While development teams around the world, including those in Silicon Valley, are enthusiastic about code generation by generative AI and its "probabilistic correctness (accuracy)," a completely ...

It would be hard to overstate the importance of making certain that critical systems like cryptographic protocols and digital circuits perform the way they’re supposed to perform. Formal verification ...

Automated theorem proving in geometry systems unites symbolic logic, computer algebra and machine learning to verify and discover geometric propositions without human intervention. Historically rooted ...

Mathematician Kevin Buzzard of Imperial College London is training computers how to prove one of the most famous problems in math history: Fermat’s last theorem. Resolving the problem isn’t the point.

Kurt Gödel, the man who ruined mathematics, was one of the most important thinkers of the 20th century. He was born in 1906, smack-bang in the middle of the greatest crisis that maths has ever known.

Abstract: Formal verification is a crucial means to assure software quality. Regrettably, the manual composition of verification scripts proves to be both laborious and time-consuming. In response, ...

DENVER — An urgent call comes in from the White House. But the recipient is skeptical: They need a way to verify that the message comes from the purported location. Quantum physics has a solution.

The central limit theorem started as a bar trick for 18th-century gamblers. Now scientists rely on it every day. No matter where you look, a bell curve is close by. Place a measuring cup in your ...

Mathematics is often seen as perfect—consistent, complete, and immune to contradiction. But in the early 20th century, a breakthrough proved that no mathematical system can ever explain everything ...

Large language models (LLMs) have astounded the world with their capabilities, yet they remain plagued by unpredictability and hallucinations – confidently outputting incorrect information. In ...

Talia Ringer is in the Siebel School of Computing and Data Science, University of Illinois at Urbana–Champaign, Urbana, Illinois, 61801, USA. Read the paper: Olympiad-level formal mathematical ...