# Uncertainty in Authorship: Why Perfect AI Detection Is Mathematically Impossible

arXiv: https://arxiv.org/abs/2509.11915 · HTML: https://mlsanity.com/paper/2509.11915/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 24 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Ethical and social risks of harm from Language Models](https://mlsanity.com/paper/2112.04359/) (2021)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [Testing of Detection Tools for AI-Generated Text](https://mlsanity.com/paper/2306.15666/) (2023)
- [Humanizing Machine-Generated Content: Evading AI-Text Detection through Adversarial Attack](https://mlsanity.com/paper/2404.01907/) (2024)
- [Detecting AI-Generated Text: Factors Influencing Detectability with Current Methods](https://mlsanity.com/paper/2406.15583/) (2024)
- [Detection of Machine-Generated Text: Literature Survey](https://mlsanity.com/paper/2402.01642/) (2024)
- [On the uncertainty principle of neural networks](https://mlsanity.com/paper/2205.01493/) (2022)
- [Stylometric Watermarks for Large Language Models](https://mlsanity.com/paper/2405.08400/) (2024)
- [Distinguishing AI-Generated and Human-Written Text Through Psycholinguistic Analysis](https://mlsanity.com/paper/2505.01800/) (2025)

## Built on by (most cited first, 2 of 2)

- [On the Detectability of LLM-Generated Text: What Exactly Is LLM-Generated Text?](https://mlsanity.com/paper/2510.20810/) (2025)
- [Detecting Cognitive Signatures in Typing Behavior for Non-Intrusive Authorship Verification](https://mlsanity.com/paper/2603.00177/) (2026)

## Abstract (arXiv)

As large language models (LLMs) become more advanced, it is increasingly difficult to distinguish between human-written and AI-generated text. This paper draws a conceptual parallel between quantum uncertainty and the limits of authorship detection in natural language. We argue that there is a fundamental trade-off: the more confidently one tries to identify whether a text was written by a human or an AI, the more one risks disrupting the text's natural flow and authenticity. This mirrors the tension between precision and disturbance found in quantum systems. We explore how current detection methods--such as stylometry, watermarking, and neural classifiers--face inherent limitations. Enhancing detection accuracy often leads to changes in the AI's output, making other features less reliable. In effect, the very act of trying to detect AI authorship introduces uncertainty elsewhere in the text. Our analysis shows that when AI-generated text closely mimics human writing, perfect detection becomes not just technologically difficult but theoretically impossible. We address counterarguments and discuss the broader implications for authorship, ethics, and policy. Ultimately, we suggest that the challenge of AI-text detection is not just a matter of better tools--it reflects a deeper, unavoidable tension in the nature of language itself.