AI Learned to Write Like You. Detection Is Mathematically Impossible.

Without collaboration from the model (such as watermarking), the text itself contains no provable evidence of its origin.

The issue is not new, but it deserves to be addressed once again. It is 2026, and there are still people using AI detectors to determine if a text has been written by AI or by a human. Even worse, some strongly believe the task at hand is actually trivial, and they can accurately make the distinction on the spot.

But reality and math disagree. And disagreeing with reality and math is one powerful way to disseminate misinformation and promote pseudoscience.

What Folklore Says

Without dedicating time to understanding the fundamental problems associated with distinguishing between AI-generated and human-generated text, one can be tempted to undermine the complexity of the challenge. And yet, some seem very certain about how straightforward it is to make this determination. The source of this confidence is typically followed by two major justifications:

• “I just know. I can tell right away. The patterns… they are way too obvious.”

• “Because a tool I use said so.”

If only life could be this simple.

What Reality Says

It has been demonstrated that AI detectors like ZeroGPT simply don't work. Failing examples include identifying the text of the US Constitution as 96.21% generated by AI.

OpenAI used to have its own AI detection tool while being vocal about its limitations:

While some (including OpenAI) have released tools that purport to detect AI-generated content, none of these have proven to reliably distinguish between AI-generated and human-generated content.

After consecutive failures and “an abysmal 26 percent accuracy rate,” OpenAI discontinued its AI detection tool. The root of the problem: unproven detection metrics.

An article published on MIT Management alerts instructors that AI detection tools don't work and can lead them to falsely accuse students of misconduct. In the same line of concern, an article published on the Washington Post discusses an investigation into the capabilities of AI detectors:

I think we should just get used to the fact that we won’t be able to reliably tell if a document is either written by AI — or partially written by AI, or edited by AI — or by humans.

Another article on Prompt Engineering states that there is no nuance in the accuracy issue of AI detection tools. The core problem is clear: they just don't work.

The core weakness is that text characteristics alone cannot reliably indicate authorship. Without directly tracing content to an AI model at the exact point in time and settings, determinations are vulnerable to errors, manipulation, and inherent biases. Claims of accuracy should be scrutinized given these fundamental challenges.

Many universities have long decided to stop using AI detectors since they cause more harm than good. The Office of Teaching, Learning, and Technology of the University of IOWA recommends avoiding AI detection tools and seeking alternative methods for ensuring academic integrity.

An article on Forbes discuss multiple occasions where AI detectors consistently failed to provide any reasonable accuracy, including the bizarre case of a lawsuit from 1993 that was flagged as 100% written by AI:

The lawsuit Liebeck v McDonald’s was written in 1993,” she explained. “Way before ChatGPT and other generative AI programs came out.” But ZeroGPT says it is 100% sure that it was written by AI. Baffling. Mason adds, “you shouldn’t be using AI detector tools at all to identify whether AI was used to create content.”

Michael Rurup Andersen adds:

Been showing examples to my clients of how the Bible is 98.9% written by AI as well. You really can’t rely on these detectors.

What Math Says

The Intuition

The core idea is actually simple and it is not required a degree in mathematics to understand. Large language models are trained to produce text that is indistinguishable from human text. That is the explicit objective of every dollar spent on training, every GPU-hour burned, every data point fed into the model, which all pushes it closer to one goal: make the output look like something a human would write.

Now think about what we are asking an AI detector to do. We are asking it to find differences between AI text and human text. But the model was specifically trained to eliminate those differences. The better the model gets at its job, the worse every detector performs. These two goals are in direct opposition. This is a mathematical constraint that does not go away if one attempts to improve existing AI detectors.

The training process minimizes a quantity called the KL divergence, which roughly measures how different the model’s output is from human text. As this quantity shrinks, there is a hard ceiling on how accurate any detector can be. That ceiling is set by a classical result in statistics and it has nothing to do with how good the detector is. When the divergence is small, the best any detector can achieve is similar to a coin flip.

A die-hard AI-detection supporter could then say:

Alright, maybe one text is hard to detect, but I am 100% confident that if I collect several texts from the same person, I can spot a pattern.

The math addresses this too. Even with multiple samples, the detection advantage grows only as the square root of the number of texts. If the per-text difference is small, you need an astronomically large number of samples to have any chance of achieving a minimally reliable detection.

And every new generation of models makes the per-text difference even smaller and the astronomically large number of samples required even larger.

I am pretty sure AI can detect writing style.

But style is just another statistical feature. If the model’s distribution is close to the human distribution, then the style is close too. Stylometric analysis, zero-shot statistical tests, perplexity-based methods, trained classifiers: they all hit the same ceiling. The math does not care which method you use.

