3+ hour, 4+ min ago   (1468+ words) For the first time, mathematicians have found an example of a compact doughnutlike surface (as seen above) that shares its local geometric information with another surface, despite having a completely different global structure. Imagine if our skies were always filled…...

4+ day, 4+ hour ago   (452+ words) In data storage, sometimes it's best to embrace a bit of disorder. Just as there's no single best way to organize your bookshelf, there's no one-size-fits-all solution to storing information. Of course, this bin system comes with its own problems....

1+ week, 4+ day ago   (1117+ words) In these realistic theories, "a lot of people believe that there are singularities, but that they are unstable, so we never see them," said Charlie Fefferman, a mathematician at Princeton University who formulated the million-dollar Navier-Stokes challenge. "The idea of…...

1+ mon, 2+ day ago   (483+ words) Mathematics is, at its core, an art. Like painters, musicians or writers, mathematicians create and explore new worlds. They test, and then push past, the limits of their imagination. They engage with thousands of years of history, with concepts and…...

1+ mon, 4+ day ago   (114+ words) Explore the year's most surprising computational revelations, including a new fundamental relationship between time and space, an undergraduate who overthrew a 40-year-old conjecture, and the unexpectedly effortless triggers that can turn AI evil. The post The Year in Computer Science…...

1+ mon, 1+ week ago   (1747+ words) In August, a team of mathematicians posted a paper claiming to solve a major problem in algebraic geometry " using entirely alien techniques. It instantly captivated the field, stoking excitement in some mathematicians and skepticism in others. But after sorting just…...

1+ mon, 2+ week ago   (610+ words) The cognitive neuroscientist Ev Fedorenko has identified a "language network" in the brain that stores the mappings between words and their meanings. Even in a world where large language models (LLMs) and AI chatbots are commonplace, it can be hard…...

1+ mon, 2+ week ago   (883+ words) In mathematics, ubiquitous objects called groups display nearly magical powers. Though they're defined by just a few rules, groups help illuminate an astonishing range of mysteries. They can tell you which polynomial equations are solvable, for instance, or how atoms…...

1+ mon, 2+ week ago   (447+ words) In reverse mathematics, researchers replace axioms, the foundations of mathematical systems, with the theorems they want to prove. Son of Alan for Quanta Magazine For over 50 years, researchers in the field of computational complexity theory have sought to turn intuitive…...

1+ mon, 4+ week ago   (1774+ words) All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don't need to think about it when they're solving their problems. They can…...