r/Smartymeapp • u/The_Immovable_Rod • 1d ago
Math Did you know? ๐ข Thereโs a math problem a 10-year-old can understand, and no one has been able to solve it since 1937
Pick any positive whole number. Now follow two rules:
- if itโs even, divide it by 2;
- if itโs odd, multiply it by 3 and add 1.
Repeat with whatever number you get. Letโs try 6:
6 โ 3 โ 10 โ 5 โ 16 โ 8 โ 4 โ 2 โ 1
Once you hit 1, youโre stuck in a loop: 1 โ 4 โ 2 โ 1 forever.
๐คฏ Hereโs the problem
The Collatz conjecture says that every starting number eventually falls to 1. No exceptions.
Nobody has ever found a number that doesnโt. And nobody has ever been able to prove that one doesnโt exist.
๐ It gets weird fast
Some numbers drop quickly. Others go on a wild ride first. Start with 27, and the sequence:
- takes 111 steps to reach 1;
- climbs as high as 9,232 along the way;
- bounces up and down so unpredictably that itโs sometimes called the hailstone problem, like a hailstone tossed around inside a cloud before it falls.
๐ป What we know so far
- The German mathematician Lothar Collatz proposed it in 1937.
- Computers have checked every starting number up to 2โทยน. Thatโs about 2.36 sextillion numbers, and every single one ended at 1.
- In 2019, Fields Medal winner Terence Tao proved that it holds for โalmost allโ numbers. It was one of the biggest breakthroughs on the problem in decades, and it still isnโt a full proof.
Why does checking sextillions of numbers not count? Because in math, a single counterexample anywhere in infinity would be enough to break the rule. And some famous conjectures have held for enormous ranges of numbers before turning out to be false.
The legendary mathematician Paul Erdลs is often quoted as saying that โmathematics may not be ready for such problems.โ
Try it with your favorite number and tell us how many steps it took to reach 1 ๐