Researchers have solved a problem related to the quantum Hall effect. It’s the first on a wish list of open math problems to be solved.
Category: mathematics – Page 174
To Test Einstein’s Equations, Poke a Black Hole
Researchers make significant progress toward proving a critical mathematical test of the theory of general relativity.
- By Kevin Hartnett, Quanta Magazine on August 27, 2018
Katherine Johnson, who hand-crunched the numbers for America’s first manned space flight, is 100 today
Black women, especially, played a crucial role in the pool, providing mathematical data for NASA’s first successful space missions, including Alan Shepherd’s 1961 mission and John Glenn’s pioneering orbital spaceflight.
How 1 man’s brain injury turned him into a math savant
Jason Padgett grew up struggling in school — until one night in 2002 when he was attacked in a bar and everything changed. Padgett said after the incident, he was using areas of the brain he didn’t previously have access to; he experienced choppy vision, was drawing intricate shapes and was seeing complex mathematical objects everywhere. Dr. Darold Treffert, a world renowned expert on savants, later diagnosed Padgett with acquired savant syndrome, which explained Padgett’s new skills. Padgett joins Megyn Kelly TODAY to share his story.
Researchers suggest phonons may have mass and perhaps negative gravity
A trio of physicists with Columbia University is making waves with a new theory about phonons—they suggest they might have negative mass, and because of that, have negative gravity. Angelo Esposito, Rafael Krichevsky and Alberto Nicolis have written a paper to support their theory, including the math, and have uploaded it to the xrXiv preprint server.
Most theories depict sound waves as more of a collective event than as physical things. They are seen as the movement of molecules bumping against each other like balls on a pool table—the energy of one ball knocking the next, and so on—any motion in one direction is offset by motion in the opposite direction. In such a model, sound has no mass, and thus cannot be impacted by gravity. But there may be more to the story. In their paper, the researchers suggest that the current theory does not fully explain everything that has been observed.
In recent years, physicists have come up with a word to describe the behavior of sound waves at a very small scale—the phonon. It describes the way sound vibrations cause complicated interactions with molecules, which allows the sound to propagate. The term has been useful because it allows for applying principles to sound that have previously been applied to actual particles. But no one has suggested that they actually are particles, which means they should not have mass. In this new effort, the researchers suggest the phonon could have negative mass, and because of that, could also have negative gravity.
Weird circles in the sky may be signs of a universe before ours
By Chelsea Whyte
Swirling patterns in the sky may be signs of black holes that survived the destruction of a universe before the big bang.
“What we claim we’re seeing is the final remnant after a black hole has evaporated away in the previous aeon,” says Roger Penrose, a mathematical physicist at the University of Oxford.
Star Wars Math
This may be the nerdiest thing I’ve ever seen and I love it.
The Peculiar Math That Could Underlie the Laws of Nature
New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.”
This 3D-printed AI construct analyzes
Machine learning is everywhere these days, but it’s usually more or less invisible: it sits in the background, optimizing audio or picking out faces in images. But this new system is not only visible, but physical: it performs AI-type analysis not by crunching numbers, but by bending light. It’s weird and unique, but counter-intuitively, it’s an excellent demonstration of how deceptively simple these “artificial intelligence” systems are.
Machine learning systems, which we frequently refer to as a form of artificial intelligence, at their heart are just a series of calculations made on a set of data, each building on the last or feeding back into a loop. The calculations themselves aren’t particularly complex — though they aren’t the kind of math you’d want to do with a pen and paper. Ultimately all that simple math produces a probability that the data going in is a match for various patterns it has “learned” to recognize.
The thing is, though, that once these “layers” have been “trained” and the math finalized, in many ways it’s performing the same calculations over and over again. Usually that just means it can be optimized and won’t take up that much space or CPU power. But researchers from UCLA show that it can literally be solidified, the layers themselves actual 3D-printed layers of transparent material, imprinted with complex diffraction patterns that do to light going through them what the math would have done to numbers.
