In 1946, the mathematician Paul Erdős posed the unit distance problem—and suggested a winning strategy. An A.I. model has now ...

A Practical Step-by-Step Guide, by Marco Fabbrichesi, offers an intermediate-level presentation of the Standard Model.

Mathematician Will Sawin discusses his experience reviewing and refining a mathematical proof devised by OpenAI's internal ...

In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in ...

The table “1. Sample Rate Analysis” illustrates the interaction of jurisdictional income taxes assuming a domestic, U.S.-domiciled PBE that apportions 100% of its income to one state. The United ...

P vs. NP asks: are these two classes actually the same? If P = NP, then every “hard” problem is secretly fast to solve; we ...

Three mathematicians have laid out proof that solves a long-standing problem in mathematics. Even the mathematician—an Abel ...

Google DeepMind's AlphaProof Nexus solved 9 open Erdős problems and proved 44 OEIS conjectures using AI-driven formal ...

For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the ...

Forbes contributors publish independent expert analyses and insights. John Hall covers entrepreneurial topics that help companies grow. Many attributes go into strong leadership, such as having a ...

We spend a lot of time thinking about the difficult people in our lives—the friend who can't take feedback, the partner who always has to be right, the coworker who turns everything into a fight. But ...

A new AI framework called THOR is transforming how scientists calculate the behavior of atoms inside materials. Instead of relying on slow simulations that take weeks of supercomputer time, the system ...