In
In analysis and
*citation|first1=S.|last1=Flannery|first2=D.|last2=Flannery|title=In Code: A Mathematical Journey|publisher=Profile Books|year=2000
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Hilbert's seventh problem — is one of David Hilbert s list of open mathematical problems posed in 1900. It concerns the irrationality and transcendence of certain numbers ( Irrationalit auml;t und Transzendenz bestimmter Zahlen ). Two specific questions are asked:#In an… … Wikipedia
Hilbert's tenth problem — is the tenth on the list of Hilbert s problems of 1900. Its statement is as follows:Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it… … Wikipedia
Hilbert's problems — are a list of twenty three problems in mathematics put forth by German mathematician David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900. The problems were all unsolved at the time, and several of them… … Wikipedia
Hilbert's paradox of the Grand Hotel — is a mathematical paradox about infinite sets presented by German mathematician David Hilbert (1862–1943). The Paradox of the Grand Hotel Consider a hypothetical hotel with infinitely many rooms, all of which are occupied that is to say every… … Wikipedia
Hilbert's sixteenth problem — was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, together with the other 22 problems. The original problem was posed as the Problem of the topology of algebraic curves and surfaces (… … Wikipedia
Hilbert's twelfth problem — Hilbert s twelfth problem, of the 23 Hilbert s problems, is the extension of Kronecker Weber theorem on abelian extensions of the rational numbers, to any base number field. The classical theory of complex multiplication does this for any… … Wikipedia
Hilbert's ninth problem — Hilbert s ninth problem, from the list of 23 Hilbert s problems (1900), asked to find the most general reciprocity law for the norm residues of l th order in a general algebraic number field, where l is a power of a prime. Progress made The… … Wikipedia
Hilbert's thirteenth problem — is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails proving whether or not a solution exists for all 7 th degree equations using functions of two arguments. It was first presented in the… … Wikipedia
Hilbert's eleventh problem — is one of David Hilbert s list of open mathematical problems posed in 1900. A furthering of the theory of quadratic forms, he stated the problem as follows:: Our present knowledge of the theory of quadratic number fields puts us in a position to… … Wikipedia
Hilbert's seventeenth problem — is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails expression of definite rational functions as quotients of sums of squares. Original Hilbert s question was:Given a multivariate… … Wikipedia
