Mathematicians have proved the geometric Langlands conjecture, a key component of one of the most sweeping paradigms in modern mathematics. The proof involves more than 800 pages spread over five papers. https://lnkd.in/ecm6W9Bg Figurative gardens of mathematical objects called eigensheaves played an important role in the recent proof of the geometric Langlands conjecture. Our new explainer details what makes sheaves such a useful tool: https://lnkd.in/eRZhhBF9
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Big ideas in science and math. Because you want to know more.
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Quanta Magazine’s goal is to illuminate basic science and math research through public service journalism. Each article braids the complexities of science with the malleable art of storytelling and is meticulously reported, edited and fact-checked. Launched and funded by the Simons Foundation, Quanta is editorially independent — our articles do not reflect or represent the views of the foundation.
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The microbiologist Bernhard Tschitschko was part of a team of researchers searching for the ocean’s missing nitrogen producers. They discovered a pair of microbes that work together to create the vital nutrient. https://lnkd.in/eDQG5eg5
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Computer science, cognitive science and linguistics share common ground: the quest to understand intelligence. As AI becomes more apparently human-like, it is essential that these fields talk to each other. Listen to “The Joy of Why” with co-host Steven Strogatz: https://lnkd.in/eiWqf-hq
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If you had the chance to manufacture your own vital nutrient by taking on a pet, how could you resist? https://lnkd.in/eDQG5eg5
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Deep in an underground lab, a Soviet-American experiment studying solar neutrinos found that the particles were captured by gallium atoms less often than expected. 30 years later, physicists are still scratching their heads. What could possibly account for such a discrepancy? https://lnkd.in/esTY-9Vg
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The Riemann hypothesis has tantalized mathematicians for 150 years. Unable to prove it directly, mathematicians have shown that they could cap the number of exceptions to it. “It’s a sensational result,” said Henryk Iwaniec. “It’s very, very, very hard. But it’s a gem.” https://lnkd.in/effxbmwf
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The cubes that chill iced teas and Aperol spritzes on a hot summer day may not seem particularly mysterious. You learned the basics in school: Ice is made of H2O molecules, each consisting of a pair of hydrogen atoms flanking an oxygen. What else is there to know? A lot, as it turns out.
The Many Mysteries of Ice
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Physicists have no clue what’s causing the gallium anomaly, which leaves them in an uncomfortable spot. Are they just missing some error? Or, could it point to a new type of neutrino — one that might also help to explain dark matter? https://lnkd.in/esTY-9Vg
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