Mathematical physics is a research area focused on formulating and analyzing physical theories using rigorous mathematical structures and methods, and conversely, on developing new mathematics motivated by physical problems. It encompasses the study of quantum mechanics, quantum field theory, statistical mechanics, general relativity, and dynamical systems through functional analysis, operator algebras, differential geometry, probability theory, and partial differential equations. Core topics include spectral theory of Hamiltonians, rigorous renormalization, exactly solvable models, phase transitions, integrable systems, and geometric and topological methods in gauge theories and gravitation, with emphasis on precise definitions, theorems, and proofs underpinning fundamental physical concepts.
Most of us first hear about the irrational number π (pi)—rounded off as 3.14, with an infinite number of decimal digits—in school, where we learn about its use in the context of a circle. More recently, scientists have developed ...
General Physics
Dec 3, 2025
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The geometry of space, where physical laws unfold, may also hold answers to some of the deepest questions in fundamental physics. The very structure of spacetime might underlie every interaction in nature.
General Physics
Nov 10, 2025
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Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve very different scales ...
General Physics
Oct 2, 2025
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The Irish mathematician and physicist William Rowan Hamilton, who was born 220 years ago last month, is famous for carving some mathematical graffiti into Dublin's Broome Bridge in 1843.
Optics & Photonics
Sep 24, 2025
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A University of Queensland researcher has developed a new mathematical model to explain the evolution of the universe which, for the first time, includes collapsing regions of matter and expanding voids.
Astronomy
Aug 19, 2025
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An exact expression for a key process needed in many quantum technologies has been derived by a RIKEN mathematical physicist and a collaborator. This could help to guide advances in quantum technologies.
Quantum Physics
Apr 23, 2025
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How gravity causes a perfectly spherical ball to roll down an inclined plane is part of the elementary school physics canon. But the world is messier than a textbook.
General Physics
Mar 27, 2025
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A fundamental goal of physics is to explain the broadest range of phenomena with the fewest underlying principles. Remarkably, seemingly disparate problems often exhibit identical mathematical descriptions.
Condensed Matter
Mar 5, 2025
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In a new study published in Physical Review D, Professor Ginestra Bianconi, Professor of Applied Mathematics at Queen Mary University of London, proposes a new framework that could revolutionize our understanding of gravity ...
General Physics
Mar 4, 2025
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Laser diodes are semiconductors that generate light and amplify it using repeated reflection or "optical feedback." Once the light has achieved desirable optical gain, laser diodes release it as powerful laser beams.
Optics & Photonics
Feb 11, 2025
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