Think about placing dots on a flat surface. You want as many pairs as possible to be separated by the same distance. For any amount of dots, what is the greatest possible number of pairs that can be ...

“If you are a mathematician,” one of the world’s leading mathematicians recently wrote, “you may want to make sure you are sitting down before reading further.” And you’ll definitely need to sit down ...

For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the planar unit distance problem. The question posed by the legendary Hungarian ...

OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946. If this sounds ...

In October 2024 I attended a workshop at Harvard University where mathematicians talked through the uses of artificial intelligence in their field. Most were less worried about the future of math than ...

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: Aiming at the problem of large errors in blind symbol rate estimation of Frequency Shift Keying (FSK) signals under low signal-to-noise ratio (SNR) and multipath fading, this paper proposes ...

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In recent months, leaders in several cities and states have touted their schools’ sky-high graduation rates. Such figures usually justify celebration—but not when state exams and standardized test ...

The U.S. high school graduation rate is among the highest in years, with 86 percent of seniors attaining a diploma after four years of study. The rate should be a reason to crow. But it isn’t. The ...