arXiv:2606. 14688v1 Announce Type: cross Abstract: AI systems coupled to proof assistants now generate formal mathematics at scale, and the gap between what a checker can verify and what a mathematician would value has become the binding constraint.
arXiv:2606. 28572v1 Announce Type: cross Abstract: The axiom of choice has divided the foundations of mathematics for over a century, but the distinction between classical and constructive proofs has remained a philosophical and methodological one.
arXiv:2606. 16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended.
arXiv:2606. 25777v1 Announce Type: cross Abstract: We initiate a resource-aware theory of \textit{language generation in the limit} under the minimal constraint of space efficiency.
arXiv:2607. 23361v1 Announce Type: cross Abstract: Language generation in the limit is an elegant model introduced by Kleinberg and Mullainathan [KM24] to formally study language generation by an algorithm that learns solely based on example strings.
arXiv:2608. 15979v1 Announce Type: new Abstract: Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules.
arXiv:2608. 01320v1 Announce Type: cross Abstract: Language generation in the limit is a theoretical framework for studying how a generator can learn to produce new valid strings from a stream of positive examples.
arXiv:2303. 04203v4 Announce Type: replace Abstract: The theory of computation was built to answer Turing's question: what is effectively calculable by an unbounded, immortal, disembodied agent following rules?
arXiv:2608. 15147v1 Announce Type: new Abstract: Machine intelligence has conquered the symbolic world but stalled at the physical one.
arXiv:2505. 18492v5 Announce Type: replace Abstract: Mathematical competition problems fall into two broad types: theorem proving, which asks for a proof of a given statement, and answer construction, which requires constructing a property-satifying object with proofs.
arXiv:2606. 19354v1 Announce Type: cross Abstract: Test-time scaling (TTS) has emerged as a powerful paradigm for improving the reasoning performance of large language models (LLMs) by investing additional compute at inference time.
arXiv:2606. 31845v1 Announce Type: cross Abstract: A transformer's feed-forward (FFN) sublayer materializes the distinctions attention gathers, yet gives no account of what it computes.
arXiv:2607. 04505v1 Announce Type: new Abstract: We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction.