According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.

According to (), the first historical mention of the statement of this theorem appears in ().

According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

According to the theorem, it is possible to expand any power of x + y into a sum of the form

According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time.

According to the theorem, within every sufficiently powerful logical system ( such as Principia ), there exists a statement G that essentially reads, " The statement G cannot be proved.

* According to a theorem of Nikolay Nikolov and Dan Segal, in any topologically finitely-generated profinite group ( that is, a profinite group that has a dense finitely-generated subgroup ) the subgroups of finite index are open.

According to the spin-statistics theorem, particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states ; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics.

According to Rice's theorem, if there is at least one computable function in a particular class C of computable functions and another computable function not in C then the problem of deciding whether a particular program computes a function in C is undecidable.

According to the Rouché – Capelli theorem, the system is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix.

According to the optical Raychaudhuri's theorem, this requires a violation of the averaged null energy condition.

According to the theorem, the reconstructed signal will match the original signal provided that the original signal contains no frequencies at or above this limit.

According to the Nyquist theorem, error-free detection of the line code requires a channel bandwidth of at least the Nyquist rate, which is half the line code pulse rate.

According to Shannon's source coding theorem, the optimal code length for a symbol is − log < sub > b </ sub > P, where b is the number of symbols used to make output codes and P is the probability of the input symbol.

According to the CPT theorem of particle physics, antihydrogen atoms should have many of the characteristics regular hydrogen atoms have ; i. e., they should have the same mass, magnetic moment, and transition frequencies ( see atomic spectroscopy ) between their atomic quantum states.

According to Liouville's theorem, any bounded complex analytic function defined on the whole complex plane is constant.

According to Allen Weiss, in Mirrors of Infinity, this optical effect is a result of the use of the tenth theorem of Euclid ’ s Optics which asserts that “ the most distant parts of planes situated below the eye appear to be the most elevated .” In Fouquet ’ s time, interested parties could cross the canal in a boat, but walking around the canal provides a view of the woods that mark what is no longer the garden and shows the distortion of the grottos previously seen as sculptural.

According to the correspondence principle and Ehrenfest's theorem as a system becomes larger or more massive ( action >> Planck's constant ) the classical dynamics tends to emerge, with some exceptions, such as superfluidity.

According to the Kutta – Joukowski theorem, lift is the product of circulation, airspeed, and air density.

According to the Shannon – Hartley theorem, the channel capacity of a properly-encoded signal is proportional to the bandwidth of the channel and the logarithm of the signal-to-noise ratio ( SNR ) ( assuming the noise is additive white Gaussian noise ).

According to Ptolemy's second theorem,

According to the inverse function theorem, the matrix inverse of the Jacobian matrix of an invertible function is the Jacobian matrix of the inverse function.

According to one leading historian of statistics, he may have been the earliest discoverer of Bayes theorem.

According to general relativity, objects in a gravitational field behave similarly to objects within an accelerating enclosure.

According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space.

According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular Schwarzschild black hole.

According to this model, the two stars in a binary slowly spiral towards each other due to the release of energy via gravitational radiation until the neutron stars suddenly rip each other apart due to tidal forces and collapse into a single black hole.

According to general relativity, mass " warps " space – time to create gravitational fields and therefore bend light as a result.

According to general relativity, the conservation laws of linear momentum, energy and angular momentum are only exactly true globally when expressed in terms of sum of the stress – energy tensor ( non-gravitational stress – energy ) and Landau – Lifshitz stress – energy – momentum pseudotensor ( gravitational stress – energy ).

According to Rusty Schweickart, the gravitational tractor method is also controversial because during the process of changing an asteroid's trajectory the point on Earth where it could most likely hit would be slowly shifted across different countries.

According to Gauss, who first described it, it is the " mathematical figure of the Earth ", a smooth but highly irregular surface that corresponds not to the actual surface of the Earth's crust, but to a surface which can only be known through extensive gravitational measurements and calculations.

According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular black hole.

According to the currently accepted model of star formation, sometimes referred to as the nebular hypothesis, a star is formed by the gravitational collapse of a pocket of matter within a giant molecular cloud.

According to Newton's law of gravitation, the gravitational force,, acting on a mass, due to a mass which is a distance away, obeys the equation

According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular black hole.

According to general relativity, inertial mass and gravitational mass are the same.

* According to General Relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame.

According to the rules, " This occurs because the ship must escape the gravitational pull of the planet or moon.

According to general relativity, the observed gravitational attraction between masses results from their warping of space and time.

* According to general relativity, light does not travel along straight lines when it propagates in a gravitational field.

According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.

According to general relativity, the various algebraically special Petrov types have some interesting physical interpretations, the classification then sometimes being called the classification of gravitational fields.

According to the Einstein field equation, the gravitational field is locally coupled not only to the distribution of non-gravitational mass-energy, but also to the distribution of momentum and stress ( e. g. pressure, viscous stresses in a perfect fluid ).

According to contemporary models, the scattered disc formed when Kuiper belt objects ( KBOs ) were " scattered " into eccentric and inclined orbits by gravitational interaction with Neptune and the other outer planets.