Learning to Discover Interesting Mathematics

arXiv:2609.28603 · cs.LG, cs.AI · Submitted 2026-09-23 · Read on arXiv

cs.LG, cs.AI

Submitted: 2026-09-23

Updated: 2026-09-23

Code: https://github.com/radixark/miles

Terminology

• Pruning — 17× in this paper · explained in 4 episodes
• GRPO — 5× in this paper · explained in 6 episodes
• Reinforcement Learning — 4× in this paper · explained in 4 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Axioms — 3× in this paper · explained in 2 episodes
• Core — 3× in this paper · explained in 2 episodes
• Verification — 3× in this paper · explained in 2 episodes
• Ablation — 2× in this paper · explained in 1 episode
• Abstraction — 2× in this paper · explained in 1 episode
• Commentary — 2× in this paper · explained in 2 episodes
• Grounding — 2× in this paper · explained in 3 episodes
• LLM-as-a-Judge — 2× in this paper · explained in 3 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Calibration — 1× in this paper · explained in 7 episodes
• Hypergraph — 1× in this paper · explained in 2 episodes
• LLM judge — 1× in this paper · explained in 2 episodes
• Large Language Models (LLMs) — 1× in this paper · explained in 6 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Compression is all you need: Modeling Mathematics
• Short proofs in combinatorics and number theory
• Short proofs in combinatorics, probability and number theory II
• Remarks on the disproof of the unit distance conjecture
• Formalization of De Giorgi--Nash--Moser Theory in Lean
• ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics
• Artificial Intelligence and the Structure of Mathematics
• Moonshine: An Autonomous Mathematical Research Agent Centered on Conjecture Generation
• Automated conjecturing with \emph{TxGraffiti}
• In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator
• Automatic Textbook Formalization
• Autonomous disproofs of the sum-product conjecture over $\mathbb R$ with GPT-5.5 Pro
• Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving
• A Matter of Interest: Understanding Interestingness of Math Problems in Humans and Language Models
• AlphaEvolve: A coding agent for scientific and algorithmic discovery
• A proof of the cycle double cover conjecture by OpenAI: An exposition
• Learning Formal Mathematics From Intrinsic Motivation
• Generative Language Modeling for Automated Theorem Proving
• Formalizing Mathematics at Scale
• DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition

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