No importance ranking can be simultaneously faithful, stable, and complete under symmetry — at any level of a model, from input features to internal circuits — and we prove it in Lean 4. If you have ...

Metric geometry is a considerable extension of Riemannian geometry that, in recent decades, has proven very useful. A newer direction described in this article can moreover be viewed as an extension ...

Maybe people who are all excited about the “field with one element” should start at the beginning and think a bit about the “group with no elements”. Why? Clearly every group has such a multiplication ...

We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison [Fuglede B, Kadison R (1952) Ann Math 55:520–530], and a generalization for appropriate groups of ...

The discussion on Tom’s recent post about ETCS, and the subsequent followup blog post of Francois, have convinced me that it’s time to write a new introductory blog post about type theory. So if ...