3+ hour, 26+ min ago  (44+ words) Intuition breaks down once we're dealing with the endless. To begin with: Some infinities are bigger than others. The post How Can Infinity Come in Many Sizes? first appeared on Quanta Magazine Use your social network Forgot your password ? Enter…...

6+ day, 6+ hour ago  (736+ words) Traditional complexity theory can't accommodate problems with quantum inputs and outputs. Henry Yuen wants to build a new theory that can. Researchers in the field of computational complexity theory study why some of these transformations are harder to implement than…...

2+ week, 6+ hour ago  (734+ words) A machine learning algorithm created maps of the mouse brain with 1,300 subregions by predicting how brain cell types tend to group together, like buildings in a neighborhood. Irena Gajic for'Quanta Magazine Real estate agents will tell you that a home's…...

2+ week, 3+ day ago  (1135+ words) To study the flow of air around an airplane's wing, the distribution of stress on a bridge, or various other situations, researchers use elliptic partial differential equations. These equations are notoriously difficult to understand. The trajectory of a storm, the…...

3+ week, 5+ day ago  (1272+ words) Two centuries ago, Joseph Fourier gave mathematicians a magical technique. He conjectured that it's possible to write almost any function as a sum of simple waves, a trick now called the Fourier transform. These days, the Fourier transform is used…...

1+ mon, 3+ day 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…...

1+ mon, 1+ week 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+ mon, 2+ week 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…...

2+ mon, 5+ 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…...

2+ mon, 1+ week 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…...