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This is a list of mathematical theories. Almgren–Pitts min-max theory. Approximation theory. Arakelov theory. Asymptotic theory. Automata theory. Bass–Serre theory. Bifurcation theory. Braid theory.
- General Relativity
- The Standard Model
- Calculus
- Pythagorean Theorem
- 0.999999999….
- Special Relativity
- Euler's Equation
- Euler-Lagrange Equations and Noether's Theorem
- The Callan-Symanzik Equation
- The Minimal Surface Equation
The equation above was formulated by Einstein as part of his groundbreaking general theory of relativityin 1915. The theory revolutionized how scientists understood gravity by describing the force as a warping of the fabric of space and time. "It is still amazing to me that one such mathematical equation can describe what space-time is all about," ...
Another of physics' reigning theories, the standard modeldescribes the collection of fundamental particles currently thought to make up our universe. The theory can be encapsulated in a main equation called the standard model Lagrangian (named after the 18th-century French mathematician and astronomer Joseph Louis Lagrange), which was chosen by the...
While the first two equations describe particular aspects of our universe, another favorite equation can be applied to all manner of situations. The fundamental theorem of calculus forms the backbone of the mathematical method known as calculus, and links its two main ideas, the concept of the integral and the concept of the derivative. "In simple ...
An "oldie but goodie" equation is the famous Pythagorean theorem, which every beginning geometry student learns. This formula describes how, for any right-angled triangle, the square of the length of the hypotenuse, c, (the longest side of a right triangle) equals the sum of the squares of the lengths of the other two sides (a and b). Thus, a^2 + b...
This simple equation, which states that the quantity 0.999, followed by an infinite string of nines, is equivalent to one, is the favorite of mathematician Steven Strogatz of Cornell University. "I love how simple it is — everyone understands what it says — yet how provocative it is," Strogatz said. "Many people don't believe it could be true. It's...
Einstein makes the list again with his formulas for special relativity, which describes how time and space aren't absolute concepts, but rather are relative depending on the speed of the observer. The equation above shows how time dilates, or slows down, the faster a person is moving in any direction. "The point is it's really very simple," said Bi...
This simple formula encapsulates something pure about the nature of spheres: "It says that if you cut the surface of a sphere up into faces, edges and vertices, and let F be the number of faces, E the number of edges and V the number of vertices, you will always get V – E + F = 2," said Colin Adams, a mathematician at Williams College in Massachuse...
"These are pretty abstract, but amazingly powerful," NYU's Cranmer said. "The cool thing is that this way of thinking about physics has survived some major revolutions in physics, like quantum mechanics, relativity, etc." Here, L stands for the Lagrangian, which is a measure of energy in a physical system, such as springs, or levers or fundamental ...
"The Callan-Symanzik equation is a vital first-principles equation from 1970, essential for describing how naive expectations will fail in a quantum world," said theoretical physicist Matt Strassler of Rutgers University. The equation has numerous applications, including allowing physicists to estimate the mass and size of the proton and neutron, w...
"The minimal surface equation somehow encodes the beautiful soap filmsthat form on wire boundaries when you dip them in soapy water," said mathematician Frank Morgan of Williams College. "The fact that the equation is 'nonlinear,' involving powers and products of derivatives, is the coded mathematical hint for the surprising behavior of soap films....
The main difficulty of the theory of equations was to know when an algebraic equation has an algebraic solution. In this article, we will learn about the theory of equations and examples of solving equations. The following are some important concepts covered under the theory of equations. Linear equations; Simultaneous linear equations
theories [3]. It also clarifies the different notions of an "equational theory" that had been circulating until its publication. Lastly, G. Srour’s The notion of Independence In Categories Of Algebraic Structures, Part II: S-Minimal Extensions takes a non model theory approach to the notion of equations [9]. As such it is the most
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2 days ago · Number theory is the study of properties of the integers. Because of the fundamental nature of the integers in mathematics, and the fundamental nature of mathematics in science, the famous mathematician and physicist Gauss wrote: "Mathematics is the queen of the sciences, and number theory is the queen of mathematics." There are an abundance of simply formulated questions about the ...
Theory of equations. In algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial. The main problem of the theory of equations was to know when an algebraic equation has an algebraic solution. This problem was completely solved in 1830 by Évariste ...
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This is Number theory, a branch of mathematics that explores the properties and relationships of integers. The cool part is that anyone can join in, it is mostly basic operations like multiplication and addition! And along the way we will discover many interesting concepts, surprising relationships, and get to rub shoulders with great thinkers ...
