Riemann Hypothesis The Riemann Hypothesis, proposed by Bernhard Riemann in 1859, concerns the non-trivial zeros of the Riemann zeta function—a complex function deeply connected to the distribution of prime numbers. It asserts that all non-trivial zeros lie on the "critical line" where the real part equals 1/2. If true, it would provide unprecedented precision in estimating the number of primes below a given value, refining the Prime Number Theorem. Despite extensive numerical verification (billions of zeros align with the hypothesis), no general proof exists. The hypothesis underpins many results in analytic number theory that assume its truth. Its resolution would impact cryptography, quantum chaos, and random matrix theory. As one of Hilbert’s 23 problems and a Clay Millennium Prize problem, it remains the most famous open question in mathematics, symbolizing the mysterious link between analysis and arithmetic.
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