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 ...

The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...

ABSTRACT: The Collatz Conjecture asserts that for all positive integers s , every Syracuse integer sequence defined by T( s )=s/2 if s is even, and T( s )= ( 3s+1 )/2 otherwise, eventually reaches 1 ...

1 The Official College of Telecommunications Engineers, Madrid, Spain. 2 Independent Researcher, Majadahonda, Spain. A reduced conjecture, equivalent to the Collatz conjecture, has been proposed; see ...

Mathematicians from New York University and the University of British Columbia have resolved a decades-old geometric problem, the Kakeya conjecture in 3D, which studies the shape left behind by 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, ...

Three new books warn against turning into the person the algorithm thinks you are. Like a lot of Netflix subscribers, I find that my personal feed tends to be hit or miss. Usually more miss. The ...

Abstract: Collatz conjecture (or 3x+1 problem) has been explored for about 80 years. By now the largest number that has been verified for Collatz conjecture is about 60 bits. In this paper, we propose ...

Companies, nonprofit organizations, and governments design algorithms to learn and predict user preferences. They embed these algorithms in recommendation systems that help consumers make choices ...