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The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…
LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this…
The ability of large language models to solve complex mathematical problems has progressed significantly, particularly for tasks requiring advanced reasoning. However, the scarcity of sufficiently challenging problems, particularly at the…
Artificial intelligence (AI) has demonstrated impressive progress in mathematical reasoning, yet its integration into the practice of mathematical research remains limited. In this study, we investigate how the AI Mathematician (AIM) system…
Recent advancements have seen Large Language Models (LLMs) and Large Multimodal Models (LMMs) surpassing general human capabilities in various tasks, approaching the proficiency level of human experts across multiple domains. With…
Mathematical reasoning poses significant challenges for Large Language Models (LLMs) due to its demand for multi-step reasoning and abstract conceptual integration. While recent test-time scaling techniques rely heavily on high-quality,…
We present AlphaGeometry2 (AG2), a significantly improved version of AlphaGeometry introduced in (Trinh et al., 2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend…
Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO). However, the training pipelines behind…
This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a…
Recent interest in codifying fairness in Automated Decision Systems (ADS) has resulted in a wide range of formulations of what it means for an algorithmic system to be fair. Most of these propositions are inspired by, but inadequately…
Physics is central to understanding and shaping the real world, and the ability to solve physics problems is a key indicator of real-world physical intelligence. Physics Olympiads, renowned as the crown of competitive physics, provide a…
Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing…
The ellipsoid algorithm is a fundamental algorithm for computing a solution to the system of $m$ linear inequalities in $n$ variables $(P): A^{\top}x \le u$ when its set of solutions has positive volume. However, when $(P)$ is infeasible,…
The International Mathematical Olympiad (IMO) is perhaps the most celebrated mental competition in the world and as such is among the greatest grand challenges for Artificial Intelligence (AI). The IMO Grand Challenge, recently formulated,…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
Recent breakthroughs have spurred claims that large language models (LLMs) match gold medal Olympiad to graduate level proficiency on mathematics benchmarks. In this work, we examine these claims in detail and assess the extent to which…
Bias evaluation in machine-learning based services (MLS) based on traditional algorithmic fairness notions that rely on comparative principles is practically difficult, making it necessary to rely on human auditor feedback. However, in…
AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems. While mid-20th-century symbolic approaches successfully…
Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the…
We present AMO-Bench, an Advanced Mathematical reasoning benchmark with Olympiad level or even higher difficulty, comprising 50 human-crafted problems. Existing benchmarks have widely leveraged high school math competitions for evaluating…