Is there a way to surely detect AI-generated text? Yes. But only with the cooperation of the generator. Techniques like watermarking (where the model embeds a hidden signal in its output) can work. But that requires the AI company to participate and it is not something an AI detector can do after the fact.

The Math

We have two probability distributions. One is P, the distribution of human text. The other is Q, the distribution of text produced by a language model. An AI text detector is simply a function that receives a text and guesses which distribution it came from.

How good can a detector be? There is a classical result in statistics, dating back to Neyman and Pearson in 1933, that answers this exactly. The maximum accuracy of any detector is bounded by:

\(\text{Accuracy} \leq \frac{1}{2} + \frac{1}{2} , d_{TV}(P, Q)\)

where d_TV is the total variation distance between the two distributions. Think of it as a single number that measures how different AI text is from human text. This is an exact upper bound. No detector, no matter how sophisticated, can exceed it.

Now, what happens during training? Language models are trained by minimizing cross-entropy loss, which is equivalent to minimizing the KL divergence. A classical inequality due to Pinsker connects it directly to total variation:

\(d_{TV}(P, Q) \leq \sqrt{\frac{D_{KL}(P | Q)}{2}}\)

This gives us the complete chain:

• Training reduces KL divergence

• KL divergence bounds total variation

• Total variation bounds detection accuracy.

As training improves, KL divergence shrinks. As KL divergence shrinks, total variation shrinks. As total variation shrinks, the best possible detector converges toward 50% accuracy (again, the same as flipping a coin).

That is the entire argument with three facts, chained together. In fact, each one of them is individually uncontroversial. There is no way to scape the conclusion.

What about scaling? Empirical scaling laws show that KL divergence decays as a power law in the number of training parameters N:

\(D_{KL}(P | Q) \approx \beta , N^{-\alpha}\)

where published estimates place α between 0.07 and 0.34. Substituting into the bound above, the best any detector can achieve scales as:

\(\text{Accuracy} \leq \frac{1}{2} + O(N^{-\alpha/2})\)

This is not a hypothetical. It means that every time the model doubles in size, the ceiling on detection accuracy drops by a predictable, measurable amount. The gap between the best possible detector and a coin flip, which is already substantially small, is shrinking on a schedule.

For the full formal treatment, including extensions to multi-sample detection, conditional (per-context) distributions, stylometric analysis, and the proof that generator cooperation through watermarking is the only viable path, see the complete paper: Indistinguishable by Design: On the Impossibility of AI Text Detection Without Generator Cooperation.

It's Not X. It's Y.

Gues who taught the structure “It's not X. It's Y” to LLMs? We, humans, did.

See this video from Will.I.Am. He is giving an interview about AI and he says:

It's not the AI they should be afraid of or concerned with. It's the business practices by the companies that deploy the AI.

This is how we talk, naturally.

It is not an isolated case. Below are a few more examples:

It’s not the heat. It’s the humility. - Yogi Berra

The Yogi Book (Workman Publishing, 1998).

It’s not the plan that matters. It’s the planning. - Peter Drucker

Managing the Non-Profit Organization (HarperCollins, 1990).

It’s not the tools you have faith in. It’s the people you have faith in.

The Lost Interview (1995).

It’s not greed that drives the world. It’s envy. - Warren Buffett

Berkshire Hathaway Annual Meeting (2019).

It’s not the model that matters. It’s how the model is used. - George Box

Science and Statistics, Journal of the American Statistical Association, Vol. 71, No. 356 (1976).

It’s not whether you get knocked down. It’s whether you get back up. - Vince Lombardi

The Lombardi Rules (McGraw-Hill, 2001).

It’s not the votes that count. It’s who counts the votes. - H. L. Mencken

The Chicago Tribune (1920).

It’s not what happens to us. It’s how we respond.

The 7 Habits of Highly Effective People (Free Press, 1989).

It’s not the will to win that matters. It’s the will to prepare. - Ben Hogan

Ben Hogan’s Five Lessons (1957).

“It's not X. It's why” is a linguistic construction, more specifically, a “contrastive negation followed by a corrective assertion.” It's part of a rich “grammatical context for negated restrictives in English.” Olli O. Silvennoinen wrote an entire doctoral dissertation of 131 pages on contrastive negation.

Be a Rebel

You don't want to sound like AI? You will either eventually sound more robotic than AI (since AI is getting better at sounding more and more like a human) or you will end up suppressing every feature of competent writing (syntax, nuance, cadence, argumentation), resulting in something grammatically poor, rhetorically dull, and indistinguishable from the very mediocrity you are trying to avoid.

Be a rebel in today's era. Write proper English. Use em dashes, a wide range of linguistic constructions, rich advetives and whatever else you need, as a tool, to communicate. Don't dumb it down or compromise so you “don't sould like AI.”