“Our goal was to build a clear mathematical bridge between abstract algebra and the experience of listening to music,” said study co-author Olga Ibragimova. “When we think of melodies as shapes we can ...

Why do some melodies feel instantly right, balanced, memorable and satisfying, even if you have never heard them before? New research from the University of Waterloo suggests that more than creativity ...

Why do some melodies feel instantly right, balanced, memorable and satisfying, even if you have never heard them before? New research from the ...

Large language models struggle to solve research-level math questions. It takes a human to assess just how poorly they perform. By Siobhan Roberts A few weeks ago, a high school student emailed Martin ...

02/02/2026 Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo A team of theoretical researchers have found duality can unveil non-invertible symmetry protected ...

Abstract: Output controllability and functional observability are properties that enable, respectively, the control and estimation of part of the state vector. These notions are of utmost importance ...

Abstract: Background: The COVID-19 pandemic and the shift to digital learning materials have dramatically reduced the use of paper-based textbooks in higher education. In the field of engineering, ...

The recent news about plummeting math preparation among University of California, San Diego, students was startling: Over five years, the number of incoming students deemed to need remedial math ...

American rock climber Sean Bailey has made the first ascent of 'Duality of Man' (9c) at Dry Canyon, Arizona, USA. Commenting after his ascent, he stated "After 4 total years and 3 seasons of climbing ...

Most people in the math education space agree that students need to be fluent with basic math facts. By the time kids are in upper elementary grades, they should be able to produce the answer to 6x3 ...