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2 results for “counterexamples”
SPIN Processed News Frame: The Hype
INSPIRE: An Internalize-Then-Improve Approach for Example-Driven Mathematical Reasoning
A new research paper introduces INSPIRE, a two-stage training method for LLMs that aims to improve example-driven mathematical reasoning by first internalizing the strategy and then refining correctness — addressing a gap in how models learn conceptual understanding versus pattern-matching.
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arXiv Computation and Language
Aug 31, 2026
SPIN Processed News Frame: The Shield
Fields Medalist Timothy Gowers says most famous mathematics problems solved by LLMs so far have almost all been with counterexamples rather than proofs (Timothy Gowers/Gowers's Weblog)
Fields Medalist Timothy Gowers observes that LLMs have predominantly generated counterexamples—not formal proofs—for famous unsolved mathematics problems, highlighting a persistent gap between symbolic pattern-matching and rigorous deductive reasoning.
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Techmeme
Aug 16, 2026