Four Fields Medals, one machine proof and the question of what the prize is for

Yu Deng, John Pardon, Jacob Tsimerman and Hong Wang received the 2026 Fields Medals in Philadelphia on 23 July. Seven weeks later an AI swarm settled a version of Navier–Stokes and Tristan Buckmaster said the mathematician who built the method deserves a medal. A prize for promise now has to say whose promise it means.

The word problem: five political books and the vocabulary of the authoritarian turn

Susan Neiman wants the word 'evil' back. Byung-Chul Han wants 'respect'. Žižek and Butler think the words on offer are traps. Habermas, in a volume finished before his death, denied that anything was lost. The year's other book list, read as one argument.

Byung-Chul Han, Judith Butler, Slavoj Žižek, Jürgen Habermas, Susan Neiman

Four meetings in one day, and a discipline growing only at its edges

On 16 September a congress in Freiburg, a three-day conference in Malta, an hour-long seminar in Bristol and a five-day roundtable on Zoom were all in session. None of the four could have been staffed from a single philosophy department, and that is the story.

Miranda Fricker

Althusser's theory of ideology has outlived the Marxism it defended

Louis Althusser built the concept of interpellation to protect a scientific reading of 'Capital'. The science was abandoned; the street scene went everywhere. A reckoning with what survives, what does not, and the killing that the profession spent forty years learning how to describe.

Judith Butler, Gilles Deleuze, Jacques Rancière, Louis Althusser

Jacques Rancière and the argument he has made five times

Archive research, pedagogy, political theory, film and literature: across sixty years Jacques Rancière has restated one claim in five different materials. Equality is not a destination but a premise, and politics is the moment someone demonstrates it. The claim has costs, and his critics have named them precisely.

Alain Badiou, Jacques Rancière, Louis Althusser

The proof no one has read: OpenAI, Navier–Stokes and the limits of verification

OpenAI says an internal system proved that a three-dimensional fluid can blow up in finite time, and Lean agrees. The theorem is narrower than the headlines, the credit is contested, and the deeper question is what mathematics loses when a result is certified but unread.

John Searle

Pomponazzi, Smart, Hurley and Lara: four arguments about the limits of proof

Pietro Pomponazzi was born on 16 September 1462, J. J. C. Smart on 16 September 1920, Susan Hurley and María Pía Lara on 16 September 1954. Four philosophers across five centuries, and one question between them: what can be demonstrated about the mind, and what has to be settled some other way.

David Chalmers, Andy Clark, Daniel Dennett, Saul Kripke, Pietro Pomponazzi, J. J. C. Smart, Susan Hurley