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 ...

For new discoveries, everyday mysteries, and the science behind the headlines, follow NPR's ShortWave podcast . Over a century ago, the German psychologist Wolfgang Köhler conducted what became a ...

Bumblebees faced with a challenge know how to play ball. Buff-tailed bumblebees can figure out on their own how to use a ball as a ladder to nab sugar from an out-of-reach fake flower, researchers ...

Despite having tiny brains, bumblebees have demonstrated a remarkable ability to socially learn how to use tools, solve simple puzzles, and cooperate to achieve a goal. It seems they can also solve ...

Place any number of dots on a two-dimensional plane—say, a piece of paper—and measure the distance between each pair. If you rearrange the dots, how many pairs could be positioned exactly the same ...

In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped human mathematicians for the last 80 ...

“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 ...

I cut my teeth getting grounded in principles of design thinking when I launched a strategic design MBA during my university teaching years. Design thinking is essentially a problem-solving process ...

Is America heading toward a national debt crisis? As an economic adviser to President Biden and an economist active in mainly Democratic policy circles since the late 1980s, I’ve spent most of my ...

Elon Musk has a plan for a future where jobs are wiped out by artificial intelligence: a benevolent government will provide. “Universal HIGH INCOME via checks issued by the Federal government is the ...

A chatbot solution Recently, the company behind ChatGPT, OpenAI, announced that its internal AI model had made progress on a closely related version of this problem, which suggests that Erdős may have ...

OpenAI claims its model solved a famous geometry problem that has eluded the world’s greatest mathematicians for 80 years — a breakthrough hailed as evidence of the bot’s creativity and “intuition.” ...