A Codex skill for hard theoretical proof discovery, proof debugging, and failed-proof recovery. It helps Codex stop looping on the same missing lemma. The workbench preserves the exact theorem ...

A straightforward conjecture about runners moving around a track turns out to be equivalent to many complex mathematical questions. Three new proofs mark the first significant progress on the problem ...

Self-driving cars, autonomous robots, modern airplanes, or robotic surgery: we increasingly entrust our lives to computers and therefore should strive for nothing but the highest safety standards - ...

Abstract: Learning-based methods have gained popularity for training candidate Control Barrier Functions (CBFs) to satisfy the CBF conditions on a finite set of sampled states. However, since the CBF ...

Abstract: Hardware verification is crucial to ensure the cor-rectness in the logic design of digital circuits. The purpose of verification is to either find bugs or show their absence. Prior works ...

Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a mathematician astray. Early evidence might not represent the bigger picture ...

Elon Musk's long-promised launch of encrypted direct messages on Twitter has arrived. Like most attempts to add end-to-end encryption to a massive existing platform—never an easy proposition—there's ...

This paper reviews existing computer-supported learning systems that have claimed to adopt Socratic methods for enhancing critical thinking. Several notions of Socratic methods are differentiated: the ...

We introduce a class of exactly solvable models with surprising properties. We show that even simple quantum matter is much more entangled than previously believed possible. One then expects more ...

I’ve just started teaching an advanced undergraduate course on Fourier analysis — my first lecturing duty in my new job at Edinburgh. What I hadn’t realized until I started preparing was the ...