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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.
Math on Trial consists of ten chapters, each outlining a particular mathematical fallacy, presenting a case study of a trial in which it arose, and then detailing the effects of the fallacy on the case outcome [1] [2] The cases range over a wide range of years and locations, and are roughly ordered by the sophistication of the reasoning needed to resolve them. [3]
These results include previously proved theorems, axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration. [1] Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although ...
Staircases converging pointwise to the diagonal of a unit square, but not converging to its length. In mathematical analysis, the staircase paradox is a pathological example showing that limits of curves do not necessarily preserve their length. [1]
Stone v. Graham, 449 U.S. 39 (1980), was a court case in which the Supreme Court of the United States ruled that a Kentucky statute was unconstitutional and in violation of the Establishment Clause of the First Amendment, because it lacked a nonreligious, legislative purpose.
IN THE COURT OF COMMON PLEAS OF PHILADELPHIA COUNTY FIRST JUDICIAL DISTRICT OF PENNSYLVANIA CIVIL TRIAL DIVISION ----------------------------- IN RE: RISPERDAL ...
Mathematical induction can be informally illustrated by reference to the sequential effect of falling dominoes. [1] [2]Mathematical induction is a method for proving that a statement () is true for every natural number, that is, that the infinitely many cases (), (), (), (), … all hold.
Gorenstein and Lyons's proof for the case of rank at least 4 was 731 pages long, and Aschbacher's proof of the rank 3 case adds another 159 pages, for a total of 890 pages. 1983 Selberg trace formula. Hejhal's proof of a general form of the Selberg trace formula consisted of 2 volumes with a total length of 1322 pages. Arthur–Selberg trace ...