Over the past decade, Professor L. Mahadevan's Soft Math Lab at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) has helped establish how the ancient Japanese paper arts ...

In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped human mathematicians for the last 80 ...

AI can rifle through enormous libraries of information to connect far-flung ideas—conceptual leaps remain a purely human skill. The planar unit distance problem, or Erdős problem 90, has intrigued ...

The blockbuster game Minecraft depicts a world created by cubes: everything is made of discrete building blocks. It may therefore seem particularly unsuitable for calculating pi (π), the mathematical ...

Three mathematicians have laid out proof that solves a long-standing problem in mathematics. Even the mathematician—an Abel prize winner—that first posed the problem didn't believe it would ever be ...

On May 20, 2026, OpenAI announced that its internal AI model had disproven a long-held prediction regarding the 'unit distance problem,' a central unsolved problem in discrete geometry. The unit ...

Alongside the famous gigantic black holes, physics also allows for microscopic versions. They emerge from so-called critical states, when spacetime organizes itself into a regular, crystal-like ...

Abstract: In this work, an including the switched evolution process discrete model of a DC-DC converter feeding a switched constant power load is proposed based on the Poincaré mapping rule and matrix ...

Abstract: In the design of self-checking discrete devices, the main tasks are to achieve the smallest structural redundancy of the concurrent error-detection circuits and to ensure the checkability of ...

A special set of numbers has formed the backbone of nuclear physics research for decades, and now we finally know how it arises from the quantum mix of nuclear particles and forces. Nearly 80 years ...