Abstract:
In the 10th of his 23 problems, Hilbert asked to find an algorithm that would allow one to know whether a given arbitrary Diophantine equation has a solution in integers. The solution to this problem became possible only when a mathematically rigorous general notion of algorithm was developed. In the talk, I will discuss some of the concepts and results obtained in computability theory and the role of the American mathematician Martin Davis (1928–2023) in the (negative) solution of Hilbert's 10th problem.
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