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Mathematicians Solve Decades-Old Classification Problem By STEVE NADIS August 5, 2021 A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be. READ LATER Eric Nyquist  for Quanta Magazine If you’re conducting a census of all the plants growing in a specific region, rather than tally every single plant, you might decide to organize them by species. Doing this along certain stretches of the Tuscany coast would not be too difficult, said the University of Turin mathematician  Gianluca Paolini , because you’ll mainly find a single plant — maritime pine ( pinus pinaster ). If you were in the Amazon rainforest, by contrast, you’d face a much bigger challenge trying to work out the names and numbers of all the species that have taken root there. Doing so fully would, in all likelihood, be impossible. Mathematicians, in their attempt to make sense of the sprawling landscape of mathematical objec

Mathematicians Prove 2D Version of Quantum Gravity Really Works SERIES MATH MEETS QFT Mathematicians Prove 2D Version of Quantum Gravity Really Works By CHARLIE WOOD June 17, 2021 In three towering papers, a team of mathematicians has worked out the details of Liouville quantum field theory, a two-dimensional model of quantum gravity. 18 READ LATER Olena Shmahalo/Quanta Magazine Alexander Polyakov , a theoretical physicist now at Princeton University, caught a glimpse of the future of quantum theory in 1981. A range of mysteries, from the wiggling of strings to the binding of quarks into protons, demanded a new mathematical tool whose silhouette he could just make out. “There are methods and formulae in science which serve as  master keys  to many apparently different problems,” he wrote in the introduction to a now famous four-page letter in  Physics Letters B . “At the present time we have to develop an art of handling sums over random surfaces.” Polyakov’s proposal prove

The Quantum Internet Will Blow Your Mind. Here’s What It Will Look Like The next generation of the Internet will rely on revolutionary new tech — allowing for unhackable networks and information that travels faster than the speed of light. By  Dan Hurley Oct 4, 2020 4:30 AM (Credit: Jurik Peter/Shutterstock) Newsletter Sign up for our email newsletter for the latest science news SIGN UP   This article appeared in the November 2020 issue of  Discover  magazine as "The Quest for a Quantum Internet."  Subscribe  for more stories like these. Call it the quantum Garden of Eden. Fifty or so miles east of New York City, on the campus of Brookhaven National Laboratory, Eden Figueroa is one of the world’s pioneering gardeners planting the seeds of a quantum internet. Capable of sending enormous amounts of data over vast distances, it would work not just faster than the current internet but faster than the speed of light — instantaneously, in fact, like the teleportation of Mr. Spock a