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2. Millennium Prize Problems - Wikipedia

   en.wikipedia.org/wiki/Millennium_Prize_Problems

   t. e. The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$ 1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved ...

3. Mathematical optimization - Wikipedia

   en.wikipedia.org/wiki/Mathematical_optimization

   In mathematics, conventional optimization problems are usually stated in terms of minimization. A local minimum x * is defined as an element for which there exists some δ > 0 such that ∀ x ∈ A where ‖ x − x ∗ ‖ ≤ δ , {\displaystyle \forall \mathbf {x} \in A\;{\text{where}}\;\left\Vert \mathbf {x} -\mathbf {x} ^{\ast }\right\Vert ...

4. List of unsolved problems in mathematics - Wikipedia

   en.wikipedia.org/wiki/List_of_unsolved_problems...

   Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

5. Statistical hypothesis test - Wikipedia

   en.wikipedia.org/wiki/Statistical_hypothesis_test

   Statistical hypothesis testing is a key technique of both frequentist inference and Bayesian inference, although the two types of inference have notable differences. Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect. The procedure ...

6. Mathematical universe hypothesis - Wikipedia

   en.wikipedia.org/wiki/Mathematical_universe...

   Mathematical universe hypothesis. In physics and cosmology, the mathematical universe hypothesis (MUH), also known as the ultimate ensemble theory, is a speculative "theory of everything" (TOE) proposed by cosmologist Max Tegmark. [1][2] According to the hypothesis, the universe is a mathematical object in and of itself.

7. Foundations of mathematics - Wikipedia

   en.wikipedia.org/wiki/Foundations_of_mathematics

   e. Foundations of mathematics is the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc. This may also include the philosophical study of the relation of this framework with reality.