#mathematical-proof News & Analysis

6 articles tagged with #mathematical-proof. AI-curated summaries with sentiment analysis and key takeaways from 50+ sources.

6 articles

AIBearisharXiv – CS AI · Jun 257/10

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Failure Modes of Large Language Models on Research-Level Mathematics: A Taxonomy and an Empirical Characterisation

Researchers identify four specific failure modes in large language models attempting research-level mathematics: citation fabrication, premise smuggling, silent problem reformulation, and local-to-global compatibility gaps. Testing reveals that premise smuggling—where models assert unjustified claims as fundamental results—persists even when citations are accurate, suggesting retrieval-augmented generation alone cannot solve LLM reasoning failures.

🧠 Gemini

AIBullishFortune Crypto · Jun 17/10

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Exclusive: Economists have been teaching a broken proof for 50 years. AI just found it

Axiom Math, a $1.6B AI unicorn, is using formal verification to audit economic theorems and has discovered significant gaps in foundational antitrust law that economists have relied on for 50 years. This discovery highlights how AI can identify mathematical flaws in established economic theory that human experts overlooked.

AINeutralarXiv – CS AI · May 117/10

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Limitations on Accurate, Trusted, Human-level Reasoning

Researchers prove a fundamental mathematical incompatibility between accuracy, trust, and human-level reasoning in AI systems, demonstrating that systems designed to never make false claims cannot solve certain problems that humans can easily solve. The findings parallel Gödel's incompleteness theorems and establish formal limitations on what AI systems can achieve regardless of computational power.

AINeutralarXiv – CS AI · Apr 107/10

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The Defense Trilemma: Why Prompt Injection Defense Wrappers Fail?

Researchers prove mathematically that no continuous input-preprocessing defense can simultaneously maintain utility, preserve model functionality, and guarantee safety against prompt injection attacks in language models with connected prompt spaces. The findings establish a fundamental trilemma showing that defenses must inevitably fail at some threshold inputs, with results verified in Lean 4 and validated empirically across three LLMs.

AINeutralarXiv – CS AI · May 296/10

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Real-rootedness of the Poincar\'e polynomials of $\overline{\mathcal M}_{0,n}$: an AI-assisted proof

Researchers used AI-assisted methods to prove that Poincaré polynomials of moduli spaces of rational curves have only real roots, resolving a longstanding conjecture in algebraic geometry. The breakthrough employs a novel bivariate deformation technique that reveals hidden mathematical structures, with implications for understanding the topological properties of geometric spaces.

🏢 Google

AINeutralarXiv – CS AI · Mar 53/10

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Maximin Share Guarantees via Limited Cost-Sensitive Sharing

Researchers present new theoretical frameworks for fair allocation of indivisible goods when limited sharing is allowed among agents. The study introduces cost-sensitive sharing mechanisms and proves that maximin share (MMS) allocations can be guaranteed under specific conditions, while also establishing new fairness concepts like Sharing Maximin Share (SMMS).

🏢 Meta