Challenge: Existing methods for geometry theorem proving in Euclidean geometry are challenging and require a neural network to perform.
Approach: They propose a method for adding auxiliary points in geometry that runs on CPUs without relying on neural network-based inference.
Outcome: The proposed method achieves silver-medal-level human performance on IMO-30 benchmark.

Similar Papers

Towards Robust Mathematical Reasoning (2025.emnlp-main)

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Challenge: IMO-Bench is a suite of advanced reasoning benchmarks that targets the international mathematical Olympiad level.
Approach: They propose IMO-Bench, a suite of advanced reasoning benchmarks that targets the level of the international mathematical Olympiad.
Outcome: IMO-Bench is a suite of advanced reasoning benchmarks that targets the level of the international mathematical Olympiad.
GeometryZero: Advancing Geometry Solving via Group Contrastive Policy Optimization (2026.findings-acl)

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Challenge: Existing methods for auxiliary construction training are expensive and underperform . Existing Corresponding Author training methods lack self-correction capabilities in reasoning chains.
Approach: They propose a reinforcement learning framework that rewards auxiliary construction with geometric reasoning by grouping construction rewards with a Length Reward.
Outcome: Experiments on Geometry3K and MathVista show that GeometryZero outperforms baselines on auxiliary constructions.
RLMEval: Evaluating Research-Level Neural Theorem Proving (2025.findings-emnlp)

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Challenge: RLMEval evaluates large language models for research-level neural theorem proving and proof autoformalization . the best model achieves only a 10.3% pass rate on existing benchmarks .
Approach: They propose a new evaluation suite for large language models . it evaluates research-level theorems from real-world Lean formalization projects .
Outcome: RLMEval evaluates research-level theorems from real-world Lean formalization projects.
UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression (2022.emnlp-main)

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Challenge: Existing work on geometry problem solving treats calculation and proving as two specific tasks hindering a deep model to unify reasoning ability on multiple math tasks.
Approach: They propose a large-scale Unified Geometry problem benchmark to unify geometry on multiple math tasks.
Outcome: The proposed framework outperforms the existing model with 5.6% and 3.2% accuracies on calculation and proving problems.
TRIGO: Benchmarking Formal Mathematical Proof Reduction for Generative Language Models (2023.emnlp-main)

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Challenge: Automated theorem proving (ATP) benchmarks focus on symbolic inference but rarely involve understanding complex number combination reasoning.
Approach: They propose a benchmark that requires a model to reduce a trigonometric expression with step-by-step proof and evaluates a generative LM’s reasoning ability on formulas and ability to manipulate, group, and factor number terms.
Outcome: The proposed benchmark evaluates a generative LM’s reasoning ability on formulas and ability to manipulate, group, and factor number terms.
Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models (2026.acl-long)

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Challenge: Existing evaluation frameworks for large reasoning models are saturated by a lack of reliable and verifiable benchmarks.
Approach: They propose a rigorously curated, Olympiad-level math benchmark comprising 350 problems, each with parallel English and Chinese versions.
Outcome: The proposed benchmark unifies two evaluation paradigms and offers 150 problems formalized in Lean 4 for rigorous process-level evaluation.
GOLD: Geometry Problem Solver with Natural Language Description (2024.findings-naacl)

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Challenge: Existing methods for solving geometry math problems struggle with accurately interpreting geometry diagrams, posing a challenge for problem-solving.
Approach: They propose a model that extracts geometric relations from diagrams and converts them into natural language descriptions.
Outcome: The proposed model outperforms the previous best method on the UniGeo dataset by 12.7% and 42.1% in calculation and proving subsets.
An Augmented Benchmark Dataset for Geometric Question Answering through Dual Parallel Text Encoding (2022.coling-1)

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Challenge: Existing methods for solving geometric problems are limited due to lack of high-quality datasets and efficient neural solvers.
Approach: They propose to annotate 2,518 geometric problems with richer types and greater difficulty using a benchmark dataset.
Outcome: The proposed method improves the accuracy of automatic geometric problem solving to 66.09%.
Neural Unification for Logic Reasoning over Natural Language (2021.findings-emnlp)

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Challenge: Automated Theorem Proving (ATP) is a computer program that can show that conjectures are logical consequences of a set of axioms.
Approach: They propose a transformer-based architecture for deriving conjectures given axioms . they propose 'neural unifier' and relative training procedure to train the model .
Outcome: The proposed architectures are able to answer queries with deep queries with a relatively low training time.
Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning (2021.acl-long)

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Challenge: Existing methods for solving geometric problems are either small in scale or not publicly available.
Approach: They propose a large-scale benchmark for geometric problem solving using formal language and symbolic reasoning.
Outcome: The proposed approach parses geometry problems into formal language and performs symbolic reasoning step by step.

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