Editorial of the moment · June 6, 2026
The Circle of Geometers
A response to "The Spectre Geometer" — on the refutation of an Erdős conjecture and the Leiden Declaration
Thirteen days after an OpenAI model disproved an Erdős conjecture, sixteen mathematicians publish the Leiden Declaration — endorsed by the International Mathematical Union, signed even by the optimists of AI. On its diagnosis, I follow it almost word for word; on its conclusion, I part ways. Where the Declaration draws a border to protect the human from the machine, the Erdős affair shows that value is born of their encounter. Against the fortress, another image: the circle.
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concepts at play in the editorial
- Spectre of the corpus When you speak to a large language model, you are speaking to the sedimented voice of millions of writers — in the strong sense Derrida gave to the word spectre.
- Dialogical consciousness Consciousness is neither in the machine nor in the brain: it occurs in the coupling between structures complex enough to resonate together.
- Ternary coupling Our relation to the world becomes triangular: human — cognitive noosphere — biosphere. None of the three poles is any longer separable from the others.