The central limit theorem states that as the sample size of a random variable increases, the distribution of sample means becomes more and more normal, regardless of the underlying distribution of the population. It is fundamental in probability theory and #statistics . #MathType

The Fermi golden rule describes the transition rate from one eigenstate of a quantum system to a group of eigenstates in a continuum, as the consequence of a weak perturbation.

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Stefan Banach formalized the notion of complete normed space, now known as Banach space. Amongst theorems that bear his name is the Fixed Point Theorem, fundamental in #FunctionalAnalysis and #DifferentialEquations .

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A parallelepiped is a three-dimensional figure that consists of six parallelograms. How would you get to this formula?

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In geometry, an epicycloid is a plane curve defined as the path of a point P on the circumference of a circle (epicycle) that rolls around a fixed circle without slipping.

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Here’s a model of an orbit equation for a two-body system that defines the path of the orbiting body.

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Trott Constants are numbers whose decimal expansion is the same as their continued fraction expansion. Very little is known about them. Aren’t they fascinating?

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The continuity equation, also called the transport equation, describes the transport of some quantity, and represents stronger, local forms of conservation laws.

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Karol Borsuk is the inventor of #ShapeTheory . One of his most famous theorems is the Borsuk-Ulam Theorem, which allows to make claims such as that there are 2 points on Earth with exactly the same temperature and pressure.

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Null space is an essential tool in linear algebra, as it provides insight into the properties of a linear transformation. For example, if the kernel of a linear transformation is trivial, then the transformation is injective.

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Have you heard of Proizvolov's identity? It is an identity concerning sums of differences of positive integers.

If you're feeling brave, try to demonstrate it!

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A topological space is a geometrical space where we can define the notion of closeness but where there's not necessarily a distance to measure it. Topological spaces are a fundamental concept used in every modern mathematics branch.

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Bayes' Theorem is a mathematical formula used in probability theory and #statistics to calculate conditional probability. This theorem helps to determine the probability of an event, considering prior knowledge of conditions that may be linked to the event.

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Tijdeman's theorem states that only a finite number of consecutive powers can exist. Do you know how it was proved?

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Twin primes are pairs of primes that differ only by 2. It remains an open problem to prove whether there exists an infinite number of them. What are your thoughts?

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Werner Karl Heisenberg stated that 'The more precise the measurement of position, the more imprecise the measurement of momentum, and vice versa'.

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Newton’s method is a root-finding #algorithm that produces better approximations to the roots of a real-valued function f successively. The most basic version is a single-variable function f, defined for a real variable x and with derivative f’.

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The Dirac Equation describes all spin-½ massive particles and also implies the existence of Antimatter. Paul Dirac predicted the possibility of antielectrons in 1928 with this equation, but it wasn't until 1932 that Carl D. Anderson discovered positrons.

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Rolle's theorem states that for a differentiable function with real values, if it takes the same value at two distinct points, then there exists at least one point between them where the first derivative is zero.

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By utilizing this algorithm, we can construct a set of orthonormal vectors from a set of linearly independent vectors that span the same space.

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