Quanta
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Why Everything in the Universe Turns More Complex
A new suggestion that complexity increases over time, not just in living organisms but in the nonliving world, promises to rewrite notions of time and evolution.
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‘Once in a Century’ Proof Settles Math’s Kakeya Conjecture
The deceptively simple Kakeya conjecture has bedeviled mathematicians for 50 years. A new proof of the conjecture in three dimensions illuminates a whole crop of related problems.
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Years After the Early Death of a Math Genius, Her Ideas Gain New Life
A new proof extends the work of the late Maryam Mirzakhani, cementing her legacy as a pioneer of alien mathematical realms.
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The Largest Sofa You Can Move Around a Corner
A new proof reveals the answer to the decades-old “moving sofa” problem. It highlights how even the simplest optimization problems can have counterintuitive answers.
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New Proofs Probe the Limits of Mathematical Truth
By proving a broader version of Hilbert’s famous 10th problem, two groups of mathematicians have expanded the realm of mathematical unknowability.
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Mathematicians Discover New Way for Spheres to ‘Kiss’
A new proof marks the first progress in decades on important cases of the so-called kissing problem. Getting there meant doing away with traditional approaches.
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The Ocean Teems With Networks of Interconnected Bacteria
Nanotube bridge networks grow between the most abundant photosynthetic bacteria in the oceans, suggesting that the world is far more interconnected than anyone realized.
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Quantum Computers Cross Critical Error Threshold
In a first, researchers have shown that adding more “qubits” to a quantum computer can make it more resilient. It’s an essential step on the long road to practical applications.
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Teen Mathematicians Tie Knots Through a Mind-Blowing Fractal
Three high schoolers and their mentor revisited a century-old theorem to prove that all knots can be found in a fractal called the Menger sponge.