Mathematics
Solving linear systems with a vector-sized workspace
A 2025 result published at SODA 2026 separates linear solves from quadratic working memory. Its scope depends on integer inputs, access models, and bit complexity.
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203 articlesMathematics
25–48 of 50 articles
Mathematics
Why Curvature Gaps Matter: Lu’s Conjecture for Minimal Spheres in 2026
A January 2026 preprint resolves Lu’s curvature-gap conjecture for minimal two-spheres, revealing how topology and normal directions restrict bending.
Mathematics
What Remains Smooth When Mean Curvature Flow Breaks?
An October 2026 preprint controls tangent-flow geometry under a scale-invariant curvature bound, while leaving multiplicity and continuation separate.
Mathematics
Moving fewer bytes without losing a linear solve
An October 2026 preprint studies lower precision storage in matrix splitting iterations, connecting memory traffic, convergence, and accurate residual corrections.
Mathematics
Computing a matrix square root without spending double precision everywhere
A July 2026 preprint combines a cheaper Schur decomposition with careful correction. Its central challenge is that matrices do not multiply like scalars.
Mathematics
What the 2026 multicolour Ramsey improvements actually save
Two 2026 preprints sharpen multicolour Ramsey upper bounds. The savings concern exponential estimates under explicit growth conditions, not exact values.
Mathematics
Can a Finite Computation Certify High-Dimensional Percolation?
A September 2026 preprint gives a semi-decision route to mean-field percolation, separating a finite certificate from an unconditional theorem in every dimension.
Mathematics
Random Growth on a Ring Gets a General Starting Shape
A 2026 probability preprint constructs periodic KPZ fixed-point distributions from general starting profiles, extending beyond specially solvable initial shapes.
Mathematics
When one fractal viewpoint sees an entire interval of distances
A 2026 version of a pinned-distance theorem shows how planar fractals above dimension 7/4 contain a viewpoint realizing every distance in an interval.
Mathematics
Why Polynomial Subalgebras Have Their Own Complexity Frontier
A 2025 complexity classification and June 2026 structural algorithms reveal why membership in polynomial subalgebras needs carefully stated input assumptions.
Mathematics
Why prime-gap bounds depend on distribution in progressions
Julia Stadlmann’s August 2026 preprint gives a 240 bound for recurring prime gaps by combining distribution information suited to different moduli.
Mathematics
The Quantum Stein Lemma’s Formal Proof: From 2025 Milestone to 2026 Completion
The quantum Stein formalization reached a 2025 milestone with admitted facts. Its authors report an April 2026 completion; the distinction matters mathematically.
Mathematics
Why randomized Arnoldi needs to restore similarity
A January 2026 preprint repairs a projection problem in randomized Krylov methods. A small example shows why a good basis cannot guarantee familiar convergence.
Mathematics
Why Rank-Zero Elliptic Curves Unlock Modular-Curve Point Searches
A September 2026 revision turns maps to rank-zero elliptic curves into certified searches for rational points, with a carefully bounded level range.
Mathematics
Restriction implies decoupling, but in a different dimension
Changkeun Oh’s 2025 theorem connects Fourier restriction in one dimension of ambient space to decoupling in another, with a precise conditional step.
Mathematics
Fast Fourier decay does not guarantee a stable Fourier frame
Li and Liu’s 2025 Salem-measure examples separate strong Fourier decay from the existence of stable exponential expansions on fractal measures.
Mathematics
The algebra hidden in a fractal shadow
Morris and Sert’s 2026 revision reveals why projections of self-affine fractals can depend on matrix algebra and can lose regular local dimension.
Mathematics
Noise Can Fix a Distribution Without Fixing a Path
A 2026 stochastic-analysis preprint constructs rough drifts with unique weak laws but pathwise nonuniqueness, locating a sharp boundary for regularization by noise.
Mathematics
Spreadness offers a new language for arithmetic progressions
Raghu Meka’s July 2026 ICM survey connects a recent progression breakthrough to a principle: objects can mix strongly without individually looking random.
Mathematics
A Steiner design on 42 points turns admissibility into a construction
A 2025 construction, published in 2026, resolves a small Steiner-design parameter set. Counting triples explains its 574 blocks and the role of symmetry.
Mathematics
An ellipsoid that makes room for more spheres
A 2026 revision of Boaz Klartag’s sphere-packing proof shows how a randomly evolving ellipsoid improves a general density guarantee in high dimensions.
Mathematics
The Last Unvisited Site Is More Than a Coupon Collector
An October 2026 preprint identifies a randomly shifted Gumbel cover-time law for the two-dimensional torus, revealing persistent large-scale correlations.
Mathematics
Fractional coloring after the triangle-free degeneracy breakthrough
Martinsson’s 2025 result resolves a fractional coloring conjecture for triangle-free graphs. An explicit five-cycle explains the crucial relaxation.
Mathematics
Twisted approximation must work at every scale
September 2026 preprints examine approximation with a fixed matrix, showing why repeated success and success at every large scale require different geometry.