Millenium Problems

The Hodge Conjecture ★★★★

Author(s): Hodge

\begin{conjecture} Let $X$ be a complex projective variety. Then every Hodge class is a rational linear combination of the cohomology classes of complex subvarieties of $X$. \end{conjecture}

Keywords: Hodge Theory; Millenium Problems

P vs. NP ★★★★

Author(s): Cook; Levin

\begin{problem} Is P = NP? \end{problem}

Keywords: Complexity Class; Computational Complexity; Millenium Problems; NP; P; polynomial algorithm

The Riemann Hypothesis ★★★★

Author(s): Riemann

The zeroes of the Riemann zeta function that are inside the Critical Strip (i.e. the vertical strip of the complex plane where the real part of the complex variable is in ]0;1[), are actually located on the Critical line ( the vertical line of the complex plane with real part equal to 1/2)

Keywords: Millenium Problems; zeta

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