Experienced mathematicians warn up-and-comers to stay away from the Collatz conjecture. It’s a siren song, they say: Fall under its trance and you may never do meaningful work again. The Collatz ...

The Collatz conjecture is also known as the “3n + 1” problem. It’s an easy problem to explain and check, and has been tested up into the nineteen figure range. But it’s only now that anyone has come ...

Some years ago, I wrote here about “hailstone numbers” (Follow that hailstone, 8 April 2016). These are numbers that are generated when you try your hand at the Collatz Conjecture—sometimes described ...

Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades. Experienced mathematicians warn ...

The number theoretic function $s(n) = \frac{1}{2} n$ if $n$ is even, $s(n) = 3n + 1$ if $n$ is odd, generates for each $n$ a Collatz sequence $\{ s^k(n)\}^\infty_{k ...

Seaweed? Worms? Bad hair day? The animation below is a new way to look at the Collatz conjecture, one of the most high-profile open problems in mathematics. The conjecture is easy to explain, given ...