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2. Hilbert's problems - Wikipedia

   en.wikipedia.org/wiki/Hilbert's_problems

   Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer. For other problems, such as the 5th, experts have traditionally agreed on a single interpretation, and a solution to ...

3. Archimedes's cattle problem - Wikipedia

   en.wikipedia.org/wiki/Archimedes's_cattle_problem

   The second part of the problem states that + is a square number, and + is a triangular number. The general solution to this part of the problem was first found by A. Amthor [ 11 ] in 1880. The following version of it was described by H. W. Lenstra , [ 5 ] based on Pell's equation : the solution given above for the first part of the problem ...

4. Hilbert's second problem - Wikipedia

   en.wikipedia.org/wiki/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. Hilbert stated that the axioms he considered for arithmetic were the ones given in Hilbert (1900) , which include a second order completeness axiom.

5. Mathematical problem - Wikipedia

   en.wikipedia.org/wiki/Mathematical_problem

   A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems .

6. Smale's problems - Wikipedia

   en.wikipedia.org/wiki/Smale's_problems

   Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.

7. Goat grazing problem - Wikipedia

   en.wikipedia.org/wiki/Goat_grazing_problem

   The answer to the problem as proposed was given in the 1749 issue of the magazine by a Mr. Heath, and stated as 76,257.86 sq.yds. which was arrived at partly by "trial and a table of logarithms". The answer is not so accurate as the number of digits of precision would suggest. No analytical solution was provided.