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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.
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
The Penguin Dictionary of Curious and Interesting Numbers is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, and a revised edition appeared in 1997 (ISBN 0-14-026149-4).
Although a common classroom experiment is often explained this way, [442] Bernoulli's principle only applies within a flow field, and the air above and below the paper is in different flow fields. [443] The paper rises because the air follows the curve of the paper and a curved streamline will develop pressure differences perpendicular to the ...
The three-part original paper is more than 300 pages long. (Britton later published a 282-page paper attempting to solve the problem, but his paper contained a serious gap.) 1960-1970 Fondements de la Géometrie Algébrique, Éléments de géométrie algébrique and Séminaire de géométrie algébrique. Grothendieck's work on the foundations ...
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales.
The questions remained whether a contradiction could be derived from the Principia's axioms, and whether there exists a mathematical statement which could neither be proven nor disproven in the system. These questions were settled, in a rather surprising way, by Gödel's incompleteness theorem in 1931.
In 1996, Penguin Books published as a paperback A Complete Annotated Listing of Penguin Classics and Twentieth-Century Classics (ISBN 0-14-771090-1). This article covers editions in the series: black label (1970s), colour-coded spines (1980s), the most recent editions (2000s), and Little Clothbound Classics Series (2020s).