4arXiv cs.AI (Artificial Intelligence)·
FormalAnalyticGeo: Neural-symbolic framework for automatic analytic geometry problem generation yields 7K-problem dataset
Researchers introduce FormalAnalyticGeo, a pipeline using four specialized LLM components and a formal intermediate language (CDL) to automatically generate multimodal analytic geometry problems with diagram rendering via a Signed Distance Field engine. The closed-loop system requires no human annotation and produces AnalyticGeo7K, a dataset of over 7,000 verified problems with aligned text, diagrams, formal annotations, and ground-truth answers. Generated problems achieve a median ground-truth relative error of 0.70%, with 82.3% of answers within 5% of exact symbolic solutions. The work addresses a recognized gap in math reasoning benchmarks where analytic geometry is underrepresented due to data scarcity.
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SD-GPS: Solver-Driven Autoformalization and Theorem Proposing for Geometry Problem Solving
Researchers propose SD-GPS, a neuro-symbolic framework for geometry problem solving that treats a symbolic solver as an execution oracle during both formalization and deduction stages. The system combines solvability-guided reinforcement learning for autoformalization (built on QwenVL3-2B) with an impasse-aware agent that proposes and symbolically verifies auxiliary lemmas. Evaluations on Geometry3K and PGPS9K show SD-GPS outperforms existing multimodal, neural, and neuro-symbolic baselines across multiple task regimes. The work advances the line of research on grounding neural agents in formal systems for verifiable mathematical reasoning.
Large-Scale Evaluation of LLM-Driven Formal Proof Search on Open Mathematical Problems
Researchers present the first large-scale evaluation of LLM-based formal proof search on genuinely open mathematical problems, using Lean as a verification backend. Their most capable agent autonomously resolved 9 of 353 open Erdős problems and proved 44 of 492 OEIS conjectures, at a cost of a few hundred dollars per problem. The system is already being deployed in active research across combinatorics, optimization, graph theory, algebraic geometry, and quantum optics. The study also compares agent architectures, finding that more sophisticated designs outperform simple generate-and-verify loops on the hardest problems.
SGA: Plug-and-play geometric verification module for LLM-generated educational animations
Researchers introduce the Symbolic Geometric Agent (SGA), a modular component that intercepts LLM-generated Manim animation code, extracts symbolic scene graphs via partial execution, and applies targeted refinement to resolve spatial conflicts and occlusions. They also propose MVQS (Manim Visual Quality Score), a deterministic rendering-free proxy metric for spatial integrity. Evaluated on the MMMC-Code benchmark across four LLM backbones and two agentic pipelines, SGA achieves a 16.1% relative improvement in MVQS over baseline. The work addresses a gap in LLM-driven code generation pipelines where geometric correctness is underserved.
OpenAI Neural Theorem Prover Solves Formal Math Olympiad Problems in Lean
OpenAI developed a neural theorem prover integrated with the Lean proof assistant that can solve challenging high-school olympiad problems, including problems from AMC12, AIME, and two IMO-adapted problems. The system demonstrates automated formal mathematical reasoning at a level previously requiring human expertise. This represents a significant capability milestone in AI-assisted formal verification and mathematical problem-solving.
CARLA-GS: Modular pipeline for photorealistic autonomous driving corner-case synthesis using LLMs and Gaussian splatting
CARLA-GS is a new modular framework for synthesizing safety-critical corner cases for autonomous driving evaluation, decoupling visual representation (editable Gaussian scenes), semantic reasoning (multi-agent LLM for waypoint generation), and physics simulation (CARLA with PID control). The pipeline reconstructs real driving scenes from the Waymo Open Dataset, uses LLMs to identify risky interactions and generate intent-level trajectories, then re-projects simulated states into Gaussian scenes for photorealistic ego-centric rendering. The approach addresses a key gap in AV safety evaluation: generating spatiotemporally consistent, physically feasible, and semantically meaningful rare scenarios at scale.
Goedel-Architect achieves state-of-the-art formal theorem proving with blueprint-based agentic framework
Goedel-Architect is an agentic framework for formal theorem proving in Lean 4 that uses blueprint generation — a dependency graph of definitions and lemmas — rather than recursive decomposition, enabling parallel lemma closure and global refinement. Built on DeepSeek-V4-Flash (284B-A13B), it achieves 99.2% pass@1 on MiniF2F-test and 75.6% on PutnamBench, scaling to 100% on MiniF2F, 88.8% on PutnamBench, and 4/6 on IMO 2025 when seeded with natural-language proofs. The authors claim state-of-the-art performance for an open-source pipeline at up to 500x lower cost than comparable systems.
AdvancedMathBench: New benchmark suite for advanced mathematical proof generation and verification
Researchers introduce AdvancedMathBench, a benchmark suite targeting advanced mathematical reasoning beyond olympiad-level problems, comprising ProverBench (296 undergraduate and doctoral qualifying-exam problems) and VerifierBench (888 model-generated proof trajectories). The suite includes an automatic verification pipeline trained on expert annotations to assess proof correctness and error types. Frontier models struggle significantly: the best performer (GPT-5.5-xhigh) achieves only 75.8% and 66.1% on undergraduate and qualifying-exam splits respectively, while proof verification tops out at 65.1 Balanced F1, with models particularly weak at detecting proof errors.
Latent Space profiles Axiom Math on verified generation and compounding intelligence
Latent Space interviews Carina Hong of Axiom Math, a company focused on formal verification applied to AI-generated mathematics. The discussion centers on 'verified generation' and 'compounding intelligence' as frameworks for scaling AI reasoning beyond informal, unverified outputs. The piece is relevant to the growing intersection of formal methods, mathematical reasoning, and AI capability development.