mathematics

Researchers have made a significant advance in spectral geometry by proving a special case of Pólya’s conjecture related to the eigenvalues of a disk. Their work, blending theoretical elegance with potential practical applications, highlights the universal value and artistic beauty of mathematical research. Credit: SciTechDaily.comA professor and his collaborators have proven Pólya’s conjecture for the eigenvalues of a disk, a tricky problem in mathematics.Is it possible to deduce the shape of a drum from the sounds it…

With its bright colors, easy-to-learn rules and familiar music, the video game Tetris has endured as a pop culture icon over the last 40 years. Many people, like me, have been playing the game for decades, and it has evolved to adapt to new technologies like game systems, phones, and tablets. But until January 2024, nobody had ever been able to beat it.A teen from Oklahoma holds the Tetris title after he crashed the game on Level 157 and beat it. Beating it means the player moved the tiles too fast for the game to keep up…

A study reveals that forests do not exhibit the fractal patterns seen in individual trees, offering new insights into understanding and comparing ecosystem complexity across different natural environments. Credit: SciTechDaily.comScientists have found that the growth patterns of trees in a forest differ significantly from the way branches expand on an individual tree.Nature is full of surprising repetitions. In trees, the large branches often look like entire trees, while smaller branches and twigs look like the larger…

Historians have discovered what may be the world's first decimal point, in an ancient manuscript written 150 years before its next known appearance. There have been many ways to split integers, but this little dot has proven uniquely powerful.The mathematics we all learn at school seems so fundamental that it doesn’t feel like individual concepts in it would need “inventing,” but these pieces arose separately as scientists and mathematicians realized they were needed. For instance, scientists recently found the oldest…

Credit: Unsplash/CC0 Public Domain Children's interest in, and competence perceptions of, mathematics are generally quite positive as they begin school, but turn less positive during the first three years. Changes in interest and self-concept are also associated with each other. In other words, if a child's interest fades, so does their competence perception, and vice versa. …

A new experimental method developed by researchers enables the identification of topological properties in materials without relying on mathematical models, simplifying research and expanding the potential applications of topology in various fields. Credit: SciTechDaily.comInnovative research introduces a practical, model-free method for exploring topological properties in materials, enhancing the scope and efficiency of topological studies.The branch of mathematics known as topology has become a cornerstone of modern…

This photograph shows fluorescein dye being ejected from the sprinkler as it spins in forward mode. Credit: NYU’s Applied Mathematics LaboratoryScientists have solved the decades-old Feynman Sprinkler Problem, showing that a sprinkler running in reverse spins oppositely to when it ejects water. This finding deepens our understanding of fluid dynamics and could inform renewable energy development.For decades scientists have been trying to solve Feynman’s Sprinkler Problem: How does a sprinkler running in reverse—in which…

Credit: SciTechDaily.comOne of the fundamental and timeless questions of life concerns the mechanics of its inception. Take human development, for example: how do individual cells come together to form complex structures like skin, muscles, bones, or even a brain, a finger, or a spine?Although the answers to such questions remain unknown, one line of scientific inquiry lies in understanding gastrulation — the stage at which embryo cells develop from a single layer to a multidimensional structure with a main body axis. In…

Summer Haag and Clyde Kertzer, participating in a CU Boulder REU, disproved the long-held local-global conjecture in number theory by exploring Apollonian circle packings. Their research highlighted the creative and uncharted aspects of mathematical exploration. Credit: SciTechDaily.comSummer Haag and Clyde Kertzer made major news in the math world while working on a summer research project.Prior to the end of the 2022-2023 academic year, graduate student Summer Haag and junior Clyde Kertzer were looking for summer…

We have the solution to Wordle on January 9, as well as some helpful hints to help you figure out the answer yourself, right here. We’ve placed the answer at the bottom of the page, so we don’t ruin the surprise before you’ve had a chance to work through the clues. So let’s dive in, starting with a reminder of yesterday’s answer. Yesterday’s Wordle answer Let’s start by first reminding ourselves of yesterday’s Wordle answer for those new to the game or who don’t play it daily, which was “FINAL.” So we can say that…