Аннотация

Artificial General Intelligence (AGI) is a concept that evokes both excitement and apprehension. While some view it as a promising dream, others perceive it as a looming nightmare. This paper aims to give strong evidence - or, to be more precise: to provide mathematical proof that these anticipatory feelings are largely unfounded, suggesting that AGI will remain an aspirational dream rather than a tangible reality.

To achieve that, we will argue that AGI, as commonly defined, is logically impossible. Regardless of the sophistication, complexity, power, data volume, or expertise of the algorithmic architecture, machine, or human workforce, AGI will never materialise. This notion may seem counterintuitive, but it is rooted in the fundamental limitations of computation.

This is because the nature of computation inherently imposes certain constraints that prevent systems from generating conceptual primitives beyond their symbol set, non-computing paradigm shifts, and statistical breakdowns in heavy-tailed decision spaces.

These theoretical limits are established by building upon foundational works by Shannon, Gödel, Turing, and Kant. The Infinite Choice Barrier theorem, derived from these works, demonstrates that for any algorithmic system, there exist decision contexts where optimal performance is structurally unattainable.

While the impossibility of AGI is not empirical but mathematical, it is supported by empirical evidence from contemporary AI scaling behaviour. The latest and most impressive of them occurred after this paper was published on preprint; the first came from the Apple research group (Shoojee et al., 2025) and showed that alorithmic reasyoning models seem to have very obvious problems solving certain types of tasks.

Also, earlier research also showed: Despite exponential increases in compute and data, systems like DeepMind (2022), OpenAI (2023), and Anthropic (2023) exhibit asymptotic performance ceilings. This suggests that cognitive generality by scaling, as the prevailing narrative implies, does not seem to be a viable strategy.