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Using frontier agent harnesses to tackle mathematical research problems has emerged as an effective means of advancing mathematics. However, solving frontier problems in mathematics may require a massive number of agents working in parallel for extended periods to construct proofs, thereby generating an enormous volume...
We establish new bounds on the Grothendieck constant $K_G$: \[ \frac{6\pi}{11} \le K_G \le \frac{\pi}{2\log(1+\sqrt2)} - 10^{-4}. \] Methodologically, our lower bound approach differs from previous works by establishing limitations on the asymptotically optimal Krivine schemes, rather than giving explicit constructions...
We define the $M$-point query problem in data streams. Given a fixed matrix $M$, the goal is to maintain a vector $x$ under turnstile updates and answer each query $u$ with an estimate $\widehat{y}_u$ satisfying $|y_u-\widehat{y}_u| \leq \varepsilon \|x\|_1$, where $y=Mx$. We show that if $M$ admits a factorization $M=...
A smoothed-analysis framework that requires a learner to compete only with the best classifier that is robust to small random Gaussian perturbation is introduced, and the first algorithm for agnostic learning intersections of halfspaces in time is obtained, where $γ$ is the margin parameter.
It is argued that the next leap in AI4Math systems requires a decisive shift from predefined problem-solvers to research agents that can address frontier mathematical challenges with rigorous formal mathematical reasoning, highlighting core limitations of existing systems in serving as mathematical research agents.
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