The Simple $1,000,000 Problem No One Can Solve

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Special thanks to @stevenstrogatz for all his help with this video

The Collatz Conjecture, first posed in 1937, remains one of math's most deceptively simple yet unsolved problems. Even Paul Erdős said 'mathematics may not be ready for such problems' - it's a humbling reminder of the gap between intuition and proof.

Hi! Could you do a video on the history of logarithms—how they started as printed tables and eventually became the logarithmic functions we use in math today,I really love your videos—they’re so insightful

You have all the numbers to work with, so probably... And that answer is good enough. Why's this feel like a trick?

That's because our math is base 10 yet we try to solve these problems using counting numbers 1-9. When we count we are basing on a fraction of a whole (0.1, 0.2,.... 0.9, 1.0). In the video they talk about the circle method which basically takes this into account. Our number system counts back to a whole of 10 or 1.0. basically all the numbers are between 0 and 1, a whole. When we look at primes and consider 1-9 we end up with prime numbers 2, 3, 5, 7, and 9, yet 2 and 5 are never prime after this. They all end in 1, 3, 7, or 9. I would like to see what a mathematician would come up with if they could look at primes starting from 1.0 (essentially 10) instead of 1. When dealing with an infinite amount of numbers and trying verify a proof, if those numbers have to be verified in order to be true first, that alone breaks the system. This is not n+1, this is choosing a number and then confirming that number can then only be divisible by 1 and itself. If you add any complexity like this to prove something on an infinite scale then you only further complicate the system and add more numbers than will ever be possible to compute or verify. I think some of these math problems we try to solve are based on a problem all their own. If we say prime numbers are only divisible by 1 and itself, starting from 1, maybe that's a flawed definition/approach to begin with. It sort of creates its own world of quirks, patterns, and solutions that could be based on a false approach from the start. Were sort of chasing our tail. If it the tails fault for intriguing us or our desire to chase the tail. Like any time you try to solve things for infinity it reminds me of the ouroboros. The end is based on where you start and the start is based on where you end (Ad infinitum)