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Getty Images Two US high schoolers believe they have cracked a mathematical mystery left unproven for centuries. Calcea Johnson and Ne’Kiya Jackson looked at the Pythagorean theorem, foundational to trigonometry. The American Mathematical Society said the teenagers should submit their findings to a journal. Two high school seniors from New Orleans think they have managed to prove a 2,000-year-old theorem that has stumped mathematicians for centuries.

Neurosity’s headset uses electroencephalogram technology, or EEG, to measure brain activity by placing small metal electrodes on a person’s scalp. If the electrodes detect decreased electrical activity in the brain, the Crown plays music and sounds, or pulses vibrations, hoping those actions will help the user focus.

But some developers, it seems, have taken Neurosity’s tech a step further, turning the Crown into a more traditional brain computer interface that can allow users to control a computer using only their mind.

One owner of the gadget claimed they’ve used it to drive a Tesla, moving the electric car short distances by doing some mental math, which signals to the device that the person wearing it is exerting a lot of cognitive effort.

Continue reading “Grimes said she got a brain gadget for her birthday from a company competing with Elon Musk’s Neuralink” »

After half a century, mathematicians succeed in finding an ‘einstein,’ a shape that forms a tiled pattern that never repeats.

A quantum computer in the next decade could crack the encryption our society relies on using Shor’s Algorithm. Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.

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A huge thank you to those who helped us understand this complex field and ensure we told this story accurately — Dr. Lorenz Panny, Prof. Serge Fehr, Dr. Dustin Moody, Prof. Benne de Weger, Prof. Tanja Lange, PhD candidate Jelle Vos, Gorjan Alagic, and Jack Hidary.

Continue reading “How Quantum Computers Break The Internet… Starting Now” »

Philosophy and theology are filled with far more questions than universally compelling answers and evidence.

Just a couple of years earlier, in 1963, New Zealand mathematician Roy Kerr found a solution to Einstein’s equation for a rotating black hole. This was a “game changer for black holes,” Giorgi noted in a public lecture given at the virtual 2022 International Congress of Mathematicians. Rotating black holes were much more realistic astrophysical objects than the non-spinning black holes that Karl Schwarzschild had solved the equations for.

“Physicists really had believed for decades that the black hole region was an artifact of symmetry that was appearing in the mathematical construction of this object but not in the real world,” Giorgi said in the talk. Kerr’s solution helped establish the existence of black holes.

In a nearly 1,000-page paper, Giorgi and colleagues used a type of “proof by contradiction” to show that Kerr black holes that rotate slowly (meaning they have a small angular momentum relative to their mass) are mathematically stable. The technique entails assuming the opposite of the statement to be proved, then discovering an inconsistency. That shows that the assumption is false. The work is currently undergoing peer review. “It’s a long paper, so it’s going to take some time,” Giorgi says.

Argentinian-born mathematician Luis Caffarelli has won the 2023 Abel Prize — one of the most coveted awards in mathematics — for his work on equations that are important for describing physical phenomena, such as how ice melts and fluids flow. He is the first person born in South America to win the award.

Caffarelli’s results “are technically virtuous, covering many different areas of mathematics and its applications”, says a statement by Helge Holden, a mathematician at the Norwegian University of Science and Technology in Trondheim who chairs the Abel Committee.

The winner says receiving the news was an emotional moment, because “it shows that people have some appreciation for me and for my science”.

If you go running over a trail in the woods or a grassy field, there are countless bumps and dips in the terrain, each with the potential to trip you up. But typically, runners manage just fine. It’s a remarkable physical feat that we tend to take for granted. A team of researchers set out to better understand it.

With a specially made running track and mathematical modeling, the lab of Madhusudhan Venkadesan found that when running on uneven terrain, humans mostly rely on the body’s mechanical response for stability rather than consciously plot out their footsteps to find level ground. Further, they found that the runners were just as efficient in their movements and physical exertion as when running on flat ground. The results are published in eLife.

Even without occasional hazards like steep drops, runners must contend with gentler, but still uneven, ground that can be destabilizing. So why aren’t trails typically littered with toppled runners? One possibility is that visual cues allow runners to carefully observe the land to step on mostly level areas. On the other hand, running played a huge role in human evolution, particularly in how it benefited humans in hunting. That means sight cannot be devoted solely to find areas to step on; it’s also needed to watch out for the prey, trees or other obstacles to avoid, and decide which path to take.

Unfortunately for the field of cosmology, there is only one universe. This makes performing experiments in the same way as other scientific fields quite a challenge. But it turns out that the universe and the quantum fields that permeate it are highly analogous to quantum fluids like Bose-Einstein condensates (BECs), at least from a mathematical point of view. These fluids can be the subject of experiments, allowing cosmology to be studied in the lab.

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In a paper published in Nature, researchers at Heidelberg University in Germany have for the first time used a BEC to simulate an expanding universe and certain quantum fields within it. This allows for the study of important cosmological scenarios. Not only is the universe currently expanding, but it is believed that in the first fractions of a second after the Big Bang it underwent a period of extremely rapid expansion known as “inflation.” This process would have expanded the microscopic fluctuations of quantum fields in the early universe to the size of galaxy clusters, seeding the large-scale structure of our universe today.