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Category: mathematics – Page 85

Still, Larsen’s most recent obsession felt different, “longer and more intense than most of his other projects,” she said. For more than a year and a half, Larsen couldn’t stop thinking about a certain math problem.

Then, in November 2021, Granville opened up an email from Larsen, then 17 years old and in his senior year of high school. A paper was attached — and to Granville’s surprise, it looked correct. “It wasn’t the easiest read ever,” he said. “But when I read it, it was quite clear that he wasn’t messing around. He had brilliant ideas.”

Pomerance, who read a later version of the work, agreed. “His proof is really quite advanced,” he said. “It would be a paper that any mathematician would be really proud to have written. And here’s a high school kid writing it.”

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Just over a decade ago, physicist and Nobel laureate Frank Wilczek from MIT wrote a paper musing about the potential properties of a theoretical object he called quantum time crystal. To the surprise of many, over the last few years, those time crystals have been found aplenty both in specific lab experiments and inside common things like children’s toys.

As is often the case, the exact nature of these objects is not widely understood. So let’s tackle this question together: what is a time crystal? First and foremost, let’s define what a crystal is. Let’s consider empty space like a blank sheet of paper extending as far as the eye can see. There is no special point to it because every point is the same.

That’s where the translational symmetry comes in. No point is special – but now let’s imagine that the paper is graphed, like sheets you might have used in math lessons. Now you will have a lot of empty space, but every little while you have lines and corners, etc. That is a repeating regular structure. In your regular crystal, from diamonds to snowflakes, their atoms are organized in repeating patterns like that.

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Researchers at DeepMind in London have shown that artificial intelligence (AI) can find shortcuts in a fundamental type of mathematical calculation, by turning the problem into a game and then leveraging the machine-learning techniques that another of the company’s AIs used to beat human players in games such as Go and chess.

The AI discovered algorithms that break decades-old records for computational efficiency, and the team’s findings, published on 5 October in Nature1, could open up new paths to faster computing in some fields.

“It is very impressive,” says Martina Seidl, a computer scientist at Johannes Kepler University in Linz, Austria. “This work demonstrates the potential of using machine learning for solving hard mathematical problems.”

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Since the discovery of genetics, people have dreamed of being able to correct diseases, select traits in children before birth, and build better human beings. Naturally, many serious technical and ethical questions surround this endeavor. Luckily, tonights’ guest is as good a guide as we could hope to have.

Dr. Steve Hsu is Professor of Theoretical Physics and of Computational Mathematics, Science, and Engineering at Michigan State University. He has done extensive research in the field of computational genomics, and is the founder of several startups.

#geneticengineering #intelligence

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In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is “closed”, returning to its starting point. This possibility was first discovered by Willem Jacob van Stockum in 1937[1] and later confirmed by Kurt Gödel in 1949,[2] who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes.

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