Starting at a corner, could you walk around the surface of this Platonic solid without crossing other corners? To get the answer, you need an 81-holed doughnut.

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Shape memory alloys and a kind of plastic crystal chill quickly under force or pressure. They could lead to eco-friendly fridges and air conditioners.

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By translating Ott-Heinrich Keller’s conjecture into a computer-friendly search, researchers confirmed a conjecture about seven-dimensional space.

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Two mathematicians have proved the first leg of the Hungarian scholar's all-time favorite problem about number patterns.

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New computer simulations model an alternate way of thinking about the cosmos: as a cyclic universe that has no beginning or end.

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A new model of photosynthesis points to an evolutionary principle governing light-harvesting organisms that might apply throughout the universe.

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His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.

It’s become increasingly clear as we reach its limits that deep learning – a specific subset of AI technology – isn’t going to magically lead to human-level artificial intelligence.Curiosity and exploration are the two key components of the human intellect that deep learning simply doesn’t provide.In a recent article in Quanta Magazine, writer Matthew Hutson describes the work of computer scientist Kenneth Stanley, who is currently working at Uber’s AI lab.Stanley’s pioneering work in the field of “neuroevolution” has paved the way for a new artificial intelligence paradigm that eschews traditional objective-based training models in favor of AI models that have no purpose but to explore and be creative.Instead of hard-coding the rules of reasoning, or having computers learn to score highly on specific performance metrics, they argue, we must let a population of solutions blossom.They may discover an indirect path, a set of steppingstones, and wind up walking and talking better than if they’d sought those skills directly.

In late August, paleontologists reported finding the fossil of a flattened turtle shell that “was possibly trodden on” by a dinosaur, whose footprints spanned the rock layer directly above.The rare discovery of correlated fossils potentially traces two bygone species to the same time and place.Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.Like fossils, astronomical objects are not randomly strewn throughout space.“Paleontologists infer the existence of dinosaurs to give a rational accounting of strange patterns of bones,” said Nima Arkani-Hamed, a physicist and cosmologist at the Institute for Advanced Study in Princeton, New Jersey.“We look at patterns in space today, and we infer a cosmological history in order to explain them.”

Despite their abundance, however, neutrinos are hard to catch and inspect, as they interact with matter only very weakly.Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.“The fact that they’re ubiquitous, yet we don’t even know what they weigh, is kind of crazy,” said Deborah Harris, a physicist at the Fermi National Accelerator Laboratory near Chicago and York University in Toronto.And in September, after 18 years of planning, building and calibrating, the Karlsruhe Tritium Neutrino (KATRIN) experiment in southwestern Germany announced its first results: It found that the neutrino can’t weigh more than 1.1 electron-volts (eV), or about one-five-hundred-thousandth the mass of the electron.This initial estimate, from only one month’s worth of data, improves on previous measurements using similar techniques that placed the upper limit on the neutrino mass at 2 eV.The neutrino is the only known particle whose mass remains a mystery.

A recent paper from Google’s quantum computing lab announced that the company had achieved quantum supremacy.In 2012, I proposed the term “quantum supremacy” to describe the point where quantum computers can do things that classical computers can’t, regardless of whether those tasks are useful.Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.The words “quantum supremacy”—if not the concept—proved to be controversial for two reasons.One alternative is “quantum advantage,” which is also now widely used.The recent Google paper illustrates the point.

Humans today are mosaics, our genomes rich tapestries of interwoven ancestries.With every fossil discovered, with every DNA analysis performed, the story gets more complex: We, the sole survivors of the genus Homo, harbor genetic fragments from other closely related but long-extinct lineages.Modern humans are the products of a sprawling history of shifts and dispersals, separations and reunions—a history characterized by far more diversity, movement and mixture than seemed imaginable a mere decade ago.Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.But it’s one thing to say that Neanderthals interbred with the ancestors of modern Europeans, or that the recently discovered Denisovans interbred with some older mystery group, or that they all interbred with each other.“We’ve got this picture where these events are happening all over the place,” said Aylwyn Scally, an evolutionary geneticist at the University of Cambridge.

In September 16, 2011, an anime fan posted a math question to the online bulletin board 4chan about the cult classic television series The Melancholy of Haruhi Suzumiya.Fans were arguing online about the best order to watch the episodes, and the 4chan poster wondered: If viewers wanted to see the series in every possible order, what is the shortest list of episodes they’d have to watch?Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.In less than an hour, an anonymous person offered an answer — not a complete solution, but a lower bound on the number of episodes required.The argument, which covered series with any number of episodes, showed that for the 14-episode first season of Haruhi, viewers would have to watch at least 93,884,313,611 episodes to see all possible orderings.But in a plot twist last month, the Australian science fiction novelist Greg Egan proved a new upper bound on the number of episodes required.

The dusty leftovers started to coalesce in some spots, forming larger rocky objects.Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.Something similar happened around countless other suns, the vast majority of which are thought to have planets.Astronomers are trying to figure out how exactly the planetary formation process happens and how long it takes, partly by studying how much material exists in planets now, and how much there would need to have been in the disks of dust from which they were forged.The authors behind the new paper set out to compare the masses of hundreds of exoplanets and protoplanetary disks, where baby planets are being forged.The best telescope for studying the dust and gas in a protoplanetary disk is the Atacama Large Millimeter/submillimeter Array (ALMA), a flock of radio antennas in Chile’s high desert.