Abstract: In this paper, we propose a homogenized Chebyshev-Arnold map (HCAM) by homogenizing the linear coupling of Chebyshev map and Arnold map. The proposed HCAM has complex dynamical behaviors and ...
Large language models (LLMs) have astounded the world with their capabilities, yet they remain plagued by unpredictability and hallucinations – confidently outputting incorrect information. In ...
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This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...
The original version of this story appeared in Quanta Magazine. In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last ...
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The Obviously True Theorem No One Can Prove
This deceptively simple math problem has stumped mathematicians for almost 300 years! Donald Trump floats move to new state New Mexico fire victims await payments. A FEMA director got his. Disney ...
Emmy Noether was a mathematician who discovered perhaps the most profound idea in contemporary physics. Noether’s theorem, which she formulated in 1915, says that symmetries in the universe give rise ...
Emmy Noether showed that fundamental physical laws are just a consequence of simple symmetries. A century later, her insights continue to shape physics. In the fall of 1915, the foundations of physics ...
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