Hilbert's problems Hilbert's problems (Consistency proof) In mathematical logic, a formal system is consistent if it does not contain a contradiction, or, more precisely, for no proposition are both and provable. ...more on Wikipedia about "Consistency proof"
In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. Georg Cantor introduced the concept of cardinality to compare the sizes of infinite sets, and he showed that the set of integers is strictly smaller than the set of real numbers. The continuum hypothesis states the following: ...more on Wikipedia about "Continuum hypothesis"
In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states: ...more on Wikipedia about "Goldbach's conjecture"
Hilbert's eighteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks three separate questions. ...more on Wikipedia about "Hilbert's eighteenth problem"
Hilbert's eleventh problem, a furthering of the theory of quadratic forms, was stated thus in his landmark speech: ...more on Wikipedia about "Hilbert's eleventh problem"
Hilbert's fifteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails a rigorous foundation of Schubert's enumerative calculus. ...more on Wikipedia about "Hilbert's fifteenth problem"
Hilbert's fifth problem, or in other words Problem 5 on the Hilbert problems list promulgated in 1900 by David Hilbert, concerns the characterization of Lie groups. ...more on Wikipedia about "Hilbert's fifth problem"
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Hilbert's fourteenth problem in mathematics, that is, number 14 of Hilbert's problems proposed in 1900, asks whether certain rings are finitely generated. ...more on Wikipedia about "Hilbert's fourteenth problem"
In mathematics, Hilbert's fourth problem in the 1900 Hilbert problems was a foundational question in geometry. In one statement derived from the original, it was to find geometries whose axioms are closest to those of Euclidean geometry if the ordering and incidence axioms are retained, the congruence axioms weakened, and the equivalent of the parallel postulate omitted. A solution was given by Georg Hamel. ...more on Wikipedia about "Hilbert's fourth problem"
Hilbert's nineteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks whether the solutions of Lagrangians are always analytic. It was solved in the doctoral dissertation of Sergei Natanovich Bernstein, submitted in 1904 to the Sorbonne. ...more on Wikipedia about "Hilbert's nineteenth problem"
In mathematics, Hilbert's ninth problem was to find the most general law of reciprocity in an algebraic number field. It is one of Hilbert's problems, a list of unsolved problems proposed by David Hilbert in 1900. ...more on Wikipedia about "Hilbert's ninth problem"
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 turned out to be very influential for 20th century mathematics. Hilbert presented ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21 and 22) at the conference, speaking on 8 August in the Sorbonne; the full list was published later. ...more on Wikipedia about "Hilbert's problems"
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. ...more on Wikipedia about "Hilbert's seventeenth problem"
In mathematics, Hilbert's seventh problem concerns the irrationality and transcendence of certain numbers (Irrationalität und Transzendenz bestimmter Zahlen). In its geometric formulation, it asks whether the following statement is provably true: ...more on Wikipedia about "Hilbert's seventh problem"
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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. ...more on Wikipedia about "Hilbert's sixteenth problem"
Hilbert's sixth problem is to axiomatize those branches of science in which mathematics is prevalent. It occurs on the list of Hilbert's problems given out in 1900. ...more on Wikipedia about "Hilbert's sixth problem"
(Hilbert's third problem) We call two polyhedra scissors-congruent iff the first can be cut into finitely many polyhedral pieces which can be reassembled to yield the second. Obviously, any two scissors-congruent polyhedra have the same volume. Hilbert asks about the converse. ...more on Wikipedia about "Hilbert's third problem"
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 context of nomography, and in particular "nomographic construction" — a process whereby a function of several variables is constructed using functions of two variables. The actual question is more easily posed however in terms of continuous functions. Hilbert asked whether it was possible to construct the solution of the general seventh degree equation ...more on Wikipedia about "Hilbert's thirteenth problem"
Hilbert's twelfth problem, of the 23 Hilbert's problems, is the extension of Kronecker's theorem on abelian extensions of the rational numbers, to any base number field. The classical theory of complex multiplication does this for any imaginary quadratic field. The more general cases, now often known as the Kronecker Jugendtraum (although not so accurately), are still open as of 2005. Leopold Kronecker is supposed to have described the complex multiplication issue as his 'liebster Jugendtraum' or dearest dream of his youth. ...more on Wikipedia about "Hilbert's twelfth problem"
Hilbert's twentieth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks whether all boundary value problems can be solved (that is, do variational problems with certain boundary conditions have solutions). ...more on Wikipedia about "Hilbert's twentieth problem"
The twenty-first problem of the 23 Hilbert problems, from the celebrated list put forth in 1900 by David Hilbert, was phrased like this (English translation from 1902). ...more on Wikipedia about "Hilbert's twenty-first problem"
Hilbert's twenty-second problem is the penultimate entry in the celebrated list of 23 Hilbert problems compiled in 1900 by David Hilbert. It entails the uniformization of analytic relations by means of automorphic functions. ...more on Wikipedia about "Hilbert's twenty-second problem"
Hilbert's twenty-third problem is one of the last of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails the further development of the calculus of variations. ...more on Wikipedia about "Hilbert's twenty-third problem"
Matiyasevich's theorem, proven in 1970 by Yuri Matiyasevich, implies that Hilbert's tenth problem is unsolvable. This problem is the challenge to find a general algorithm which can decide whether a given system of Diophantine equations ( polynomials with integer coefficients) has a solution among the integers. David Hilbert posed the problem in his 1900 address to the International Congress of Mathematicians. ...more on Wikipedia about "Matiyasevich's theorem"
In mathematics, the Riemann hypothesis (also called the Riemann zeta hypothesis), first formulated by Bernhard Riemann in 1859, is one of the most famous of all unsolved problems. It has been an open question for well over a century, despite attracting concentrated efforts from many outstanding mathematicians. Unlike some other celebrated problems, it is more attractive to professionals in the field than to amateurs. ...more on Wikipedia about "Riemann hypothesis"
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