How can you have a proof without proving anything? Mathematicians found a way and, in the process, came to blows over it – ...

Some people find it useful to talk through their problems—but language isn't necessary for logical reasoning, cognitive ...

More than a decade after Alice Corp. v. CLS Bank Int’l, the two-step framework for patent eligibility under 35 U.S.C. § 101 remains as contentious ...

Summary: Researchers discovered the first definitive neural evidence of how the brain creates and reuses abstract symbols to think creatively. The research tracks the neural substrates of ...

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 ...

Last year, I had a wake-up call. My mom needed more support. Without warning, my sister and I were coordinating her care in ways we had never had to before. Like so many in the sandwich generation, we ...

Abstract thinking helps you find patterns in data and explain meaning through stories and ideas. It also supports humor, creativity, and problem-solving beyond what you can observe. Concrete thinking ...

Another day, another Google AI model. Google has really been pumping out new AI tools lately, having just released Gemini 3 in November. Today, it’s bumping the flagship model to version 3.1. The new ...

Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly reflecting shapes to tile a surface, researchers uncovered a method that links ...

In a recent study, mathematicians from Freie Universität Berlin have demonstrated that planar tiling, or tessellation, is much more than a way to create a pretty pattern. Consisting of a surface ...

Creating opportunities to talk about math builds understanding and strengthens language development for all students—and particularly English language learners. The National Council of Teachers of ...

A modern Red Riding Hood on her way to Grandma’s house can meander through the woods, or drive down the interstate, or even climb a mountain to come around the back way. All those routes will get her ...