arXiv:2606. 14108v1 Announce Type: cross Abstract: We introduce Adelic operation-preserved embeddings (AOE), a training-free representation that captures both a number's real value and its modular (p-adic) signatures.
arXiv:2608. 13129v1 Announce Type: new Abstract: Large language models (LLMs) achieve strong results on mathematical reasoning benchmarks yet remain unreliable on elementary numerical tasks, including magnitude comparison, large-integer arithmetic, fractions, and scientific notation.
arXiv:2606. 01372v1 Announce Type: cross Abstract: Can neural networks learn abstract algebraic rules, or do they merely memorize training patterns?
Large language models (LLMs) achieve strong results on mathematical reasoning benchmarks yet remain unreliable on elementary numerical tasks, including magnitude comparison, large-integer arithmetic, fractions, and scientific notation. This survey examines basic numerical understanding as a capability distinct from high-level mathematical reasoning.
arXiv:2606. 23044v2 Announce Type: replace-cross Abstract: Numbers have algebraic structure that standard neural embeddings often fail to expose.
arXiv:2606. 03645v1 Announce Type: cross Abstract: Large Language Models exhibit paradoxical fragility in fundamental arithmetic, implying a disconnect between internal computation and discrete output.
arXiv:2608. 14585v1 Announce Type: new Abstract: Euclidean geometry is a compelling testbed for AI reasoning, as it demands the combination of intuitive diagram understanding, axiomatic deduction, and algebraic computation.
arXiv:2505. 23851v2 Announce Type: replace-cross Abstract: Large language models (LLMs) are increasingly applied to symbolic mathematics, yet existing evaluations often conflate pattern memorization with genuine reasoning.
arXiv:2505. 23696v2 Announce Type: replace Abstract: Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields.
arXiv:2607. 07066v1 Announce Type: cross Abstract: Transformers have demonstrated a remarkable ability to learn algorithmic reasoning, yet mechanistic analyses have mostly focused on globally invertible operations such as cyclic addition and group composition.
arXiv:2607. 09721v1 Announce Type: cross Abstract: To help evaluate the mathematical skills of current AI systems, we present a set of formulas for fundamental mathematical constants.
arXiv:2606. 03858v1 Announce Type: new Abstract: Despite the pivotal role of numerical reasoning as the cornerstone of mathematical capabilities in large language models (LLMs) across applications, few benchmarks evaluate LLMs by integrating numerical processing and mathematical reasoning, hindering the interpretability of failures in math tasks.
arXiv:2603. 05556v2 Announce Type: replace Abstract: Integer sequences in the OEIS span values from single-digit constants to astronomical factorials and exponentials, making prediction challenging for standard tokenised models that cannot handle out-of-vocabulary values or exploit periodic arithmetic structure.