arXiv:2606.08728v2 Announce Type: replace-cross 
Abstract: Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers. This survey provides a unified account of the field's evolution, from early rule-based math word problem (MWP) solvers and template-driven geometry systems, through neural expression generation and LLM prompting, to contemporary reasoning models, multi-agent systems, neuro-symbolic theorem provers, and verified discovery workflows. We organize the landscape along four axes: (i) informal reasoning over text and diagrams, spanning MWP solving, multimodal geometry, and VLMs; (ii) formal reasoning in proof assistants, including autoformalization, tactic prediction, compiler-guided repair, and proof search; (iii) mathematical discovery, where systems propose constructions, improve bounds, or assist attacks on open problems; and (iv) the inference and training-time techniques, including CoT prompting, tool use, process reward models, and RLVR, that increasingly connect generation with verification. We catalog major benchmarks across grade-school arithmetic, competition mathematics, geometry, formal proving, multimodal and multilingual reasoning, and expert evaluation, and we examine benchmark saturation, contamination, reporting mismatches, and the distinction between pass@1, majority voting, and verifier-assisted pass@$k$. We critically assess failure modes: brittleness under perturbation, reward hacking, multimodal grounding failures, fragile formalization, and the energy cost of reasoning-scale inference. Drawing on recent perspectives from working mathematicians, we identify future directions centered on verified-discovery workflows, reasoning efficiency, and infrastructure to make AI-assisted formalization broadly usable. Companion materials: https://github.com/Starscream-11813/awesome-AI4Math.

استعرضت دراسة حديثة نُشرت على arXiv تطور الذكاء الاصطناعي في مجال التفكير الرياضي، مسلطةً الضوء على التقدم من الأنظمة المعتمدة على القواعد إلى النماذج المعاصرة التي تدمج معالجة اللغة والنهج العصبي الرمزي. تصنف الدراسة التطورات إلى أربعة مجالات رئيسية: التفكير غير الرسمي، المساعدة الرسمية في الإثبات، الاكتشاف الرياضي، وسير العمل الموثق.

Una reciente encuesta publicada en arXiv explora la evolución de la inteligencia artificial en el razonamiento matemático, destacando los avances desde los sistemas basados en reglas hasta los modelos contemporáneos que integran el procesamiento del lenguaje y enfoques neuro-simbólicos. El estudio categoriza los desarrollos en cuatro áreas principales: razonamiento informal, asistencia formal a la prueba, descubrimiento matemático y flujos de trabajo verificados.

Une récente enquête publiée sur arXiv examine l'évolution de l'intelligence artificielle dans le raisonnement mathématique, mettant en lumière les avancées allant des systèmes basés sur des règles aux modèles contemporains intégrant le traitement du langage et des approches neuro-symboliques. L'étude classe les développements en quatre domaines principaux : le raisonnement informel, l'assistance à la preuve formelle, la découverte mathématique et les flux de travail vérifiés.

A recent survey published on arXiv explores the evolution of artificial intelligence in mathematical reasoning, highlighting advancements from early rule-based systems to contemporary models that integrate language processing and neuro-symbolic approaches. The study categorizes developments into four main areas: informal reasoning, formal proof assistance, mathematical discovery, and verified workflows.