For more than two millennia, mathematicians have produced a growing heap of pi equations in their ongoing search for methods to calculate pi faster and faster. The pile of equations has now grown into the thousands, and algorithms now can generate an infinitude. Each discovery has arrived alone, as a fragment, with no obvious connection to the others. But now, for the first time, centuries of pi formulas have been shown to be part of a unified, formerly hidden structure.
Sometimes the reason pi shows up in randomly generated values is obvious—if there are circles or angles involved, pi is your guy. But sometimes the circle is cleverly hidden, and sometimes the reason pi pops up is a mathematical mystery!
Starting today, ChatGPT will generate dynamic visuals when you ask it to explain select scientific and mathematical concepts, including the Pythagorean theorem, Coulomb's law and lens equations. When ChatGPT responds with an interactive visual, you'll be able to tweak any variables and the equation itself, allowing you to see how those changes affect the solution.
Liam Delap has an interesting party trick that you wouldn't really expect a footballer to pull out of the bag. The Chelsea forward has gone on video a few times showing off his bizarre mathematical ability to quickly calculate the cube roots of large numbers.
Which Algorithm Is This? If you step back, this maps almost perfectly to the Top K Frequent Elements problem.We usually solve it for integers in a list. Here, the "elements" are audience profiles age and body-type combinations. First, define what an audience profile looks like: case class Profile(age: Int, height: Int, weight: Int) What we want is a function like this:
On platforms like TikTok and Instagram, instead of sharing clothing hauls or skincare routines, creators are sharing their book stacks or media diets promising to make their viewers "disgustingly educated" in a matter of minutes. For further optimization potential, take note of these brain hacks to improve memory (so that your time cracking open Plato's Republic won't go to waste).
In the weeks leading up to September 1891, mathematician Georg Cantor prepared an ambush. For years he had sparred - philosophically, mathematically and emotionally - with his formidable rival Leopold Kronecker, one of Germany's most influential mathematicians. Kronecker thought that mathematics should deal only with whole numbers and proofs built from them and therefore rejected Cantor's study of infinity. "God made the integers," Kronecker once said. "All else is the work of man."
On October 1, 2022, something strange happened in the Philippines: 433 people won the jackpot in the local lottery. For this particular lotto, six numbers ranging in value from 1 to 55 were randomly selected, and the 433 winners all matched. Even more bizarre, when arranged in ascending order, the winning numbers were: 9, 18, 27, 36, 45 and 54. In other words, the winning numbers were multiples of 9 (9 1, 9 2, 9 3, etcetera).
Ministers have asked the exams watchdog, Ofqual, to extend current arrangements, providing GCSE maths, physics, and combined science students with formula sheets. Ofqual is consulting on extending this until current GCSEs are reformed following a curriculum review. The government will then consider if memorisation is required for new qualifications.
Fifty-four seconds. That's how long it took Raphael Wimmer to write up an experiment that he did not actually perform, using a new artificial-intelligence tool called Prism, released by OpenAI last month. "Writing a paper has never been easier. Clogging the scientific publishing pipeline has never been easier," wrote Wimmer, a researcher in human-computer action at the University of Regensburg in Germany, on Bluesky. Large language models (LLMs) can suggest hypotheses, write code and draft papers, and AI agents are automating parts of the research process.
"We are not taking this step lightly. Remote testing with real-time proctoring was a vital service for both test takers and schools during the pandemic, and we understand that some test takers may prefer remote testing for convenience, comfort, or other reasons," Krinsky wrote.
Nearly 60% of American teenagers say students at their school use AI chatbots to cheat "very often" or "somewhat often," according to a new Pew Research study. The researchers found that teens now view cheating with AI as "a regular feature of student life."
