Mathematics
Open problems, research attempts and community review.
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-151 Polynomial Bound for Limit Cycles of Planar Polynomial Vector Fields
- Math-152 Density Hypothesis for Riemann-Zeta Zeros
- Math-153 Unconditional Single-Prover Classical Verification of BQP Computations
- Math-154 Erdős Conjecture on Arithmetic Progressions
- Math-155 Polynomial pivot rule for the simplex method
- Math-156 Normality of Irrational Algebraic Numbers
- Math-157 The Generalized Sato-Tate Conjecture for Higher-Dimensional Abelian Varieties
- Math-158 Arithmetic QUE through Hecke packets
- Math-159 Global Gan–Gross–Prasad Conjecture (Fixed-Representation Form)
- Math-160 Indistinguishability Obfuscation from Constant-Degree Homomorphic Assumptions
- Math-161 Asymptotic tightness of the binary Gilbert–Varshamov bound
- Math-162 Congruent number decision problem
- Math-163 Uniform Subconvexity for Standard Automorphic L-Functions on GL(n)
- Math-164 Order of Magnitude of the Largest Three-Term-Progression-Free Sets
- Math-165 Brauer–Manin Obstruction for Rationally Connected Varieties
- Math-166 Reinhardt Cardinals without Choice
- Math-167 Murre's Chow-Kunneth Conjectures
- Math-168 Hyperlinearity of Every Group
- Math-169 NP versus the Existential Theory of the Reals
- Math-170 Manins Conjecture on the Asymptotic Density of Rational Points on Fano Varieties
- Math-171 Cramer Conjecture on the Limsup of Normalized Prime Gaps
- Math-172 Randomized Integer Word-RAM 3SUM Conjecture
- Math-173 Derandomizing Space-Bounded Computation
- Math-174 Tate's rational leading-term Stark conjecture
- Math-175 Algebraic independence of pi and e
- Math-176 The Weinstein Conjecture
- Math-177 Dirichlet's Divisor Problem
- Math-178 Simplicity of the Nontrivial Zeros of the Riemann Zeta Function
- Math-179 Separation of P_R from NP_R in the Blum–Shub–Smale Model
- Math-180 Conformal Invariance of the Critical Random-Cluster Model with q <= 4
- Math-181 Berman-Hartmanis Isomorphism Conjecture
- Math-182 Smooth anisotropic Calderón uniqueness from full boundary data
- Math-183 Arnold Conjecture on Hamiltonian Fixed Points
- Math-184 Inhomogeneous Landau–Coulomb Global Regularity (HST All-Moment Data)
- Math-185 Bochner-Riesz conjecture
- Math-186 L-space Conjecture
- Math-187 Voevodsky's Smash-Nilpotence Conjecture
- Math-188 Furstenberg's x2 x3 conjecture on invariant measures
- Math-189 Transcendence of Apéry's Constant
- Math-190 Polynomial-Time Quantum Algorithm for Symmetric-Group Hidden Subgroups
- Math-191 Beilinson-Soule Vanishing Conjecture for Rational Motivic Cohomology
- Math-192 Polyakov Conjecture: Absence of a Phase Transition for Planar O(n) Models with n >= 3
- Math-193 Omega(n log n) Boolean Circuit Lower Bound for Integer Multiplication
- Math-194 Landau's Fourth Problem: Primes of the Form n² + 1
- Math-195 Kimura–O'Sullivan Finite-Dimensionality Conjecture
- Math-196 Grothendieck–Serre Conjecture for Regular Local Rings
- Math-197 Exact Consistency Strength of the Proper Forcing Axiom
- Math-198 Nonvanishing conjecture for projective log canonical pairs
- Math-199 Polynomial Freiman-Ruzsa Conjecture for General Abelian Groups
- Math-200 Parity conjecture for elliptic curves