition, a separate research group claimed earlier this month to have created a time crystal in a diamond. A novel phase of matter that physicists have strived
The ‘Useless’ Perspective That Transformed Mathematics
When representation theory emerged in the late 19th century, many mathematicians questioned its worth. In 1897, the English mathematician William Burnside wrote that he doubted that this unorthodox perspective would yield any new results at all. “Basically what [Burnside was] saying is that representation theory is useless,” said Geordie Williamson of the University of Sydney in a 2015 lecture. Mo
‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem
When Andrew Wiles proved Fermat’s Last Theorem in the early 1990s, his proof was hailed as a monumental step forward not just for mathematicians but for all of humanity. The theorem is simplicity itself — it posits that xn + yn = zn has no positive whole-number solutions when n is greater than 2. Yet this simple claim tantalized legions of would-be provers for more than 350 years, ever since the F
Why Do Matter Particles Come in Threes? A Physics Titan Weighs In | Quanta Magazine
The universe has cooked up all sorts of bizarre and beautiful forms of matter, from blazing stars to purring cats, out of just three basic ingredients. Electrons and two types of quarks, dubbed “up” and “down,” mix in various ways to produce every atom in existence. But puzzlingly, this family of matter particles — the up quark, down quark and electron — is not the only one. Physicists have discov
A New Approach to Multiplication Opens the Door to Better Quantum Computers | Quanta Magazine
When I was 9, my family got a new computer. It was better than our old computer in every way save one: It couldn’t run my favorite racing game. What’s the point of a fancy new computer, I remember thinking, if it can’t run the program I care about most? A similar issue applies to quantum computers. In theory, they can do anything that a classical computer can. In practice, however, the quantumness
Milestone Experiment Proves Quantum Communication Really Is Faster | Quanta Magazine
Quantum computers are still a dream, but the era of quantum communication is here. A new experiment out of Paris has demonstrated, for the first time, that quantum communication is superior to classical ways of transmitting information. “We are the first to show a quantum advantage for transmitted information that two parties have to share to perform a useful task,” said Eleni Diamanti, an electri
Tadashi Tokieda Collects Math and Physics Surprises | Quanta Magazine
Tadashi Tokieda lives in a world in which ordinary objects do extraordinary things. Jars of rice refuse to roll down ramps. Strips of paper slip past solid obstacles. Balls swirling inside a bowl switch direction when more balls join them. Yet Tokieda’s world is none other than our own. His public mathematics lectures could easily be mistaken for magic shows, but there’s no sleight of hand, no hid
Neutral Theory of Evolution Challenged by Evidence for DNA Selection | Quanta Magazine
When Charles Darwin articulated his theory of evolution by natural selection in On the Origin of Species in 1859, he focused on adaptations — the changes that enable organisms to survive in new or changing environments. Selection for favorable adaptations, he suggested, allowed ancient ancestral forms to gradually diversify into countless species. That concept was so powerful that we might assume
Graduate Student Solves Quantum Verification Problem | Quanta Magazine
Now, after eight years of graduate school, Mahadev has succeeded. She has come up with an interactive protocol by which users with no quantum powers of their own can nevertheless employ cryptography to put a harness on a quantum computer and drive it wherever they want, with the certainty that the quantum computer is following their orders. Mahadev’s approach, Vazirani said, gives the user “levera
Math Titans Clash Over Epic Proof of the ABC Conjecture | WIRED
In a report posted online today, Peter Scholze of the University of Bonn and Jakob Stix of Goethe University Frankfurt describe what Stix calls a “serious, unfixable gap” within a mammoth series of papers by Shinichi Mochizuki, a mathematician at Kyoto University who is renowned for his brilliance. Posted online in 2012, Mochizuki’s papers supposedly prove the abc conjecture, one of the most far-r
A Short Guide to Hard Problems | Quanta Magazine
How fundamentally difficult is a problem? That’s the basic task of computer scientists who hope to sort problems into what are called complexity classes. These are groups that contain all the computational problems that require less than some fixed amount of a computational resource — something like time or memory. Take a toy example featuring a large number such as 123,456,789,001. One might ask:
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New Codes Could Make Quantum Computing 10 Times More Efficient | Quanta Magazine
Physicists Create a Holographic Wormhole Using a Quantum Computer
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