The Simple Problem That Has Trapped Mathematicians for 100 Years

In this StarTalk highlight, host Neil deGrasse Tyson and co-host Paul Mecurio sit down with mathematician Terence Tao to unpack the Collatz conjecture — a problem simple enough for a third-grader to run, yet unsolved for roughly a century. The rule: take any number, halve it if it's even, or triple it and add one if it's odd, then repeat. Every number tested (into the quintillions, partly via crowdsourced computing projects like Collatz Grid) eventually crashes into the 4-2-1 loop — but no one can prove they all do. Tao explains why brute force can never finish the job (there are infinitely many numbers), why it's nicknamed the "hailstone conjecture" after the way ice bounces up and down inside storm clouds, and how iterating dead-simple rules breeds genuine chaos. He shares his own partial result — proving that almost all numbers shrink dramatically — and a fun aside about the film Gifted quietly using equations from his own papers. The through-line: the deepest unsolved problems are often the ones that look the easiest.

From 'Do We Need New Math to Understand the Universe? With Terence Tao'

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