A math problem so simple a child gets it — and no one can solve it

Take any positive whole number. If it’s even, halve it; if it’s odd, triple it and add 1. Repeat. Try 27 and the sequence soars past 9,000 before plummeting — but, like every number ever tested, it eventually crashes down to 1.

The Collatz conjecture, posed by Lothar Collatz in 1937, claims this always happens, for every starting number. Despite its grade-school simplicity, it has resisted proof for nearly 90 years. Computers have verified it for every number up to roughly 2⁶⁸ — about 295 quintillion — without a single exception.

Yet checking cases isn’t proof. In 2019 Terence Tao proved that almost all numbers obey the rule, hailed as the biggest progress in decades — but the full conjecture stands open.

Mathematics may not be ready for such problems. — Paul Erdős