Kleene's Church – Turing Thesis: A few years later ( 1952 ) Kleene would overtly name, defend, and express the two " theses " and then " identify " them ( show equivalence ) by use of his Theorem XXX:

: Turing's thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i. e. by one of his machines, is equivalent to Church's thesis by Theorem XXX.

The most celebrated single question in the field, the conjecture known as Fermat's Last Theorem, was solved by Andrew Wiles but using tools from algebraic geometry developed during the last century rather than within number theory where the conjecture was originally formulated.

concluded that a certain equation considered by Diophantus had no solutions, and noted without elaboration that he had found " a truly marvelous proof of this proposition ," now referred to as Fermat's Last Theorem.

The 1621 edition of Arithmetica by Bachet gained fame after Pierre de Fermat wrote his famous " Last Theorem " in the margins of his copy:

The identity of is unique by Theorem 1. 4 below.

The inverse of is unique by Theorem 1. 5 below.

Unicity: Suppose satisfies, then by Theorem 1. 8,.

Fine, Do Correlations need to be explained ?, in Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem, edited by Cushing & McMullin ( University of Notre Dame Press, 1986 ).

* Fermat's Last Theorem Blog: Unique Factorization, A blog that covers the history of Fermat's Last Theorem from Diophantus of Alexandria to the proof by Andrew Wiles.

* " Fundamental Theorem of Arithmetic " by Hector Zenil, Wolfram Demonstrations Project, 2007.

We approach the proof of Theorem 2 by successively restricting the class of all formulas φ for which we need to prove " φ is either refutable or satisfiable ".

This theorem was established by John von Neumann, who is quoted as saying " As far as I can see, there could be no theory of games … without that theorem … I thought there was nothing worth publishing until the Minimax Theorem was proved ".

* A complete Theorem Prover for Presburger Arithmetic by Philipp Rümmer

Zero Theorem was a planned feature film project by Gilliam.

On 13 August, 2012, this project was officially announced to be The Zero Theorem, set to start shooting in Bucharest on October 22, produced by Dean Zanuck ( son to the late Richard D. Zanuck who was to originally produce in 2009 ), worldwide sales handled by Voltage Pictures, Toronto and starring Academy Award winner Christoph Waltz in the lead, replacing Billy Bob Thornton who had been attached to the project in 2009.

Using the probability calculus of Bayes Theorem, Salmon concludes that it is very improbable that the universe was created by the type of intelligent being theists argue for.

* Proof of Fermat's Last Theorem is discovered by Andrew Wiles.

Since the theorem was also discovered independently by E. T. Whittaker, by Vladimir Kotelnikov, and by others, it's also known as the Nyquist – Shannon – Kotelnikov, Whittaker – Shannon – Kotelnikov, Whittaker – Nyquist – Kotelnikov – Shannon, WKS, as well as the Cardinal Theorem of Interpolation Theory.

*" The Surprise Examination Paradox and the Second Incompleteness Theorem " by Shira Kritchman and Ran Raz, at ams. org

: Theorem ( A. Korselt 1899 ): A positive composite integer is a Carmichael number if and only if is square-free, and for all prime divisors of, it is true that ( where means that divides ).

An interesting characteristic of the Blum Blum Shub generator is the possibility to calculate any x < sub > i </ sub > value directly ( via Euler's Theorem ):

" A Completeness Theorem in Modal Logic ", Journal of Symbolic Logic 24 ( 1 ): 1 – 14.

Corollary ( Pointwise Ergodic Theorem ): In particular, if T is also ergodic, then is the trivial σ-algebra, and thus with probability 1:

Theorem ( Dini's test ): Assume a function f satisfies at a point t that

Theorem: Given A1 and A2, A3 ’ and A4 ’ imply A3 and A4.

Theorem: Given A1 and A2, A3 ” and A4 ” imply A3 and A4.

: Theorem: Given a set of FDs, if and only if.

Moreover, as long as the polynomial factors at each stage are relatively prime ( which for polynomials means that they have no common roots ), one can construct a dual algorithm by reversing the process with the Chinese Remainder Theorem.

Theorem The dual of G ^ is canonically isomorphic to G, that is ( G ^)^ = G in a canonical way.

In addition to the above characterizations of Pappus's Theorem and its dual, the following are equivalent statements:

In 1852, Genocchi was able to prove that the first case of Fermat's Last Theorem is true for an exponent p, if is not an irregular pair.

Kummer improved this further in 1857 by showing that for the " first case " of Fermat's Last Theorem ( see Sophie Germain's theorem ) it is sufficient to establish that either or fails to be an irregular pair.

The Relative Hurewicz Theorem states that if each of X, A are connected and the pair ( X, A ) is ( n − 1 )- connected then H < sub > k </ sub >( X, A ) = 0 for k < n and H < sub > n </ sub >( X, A ) is obtained from π < sub > n </ sub >( X, A ) by factoring out the action of π < sub > 1 </ sub >( A ).

: Theorem 1: For any pair of algorithms a < sub > 1 </ sub > and a < sub > 2 </ sub >

Theorem ( Fuglede ) Let T and N be bounded operators on a complex Hilbert space with N being normal.

In axial symmetry, he considered general equilibrium for distributed currents and concluded under the Virial Theorem that if there were no gravitation, a bounded equilibrium configuration could exist only in the presence of an azimuthal current.

: Theorem: Assume T is a bounded linear operator from L < sup > p </ sup > to L < sup > p </ sup > and at the same time from L < sup > q </ sup > to L < sup > q </ sup >.

Theorem: Assume T is a bounded linear operator from to and at the same time from to.

Theorem For a bounded operator T, σ < sub > r </ sub >( T ) ⊂ σ < sub > p </ sub >( T *) ⊂ σ < sub > r </ sub >( T ) ∪ σ < sub > p </ sub >( T ).

Theorem: Let T be a bounded linear operator from to and at the same time from to.

: Wernicke's Theorem: Assume G is planar, nonempty, has no faces bounded by two edges, and has minimum degree 5.