AI and Mathematics: A Layered Collaboration Framework Under Cognitive Constraints
Year: 2026
Type: preprint
Abstract: The question of whether artificial intelligence can participate in mathematical research has provoked extensive debate, yet existing discussions often overlook the deeper structural constraints that shape this domain. This paper proposes a layered collaboration framework grounded in the recognition of a fundamental mismatch: the semantic cost of mathematical knowledge (D) grows continuously, while an individual's cognitive carrying capacity (A) remains rigidly bounded. We formalize this constraint through the cognitive formula A = B × C, where B represents an improvable efficiency coefficient and C denotes effective cognitive throughput per unit time. Under this framework, we identify five intrinsic properties of mathematics—deterministic combinatorial exploration, embodiment independence, rigid verifiability, strict cumulativity with modular architecture, and aesthetic filtering—that collectively position mathematics as the discipline most naturally aligned with AI capabilities. We further analyze two complementary knowledge expansion paths (concept-first and exhaustive) and establish an equivalence principle: the cognitive value of a discovered truth is path-independent. Building on this analysis, we propose a layered collaboration strategy—Concept-First × Efficient Exhaustion—whose deep mechanism mirrors the evolutionary principle of layer-by-layer automatization with control ascension. Within this framework, black boxes emerge not as a reluctant compromise but as an inevitable consequence of cognitive limits, and AI's role is reframed not as a revolutionizer but as an accelerator that extends the cognitive system's effective capacity. The mathematician's core function consequently transforms from direct execution toward direction design, meaning filtering, cross-modal analogy, and conceptual . The future mathematical community may witness new role divisions, including "AI result interpreters" responsible for translating AI-produced truths into humanly comprehensible frameworks, thereby forming a feedback loop between exploration and assimilation. Ultimately, the relationship between AI and mathematics is not one of replacement but of structural upgrade: humans provide direction and meaning, AI provides efficiency and coverage, the black box serves as their necessary interface, and control ascension remains the only path for the system's continued complexification.
Author: Liu, Hui
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225745747
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