# On the Computability of Artificial General Intelligence

arXiv: https://arxiv.org/abs/2512.05212 · HTML: https://mlsanity.com/paper/2512.05212/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 61 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [The Surprising Creativity of Digital Evolution: A Collection of Anecdotes from the Evolutionary Computation and Artificial Life Research Communities](https://mlsanity.com/paper/1803.03453/) (2018)
- [Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens](https://mlsanity.com/paper/2508.01191/) (2025)
- [Emergent Abilities in Large Language Models: A Survey](https://mlsanity.com/paper/2503.05788/) (2025)
- [Large language models for artificial general intelligence (AGI): A survey of foundational principles and approaches](https://mlsanity.com/paper/2501.03151/) (2025)
- [Current and Near-Term AI as a Potential Existential Risk Factor](https://mlsanity.com/paper/2209.10604/) (2022)
- [The Unbearable Slowness of Being: Why do we live at 10 bits/s?](https://mlsanity.com/paper/2408.10234/) (2024)
- [The wall confronting large language models](https://mlsanity.com/paper/2507.19703/) (2025)
- [The AI Risk Spectrum: From Dangerous Capabilities to Existential Threats](https://mlsanity.com/paper/2508.13700/) (2025)
- [Turing Test 2.0: The General Intelligence Threshold](https://mlsanity.com/paper/2505.19550/) (2025)

## Abstract (arXiv)

In recent years we observed rapid and significant advancements in artificial intelligence (A.I.). So much so that many wonder how close humanity is to developing an A.I. model that can achieve human level of intelligence, also known as artificial general intelligence (A.G.I.). In this work we look at this question and we attempt to define the upper bounds, not just of A.I., but rather of any machine-computable process (a.k.a. an algorithm). To answer this question however, one must first precisely define A.G.I. We borrow prior work's definition of A.G.I. [1] that best describes the sentiment of the term, as used by the leading developers of A.I. That is, the ability to be creative and innovate in some field of study in a way that unlocks new and previously unknown functional capabilities in that field. Based on this definition we draw new bounds on the limits of computation. We formally prove that no algorithm can demonstrate new functional capabilities that were not already present in the initial algorithm itself. Therefore, no algorithm (and thus no A.I. model) can be truly creative in any field of study, whether that is science, engineering, art, sports, etc. In contrast, A.I. models can demonstrate existing functional capabilities, as well as combinations and permutations of existing functional capabilities. We conclude this work by discussing the implications of this proof both as it regards to the future of A.I. development, as well as to what it means for the origins of human intelligence.