(Phys.org)—Any number can, in theory, be written as the product of prime numbers. For small numbers, this is easy (for example, the prime factors of 12 are 2, 2, and 3), but for large numbers, prime factorization becomes ...
(Phys.org)—If you've read about how modern cosmology may imply that, in an infinite universe, the existence of planets and the life forms that live on them must be repeated an infinite number of times, you may have been ...
Numbers like π, e and φ often turn up in unexpected places in science and mathematics. Pascal's triangle and the Fibonacci sequence also seem inexplicably widespread in nature. Then there's the Riemann zeta function, a ...
General Physics
Jan 19, 2022
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3406
Many ways to approach the Riemann Hypothesis have been proposed during the past 150 years, but none of them have led to conquering the most famous open problem in mathematics. A new paper in the Proceedings of the National ...
Mathematics
May 21, 2019
2
6089
Quantum entanglement may appear to be closer to science fiction than anything in our physical reality. But according to the laws of quantum mechanics—a branch of physics that describes the world at the scale of atoms and ...
Quantum Physics
Feb 7, 2017
71
1545
Fermat's Last Theorem—the idea that a certain simple equation had no solutions— went unsolved for nearly 350 years until Oxford mathematician Andrew Wiles created a proof in 1995. Now, Case Western Reserve University's ...
Mathematics
Mar 4, 2013
11
1
Number theory, the study of the properties of positive integers, is perhaps the purest form of mathematics. At first sight, it may seem far too abstract to apply to the natural world. In fact, the influential American number ...
Mathematics
Aug 1, 2023
6
592
Do you want to know whether a very large integer is a prime number or not? Or if it is a "lucky number"? A new study by SISSA, carried out in collaboration with the University of Trieste and the University of Saint Andrews, ...
Optics & Photonics
Feb 2, 2023
0
125
UVA Health researchers have developed an important new tool to help scientists sort signal from noise as they probe the genetic causes of cancer and other diseases. In addition to advancing research and potentially accelerating ...
Biotechnology
Nov 22, 2022
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64
Discovering the properties of quantum systems that are made of many interacting particles is still a huge challenge. While the underlying mathematical equations have been long known, they are too complex to be solved in practice. ...
Astronomy
Nov 15, 2022
0
449
