Little progress had been made in solving Ramsey problems since the 1930s. Now, researchers have found the answer to r(4,t), a longstanding Ramsey problem that has perplexed the math world for decades.

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing ...

Abstract: When realizing multiagent optimal consensus control, it may encounter the situation that malicious agents transmit false information. Besides, due to the unreliability of information ...

Some readers may solve the problem procedurally: line up the two numbers, add the ones column, carry the one, and add the tens to get 43. Others might instead notice a creative shortcut: 29 + 14 is ...

In a dark room, in the middle of the night, a woman lies dreaming. Suddenly, her eyes beneath their lids dart crisply left-right, left-right. The eye signal means she knows she’s dreaming. Lucid ...

At a secret meeting in 2025, some of the world's leading mathematicians gathered to test OpenAI's newest large language model, o4-mini. Experts at the meeting were amazed by how much the model's ...

The findings, published in Personality and Individual Differences, show that people with strong ADHD symptoms, such as inattention, hyperactivity and impulsivity that can impair some aspects of daily ...

It's a well-known fact that quantum calculations are difficult, but one would think that quantum computers would facilitate the process. In most cases, this is true. Quantum bits, or qubits, use ...

This is a graphical user interface (GUI) application built with Python and Tkinter, designed to solve linear programming problems using SciPy's optimization library (linprog). Generates a plot of the ...

You probably don’t need more time. By Jancee Dunn When I look back on all the major decisions I’ve dithered over, I could scream. It took me a decade to commit to becoming a parent. I wavered for a ...

The Greek philosopher Plato wrote about Socrates challenging a student with the "doubling the square" problem in about 385 B.C.E. When asked to double the area of a square, the student doubled the ...