Mystery
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History of science
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Unsolved problems
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History of mathematics
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Mathematical problem
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Unsolved problems in mathematics
Conjecture
Proof of impossibility
Hilbert's problems
Hilbert's problems are a list of twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and several of them were very...
Hilbert's problems - Wikipedia
Hilbert's 24th problem
Hilbert's ninth problem - Slideshow
Hilbert's twenty-first problem - Slideshow
Hilbert's 24th problem
Hilbert's twenty-fourth problem is a mathematical problem that was not published as part of the list of twenty-three problems known as Hilbert's problems, but was included in David Hilbert's original ...
Hilbert's seventh problem
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 (Irrationalität und Transz...
Diophantine set
In mathematics, a Diophantine equation is an equation of the form P(x1, ..., xj, y1, ..., yk)=0 (usually abbreviated P(x,y)=0 ) where P(x,y) is a polynomial with integer coefficients. A Diophantine ...
Hilbert's first problem
In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. It states:The continuum hypothesis was advanced by Georg Cantor in 1878, andestablishing its truth o...
Hilbert's seventeenth problem
Hilbert's seventeenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It concerns the expression of positive definite rational functions as s...
Hilbert's eleventh problem
Hilbert's eleventh problem is one of David Hilbert's list of open mathematical problems posed at the Second International Congress of Mathematicians in Paris in 1900. A furthering of the theory of qua...
Hilbert's twenty-third problem
Hilbert's twenty-third problem is the last of Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. In contrast with Hilbert's other 22 problems, his 23rd is not so much a ...
Hilbert's third problem
The third on Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question: given any two polyhedra of equal volume, is it al...
Hilbert's ninth problem - Slideshow
Hilbert's eighth problem
Hilbert's eighth problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns number theory, and in particular the Riemann hypothesis, although it is also concerned ...
Hilbert's fourth 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 cl...
Hilbert's fifteenth problem
Hilbert's fifteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. The problem is to put Schubert's enumerative calculus on a rigorous found...
Hilbert's fifteenth problem - Wikipedia
Hilbert's eighteenth problem
Hilbert's eighteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by mathematician David Hilbert. It asks three separate questions about lattices and sphere...
Continuum hypothesis
In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. It states:The continuum hypothesis was advanced by Georg Cantor in 1878, andestablishing its truth o...
Hilbert's twenty-second 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 ...
Hilbert's program
In mathematics, Hilbert's program, formulated by German mathematician David Hilbert, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations o...
Hilbert's sixteenth problem
Hilbert's 16th problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, as part of his list of 23 problems in mathematics.The original proble...
Hilbert's twelfth problem
Kronecker's Jugendtraum or Hilbert's twelfth problem, of the 23 mathematical Hilbert problems, is the extension of the Kronecker–Weber theorem on abelian extensions of the rational numbers, to any bas...
Hilbert-Pólya conjecture
In mathematics, the Hilbert–Pólya conjecture is a possible approach to the Riemann hypothesis, by means of spectral theory.
In a letter to Andrew Odlyzko, dated January 3, 1982, George Pólyasaid t...
Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural numbe...
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, pro...
Gentzen's consistency proof
Gentzen's consistency proof is a result of proof theory in mathematical logic. It "reduces" the consistency of a simplified part of mathematics, not to something that could be proved in that same simp...
Hilbert's twenty-first problem - Slideshow
Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture that the non-trivial zeros of the Riemann zeta function all have real part 1/2. The name is also ...
Riemann hypothesis - Wikipedia
Hilbert's nineteenth problem
Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled in 1900 by David Hilbert. It asks whether the solutions of regular problems in the calculus of variations are...
Hilbert's second problem
In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent – free of any internal contradictions.In...
Hilbert's tenth problem
Hilbert's tenth problem is the tenth on the list of Hilbert's problems of 1900. Its statement is as follows:It took many years for the problem to be solved with a negative answer. Today, it is known t...
Hilbert's twenty-first problem
The twenty-first problem of the 23 Hilbert problems, from the celebrated list put forth in 1900 by David Hilbert, concerns the existence of a certain class of linear differential equations with spec...