Why fake proofs?
Advances in artificial intelligence and Large Language Models make it increasingly easy to generate mathematical explanations and proofs. As Terence Tao puts it, we are experiencing a transition from “proof scarcity to proof abundance”.
However, these models also produce misinformation and apparent knowledge built on incorrect reasoning. It becomes more important to read it critically: check the hypotheses, justify each implication, and distinguish a plausible argument from a valid proof.
This page collects examples of fake proofs from some mathematics courses I have taught. Some are inspired by mistakes in students’ homework; others are generated entirely by AI.
They are exercises in developing a critical mindset toward mathematical arguments, including those produced by AI.
Your task
- Identify exactly where the proof goes wrong.
- Decide whether the original statement is correct. If it is, give a correct proof. If it is not, give a counterexample.