Mathematics Atlas

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Branches of Mathematic

Mathematical Physics

Mathematical Physics, Biology and Game Theory

Mathematical physics is the development of mathematical methods for use in physics and their application to physical problems. More broadly the field also covers the development of mathematical ideas inspired by physics, sometimes called physical mathematics. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Central Question
What rigorous mathematical structures and methods correctly formalize and solve the equations that describe physical phenomena, and what new mathematics does physics itself suggest? 1
Key Debate
The branch sits at a standards boundary with theoretical physics: physicists commonly reason with heuristic, intuitive arguments toward a physical result, arguments that mathematicians do not consider rigorous until independently proved. 1
Classification
Pure or Applied
Both / Interdisciplinary 1
Connections

Includes

Bell's Theorem, Theorems
Bloch's Theorem (Solid-State Physics), Theorems
Chen-Ning Yang, Mathematicians
Claude-Louis Navier, Mathematicians
CPT Theorem, Theorems
Earnshaw's Theorem, Theorems
Goldstone's Theorem, Theorems
Kochen-Specker Theorem, Theorems
Liouville's Theorem (Hamiltonian Mechanics), Theorems
No-Cloning Theorem, Theorems
Noether's Theorem, Theorems
Source Wikipedia: Noether's Theorem
Robert Mills, Mathematicians

Co-originated Yang-Mills gauge theory, the mathematical framework underlying the standard model of particle physics.

Source Physics Today, Robert L. Mills
Spin-Statistics Theorem, Theorems
Virial Theorem, Theorems
In the Other Atlases
  • Also in Science Atlas: Physics, influenced this subject there.
Sources
1. Mathematical Physics (Wikipedia)
Wikimedia Foundation
  • lead paragraph
    the development of mathematical ideas inspired by physics, known as physical mathematics
  • body text on rigor
    Such arguments are not considered rigorous by mathematicians.
  • Lead section, pure or applied classification
    Mathematical physics is the development of mathematical methods for use in physics and their applications.
View the Source
Wikipedia: Noether's Theorem
Wikimedia FoundationIncludes: Noether's TheoremView the Source
Physics Today, Robert L. Mills
Physics Today, American Institute of PhysicsIncludes: Robert Mills, Career section, Yang-Mills collaboration
Quote, Includes: Robert Mills, Career section, Yang-Mills collaboration
In 1953 as a research associate at Brookhaven National Laboratory, Mills coauthored with Chen Ning Yang a landmark scientific paper in which they proposed the Yang-Mills theory, a generalization of Maxwell's equations that seeks to describe the behavior of elementary particles and explain the electromagnetic and nuclear forces.
View the Source
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