Top 10 Unsolved Math Problems: These profound conjectures and questions—spanning number theory, geometry, logic, and physics—have resisted proof for decades or centuries. Solving any would revolutionize mathematics, deepen our understanding of the universe, and earn a $1 million Millennium Prize (for seven of them). They represent the frontiers of human reasoning.
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 ... Show More
+ Comment+ Vote ( 1 )P vs NP Problem: The P vs NP problem asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved. "P" denotes problems solvable in polynomial time; "NP" includes those whose solutions are verifiable in ... Show More
+ Comment+ Vote ( 1 )Navier-Stokes Existence and Smoothness: The Navier-Stokes equations describe the motion of viscous fluids like water or air and are fundamental to engineering, meteorology, and aerodynamics. Despite their practical use, mathematicians lack proof that solutions always exist ... Show More
+ Comment+ Vote ( 1 )Birch and Swinnerton-Dyer Conjecture: This conjecture links algebraic geometry and number theory by connecting the arithmetic of elliptic curves to their analytic properties. Specifically, it predicts that the rank of the group of rational points on an elliptic curve (a ... Show More
+ Comment+ Vote ( 1 )Hodge Conjecture: The Hodge Conjecture, formulated by W.V.D. Hodge in 1950, sits at the intersection of algebraic geometry and topology. It proposes that certain cohomology classes (called Hodge classes) on non-singular complex projective varieties can be expressed as ... Show More
+ Comment+ Vote ( 1 )Yang-Mills Existence and Mass Gap: The Yang-Mills Existence and Mass Gap problem arises from quantum field theory, the framework underlying the Standard Model of particle physics. Yang-Mills theory describes elementary particles via non-abelian gauge fields (e.g., gluons in ... Show More
+ Comment+ Vote ( 1 )Collatz Conjecture: The Collatz Conjecture, though simple to state, has baffled mathematicians since the 1930s. Start with any positive integer: if even, divide by 2; if odd, multiply by 3 and add 1. Repeat. The conjecture claims this process always reaches 1, regardless of ... Show More
+ Comment+ Vote ( 1 )Goldbach’s Conjecture: Proposed in 1742, Goldbach’s Conjecture states that every even integer greater than 2 can be expressed as the sum of two prime numbers (e.g., 10 = 3 + 7). A weaker version—every odd number greater than 5 is the sum of three primes—was proved ... Show More
+ Comment+ Vote ( 1 )Twin Prime Conjecture: The Twin Prime Conjecture posits that there are infinitely many pairs of prime numbers differing by 2 (e.g., 3 and 5, 11 and 13). While primes become rarer as numbers grow, twin primes appear persistently. In 2013, Yitang Zhang made a breakthrough by ... Show More
+ Comment+ Vote ( 1 )Continuum Hypothesis: Proposed by Georg Cantor in 1878, the Continuum Hypothesis (CH) addresses the sizes of infinite sets. It states that there is no set whose cardinality is strictly between that of the integers (countable infinity, ℵ₀) and the real numbers (the ... Show More
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