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eminent mathematician David HilbertWired
•Science
Science
83% Informative
David Hilbert's 10th problem concerns Diophantine equations: polynomials with integer coefficients, such as x2 + y2 = 5 .
In the 1930s , Kurt Gödel demonstrated that this is impossible: In any mathematical system, there are statements that can be neither proved nor disproved.
In 1970 , a Russian mathematician named Yuri Matiyasevich shattered this dream.
Problem of interest is equivalent to famous undecidable problem in computer science called the halting problem.
For every Turing machine, there is a corresponding Diophantine equation for every single ring of integers.
Problem falls apart when equations are allowed to have non-integer solutions, such as y = x2.
Peter Koymans , a mathematician at Utrecht University , has been thinking about Hilbert ’s 10th problem since he was an undergraduate.
The mathematicians needed to get better control over the quadratic twist to solve the problem.
They used a method from a separate area of math called additive combinatorics to ensure that the right combination of primes existed for every ring.
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