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Conjectural history is a type of historiography isolated in the 1790s by Dugald Stewart, who termed it "theoretical or conjectural history," as prevalent in the historians and early social scientists of the Scottish Enlightenment. As Stewart saw it, such history makes space for speculation about causes of events, by postulating natural causes ...
In addition to theorems of geometry, such as the Pythagorean theorem, the Elements also covers number theory, including a proof that the square root of two is irrational and a proof that there are infinitely many prime numbers. Further advances also took place in medieval Islamic mathematics.
Dirichlet's theorem on arithmetic progressions. In 1808 Legendre published an attempt at a proof of Dirichlet's theorem, but as Dupré pointed out in 1859 one of the lemmas used by Legendre is false. Dirichlet gave a complete proof in 1837. The proofs of the Kronecker–Weber theorem by Kronecker (1853) and Weber (1886) both had gaps. The first ...
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [1] [2] [3] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to ...
As reformulated, it became the "paving conjecture" for Euclidean spaces, and then a question on random polynomials, in which latter form it was solved affirmatively. 2015: Jean Bourgain, Ciprian Demeter, and Larry Guth: Main conjecture in Vinogradov's mean-value theorem: analytic number theory: Bourgain–Demeter–Guth theorem, ⇐ decoupling ...
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures; List of data structures; List of derivatives and integrals in alternative calculi; List of equations; List of fundamental theorems; List of hypotheses; List of inequalities; Lists of ...
The compactness theorem first appeared as a lemma in Gödel's proof of the completeness theorem, and it took many years before logicians grasped its significance and began to apply it routinely. It says that a set of sentences has a model if and only if every finite subset has a model, or in other words that an inconsistent set of formulas must ...
In mathematics, Bertrand's postulate (now a theorem) states that, for each , there is a prime such that < <.First conjectured in 1845 by Joseph Bertrand, [1] it was first proven by Chebyshev, and a shorter but also advanced proof was given by Ramanujan.