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Open Access
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Article
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Universality in long-distance geometry and quantum complexity
Many different homogeneous metrics on Lie groups, which may have markedly different short-distance properties, are shown to exhibit nearly identical distance functions at long distances, suggesting a large universality class of definitions of quantum complexity.
- Adam R. Brown
- , Michael H. Freedman
- & Leonard Susskind
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Solid-body trajectoids shaped to roll along desired pathways
An algorithm is developed to design a shape, a trajectoid, that can trace any given infinite periodic trajectory when rolling down a slope, finding unexpected implications for quantum and classical optics.
- Yaroslav I. Sobolev
- , Ruoyu Dong
- & Bartosz A. Grzybowski
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Article
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Advancing mathematics by guiding human intuition with AI
A framework through which machine learning can guide mathematicians in discovering new conjectures and theorems is presented and shown to yield mathematical insight on important open problems in different areas of pure mathematics.
- Alex Davies
- , Petar Veličković
- & Pushmeet Kohli
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News |
Mathematicians come closer to solving Goldbach's weak conjecture
A centuries-old conjecture is nearing its solution.
- Davide Castelvecci
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Books & Arts |
Books in brief
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Books & Arts |
Mathematics: Drowning by numbers
Stefan Michalowski and Georgia Smith find that a mix of unexplained equations and thunderclaps doesn't add up.
- Stefan Michalowski
- & Georgia Smith
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News & Views |
50 & 100 years ago
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The unplanned impact of mathematics
Peter Rowlett introduces seven little-known tales illustrating that theoretical work may lead to practical applications, but it can't be forced and it can take centuries.
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Books & Arts |
Books in brief
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Maths polymath scoops Abel award
John Milnor wins 'Nobel of maths' for his manifold works.
- Philip Ball
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Books & Arts |
The crop circle evolves
A growing underground art movement combines mathematics, technology, stalks and whimsy. Richard Taylor looks forward to a bumper batch of intricate crop patterns this summer.
- Richard Taylor
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Books & Arts |
Beyond the image of the tragic genius
Our stereotypical view of mathematicians shifted during the Romantic era from worldly scholar to tortured soul, explains Jascha Hoffman.
- Jascha Hoffman
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Maths behind Internet encryption wins top award
Abel prize awarded to number theorist John Tate.
- Zeeya Merali
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Mathematical discoveries from program search with large language models
Genius who shuns the limelight