Abstract: The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research ...

The world may seem orderly, but randomness and chaos shape everything in the universe, from enormous galaxies all the way down to subatomic particles. Take a chilly window sheeting over with ice: even ...

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(via Quanta) A simple question about a spinning needle has haunted mathematicians for more than a century. It led to the Kakeya conjecture, a cornerstone of modern analysis connecting geometry, ...

The Collatz Conjecture begins with a simple sequence yet no proof has ever been found to solve it. ‘Don’t care’: Coalition split over Albo’s attire Bureau of Meteorology ordered to fix new website ...

Why is untangling two small knots more difficult than unravelling one big one? Surprisingly, mathematicians have found that larger and seemingly more complex knots created by joining two simpler ones ...

A $${\color{greenyellow}Simple \space \color{blue}Portable \space \color{green}Python}$$ Program for people to discover Collatz Conjecture $${\color{red}maximum \space \color{red}steps}$$ numbers. A ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

Soon to be the official tool for managing Python installations on Windows, the new Python Installation Manager picks up where the ‘py’ launcher left off. Python is a first-class citizen on Microsoft ...