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 ...

Movie S4. Task solution in Experiment 3. This movie shows a bee solving the task in Experiment 3. The beginning of the video (habituation phase, without the ball present) is shown at accelerated speed ...

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 ...

Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary ...

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 ...

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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 ...

Last semester, I assigned students in my energy storage systems class a problem set comparing the electrical designs of supercapacitors, lithium-ion batteries and flywheel systems. One submission ...

FORTUNATELY, NOBODY WAS INJURED. CONTROLLING THE PYTHON POPULATION HERE IN FLORIDA, GOVERNOR DESANTIS SPOKE IN STUART TODAY ABOUT SOME NEW ACTIONS THE STATE PLANS TO TAKE TO CONTROL THE GROWTH OF ...

This Pew Research Center analysis examines Americans’ views of problems facing the country. Pew Research Center conducts research to help the public, media and decision-makers understand important ...