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German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose ...
These problems, spanning many areas of mathematics, formed a central focus for much of 20th-century mathematics. Today, 10 have been solved, 7 are partially solved, and 2 are still open. The remaining 4 are too loosely formulated to be stated as solved or not. [citation needed] A map illustrating the Four Color Theorem
The History of Mathematics consists of seven chapters, [1] featuring many case studies. [2] [3] Its first, "Mathematics: myth and history", gives a case study of the history of Fermat's Last Theorem and of Wiles's proof of Fermat's Last Theorem, [4] making a case that the proper understanding of this history should go beyond a chronicle of individual mathematicians and their accomplishments ...
Many textbooks cite the following book [*] as a reference for its proof, but unfortunately I do not have access to it. In the engineering field many researchers will benefit from its proof. [*] H. Amann. Ordinary Differential Equations: An Introduction to Nonlinear Analysis, volume 13 of De Gruyter Studies in Mathematics.
Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
Under Cobham's thesis, a problem for which the best algorithm takes n 200 instructions is considered feasible, and a problem with an algorithm that takes 2 0.00001 n instructions infeasible—even though one could never solve an instance of size n = 2 with the former algorithm, whereas an instance of the latter problem of size n = 10 6 could be ...
The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is a 1960 article written by the physicist Eugene Wigner, published in Communication in Pure and Applied Mathematics. [ 1 ] [ 2 ] In it, Wigner observes that a theoretical physics's mathematical structure often points the way to further advances in that theory and to ...