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Back in 1971, the late physicist Stephen Hawking made an intriguing prediction: The total surface area of a black hole cannot decrease, only increase or remain stable. So if two black holes combine, ...

Researchers celebrate 10th anniversary of gravitational wave discovery, announce verification of a Hawking theorem. Two black holes spiral together and violently merge in this simulation of an event ...

Abstract: Chebyshev polynomials are employed in various applications, such as cryptography and pseudorandom numbers. The sequences generated by iterating Chebyshev polynomials over finite sets should ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

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 ...

Imagine this: you’re in the middle of an important project, juggling deadlines, and collaborating with a team scattered across time zones. Suddenly, your computer crashes, and hours of work vanish in ...

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 ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

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 ...