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Mathematical induction
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers. The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science. Indeed, the validity of mathematical induction is logically equivalent to the well-ordering principle.
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Computers & Math News
March 16, 2026
Mar. 15, 2026 Artificial intelligence is often portrayed as a tool that replaces human work, but new research from Swansea University suggests a far more exciting role: creative collaborator. In a large study with more than 800 participants designing virtual ...
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Mar. 5, 2026 Researchers at Cornell University have developed a powerful imaging technique that reveals atomic scale defects inside computer chips for the first time. Using an advanced electron microscopy method, the team mapped the exact positions of atoms ...
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Mar. 4, 2026 Scientists at the University of Tokyo have captured something never seen before: a frame-by-frame view of how electron spins flip inside an antiferromagnet, a material once thought to be magnetically “invisible.” By firing ultrafast electrical ...
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Mar. 4, 2026 Researchers at Kobe University have developed an AI system that can detect acromegaly, a rare hormone disorder, by analyzing photos of the back of the hand and a clenched fist. The disease often develops slowly and can take years to diagnose, even ...
Mar. 3, 2026 Researchers at the University of Basel and the ETH in Zurich have succeeded in changing the polarity of a special ferromagnet using a laser beam. In the future, this method could be used to create adaptable electronic circuits with ...
Mar. 2, 2026 As millions turn to ChatGPT and other AI chatbots for therapy-style advice, new research from Brown University raises a serious red flag: even when instructed to act like trained therapists, these systems routinely break core ethical standards of ...
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Mar. 1, 2026 Scientists have pulled off a feat long considered out of reach: getting light to mimic the famous quantum Hall effect. In their experiment, photons drift sideways in perfectly defined, quantized steps—just like electrons do in powerful magnetic ...
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Feb. 26, 2026 Researchers have discovered new ways to shape quantum light, creating high-dimensional states that can carry much more information per photon. Using advanced tools like on-chip photonics and ...
Feb. 25, 2026 Quantum computers need special materials called topological superconductors—but they’ve been notoriously difficult to create. Researchers have now shown they can trigger this exotic state by ...
Feb. 24, 2026 CU Boulder researchers have designed microscopic “racetracks” that trap and amplify light with exceptional efficiency. By using smooth curves inspired by highway engineering, they reduced energy ...
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Feb. 21, 2026 Researchers tested whether generative AI could handle complex medical datasets as well as human experts. In some cases, the AI matched or outperformed teams that had spent months building prediction ...
Feb. 20, 2026 Qubits, the heart of quantum computers, can change performance in fractions of a second — but until now, scientists couldn’t see it happening. Researchers at NBI have built a real-time monitoring ...
Feb. 19, 2026 Scientists at the University of New Hampshire have unleashed artificial intelligence to dramatically speed up the hunt for next-generation magnetic materials. By building a massive, searchable ...
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