reduction graphs
The Frontier
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The Riemann Hypothesis
Every nontrivial zero of the Riemann zeta function has real part 1/2.
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The abc Conjecture
For every epsilon > 0, only finitely many coprime triples a + b = c satisfy c > rad(abc)^(1+epsilon).
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Birch and Swinnerton-Dyer
For every elliptic curve over Q, the rank of the Mordell-Weil group equals the order of vanishing of its L-function at s = 1.
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The Collatz Conjecture
Iterating n to n/2 for even n and 3n+1 for odd n reaches 1 from every positive integer.
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Goldbach's Conjecture
Every even integer greater than 2 is a sum of two primes.
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The Hodge Conjecture
On a nonsingular complex projective variety, every rational Hodge class is a rational combination of classes of algebraic cycles.
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Navier-Stokes Regularity
Smooth, globally defined solutions exist for the three-dimensional incompressible Navier-Stokes equations with smooth initial data.
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P versus NP
Whether every language decidable in nondeterministic polynomial time is decidable in deterministic polynomial time.
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The Twin Prime Conjecture
There are infinitely many primes p such that p + 2 is prime.
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Yang-Mills Mass Gap
For every compact simple gauge group, quantum Yang-Mills theory on R^4 exists and has a mass gap greater than zero.