Computational algebra and number theory
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-54 Permanent versus Determinant over C
- Math-55 Permanent–Determinant Separation Through Geometric Complexity Theory
- Math-56 Derandomization of Polynomial Identity Testing
- Math-193 Omega(n log n) Boolean Circuit Lower Bound for Integer Multiplication
- Math-344 Real $\tau$-Conjecture for Sparse Polynomial Sums and Products
- Math-1175 Discrete Logarithm Problem
- Math-2280 Finite-field factorization and sparse-polynomial root testing
- Math-2281 Prime-factor advice in power-residue quotients
- Math-2282 Three zeta-like products, degree-count inversion, and the factorization boundary
- Math-2317 Arithmetic-Formula Lower Bounds for Permanent and Determinant
- Math-2349 Decidability of Rational Points over Number Fields
- Math-2492 Finite-field polynomial multiplication and integer-multiplication lower bounds
- Math-2967 Complex square and rectangular multiplication bounds
- Math-2980 Integer multiplication below n log n
- Math-2987 Hitting lists for noncommutative rational formulas
- Math-2994 Cubic border-determinantal lower bound for the permanent
- Math-2997 Matrix hitting points in every positive characteristic
- Math-3001 One rational matrix hitting point for noncommutative formulas
- Math-4381 Linear collapse, binomial hypersurfaces, and the image of local-odds fibers
- Math-4385 An algebraic one-mode certificate for MANOVA
- Math-4389 Transcendence-aware algebraic localization of symmetric Gaussian-mixture modes
- Math-4395 A cyclic-slice chart for balanced minimal border rank
- Math-4398 Root obstruction and outgroup-oriented algebraic clade certificates
- Math-4411 Nondefectivity and low-degree obstructions for the two-component S4 Birkhoff model
- Math-4416 Finite-field least squares as statistical decoding
- Math-4417 Cyclic-binomial structure in an early Agrawal conjecture
- Math-4418 A norm obstruction for Agrawal's conjecture
- Math-4419 Perfect-number recognition and simultaneous polynomial divisors
- Math-4420 Adjacent nonisogenous fibers in the Legendre family
- Math-4421 Irreducible line sections: exact convention-sensitive counts and monodromy status
- Math-4422 Binomial windows for prescribed-degree factors
- Math-4423 Information and conditioning audit for zeta-zero primality and factoring proposals
- Math-4424 A local-to-global screen for number-field ECM torsion
- Math-4425 Geometry, residues, and scale thresholds for prescribed-prefix prime products
- Math-4426 A nonresidue-to-witness reduction and exact witness count
- Math-4427 Finite certificate interfaces for finite-field zeta functions
- Math-4428 Deformation, specialization, and plane-curve genus
- Math-4429 Deterministic roots of X^3-2: a density-one-eighteenth residual envelope
- Math-4447 HHL, Macaulay conditioning, and presentation instability
- Math-4449 A localization-safe action of Weyl operators
- Math-4450 Degree-windowed Cech computation and the role of one b-function
- Math-4451 Fixed-ambient extraction of roots of finite Frobenius modules
- Math-4452 Random-access slices of free resolutions
- Math-4453 A fixed-basis semibasis certificate for DG-module interoperability
- Math-4454 Degree-local Hom computation and certified corner reuse
- Math-4461 Polynomial-Time Computation of Ehrhart Periods
- Math-4464 Polynomial Complexity of Greedy Lattice Reduction
- Math-4469 Quantum Hardness of Approximate Lattice Problems
- Math-4478 Optimal Algebraic Immunity of Boolean Functions
- Math-4479 Explicit Polynomial Maps Escaping Low-Degree Images