The Simplest Math Problem No One Can Solve - Collatz Conjecture

Special thanks to Prof. Alex Kontorovich for introducing us to this topic, filming the interview, and consulting on the script and earlier drafts of this video.

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References:

A. Kontorovich and Y. Sinai, Structure Theorem for (d,g,h)-Maps, Bulletin of the Brazilian Mathematical Society, New Series 33(2), 2002, pp. 213-224.

A. Kontorovich and S. Miller Benford's Law, values of L-functions and the 3x+1 Problem, Acta Arithmetica 120 (2005), 269-297.

A. Kontorovich and J. Lagarias Stochastic Models for the 3x + 1 and 5x + 1 Problems, in "The Ultimate Challenge: The 3x+1 Problem," AMS 2010.

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Special thanks to Patreon supporters: Alvaro Naranjo, Burt Humburg, Blake Byers, Dumky, Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

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Written by Derek Muller, Alex Kontorovich and Petr Lebedev
Animation by Ivy Tello, Jonny Hyman, Jesús Enrique Rascón and Mike Radjabov
Filmed by Derek Muller and Emily Zhang
Edited by Derek Muller
SFX by Shaun Clifford
Additional video supplied by Getty Images
Produced by Derek Muller, Petr Lebedev and Emily Zhang

[k.pacificnw]

Everyone here: "...but just a maaaaybe I'll be the one to solve it."

[marcokapusta]

This math problem is actually like my trading portfolio, I can start with any number but end at $ 1

[iksoype]

I love how he makes us think that he is the world's greatest mathematician by showing us his picture when saying that, but then shows the other half of the picture.

[AshenElk]

What blows my mind is when this stuff is demonstrated graphically the patterns become easy to see with my eyes. I don't know why maths is so beautiful.

[Yihtc]

“Pick a number”
Me:Fou-
“Seven? Good choice”
Me:but I-

[cosmicnomad]

I absolutely love how mathematicians always find the most random things to debate over!

[colbycrabtree]

The math homework: 1 + 1 = x

The math test: 3x + 1

[Professional_Lozer]

I was so inspired when i first saw this video. I’d always think about it. And this year, my math teacher had each student teach their own lesson at the end of the year. I chose this conjecture because of this vid. I used this vid as a source, i watched it like 20 times, and I’m so inspired by your channel. This vid is 2 yrs old as i write this, and will probably get berried in all the comments but i still want to write this for the small chance you see this. so if you are reading this, thank you for inspiring little minds like mine. ❤️❤️❤️

[ghostphalanx]

Whoever created all those graph animations is an absolute master in after effects expressions

[jokes.on.u]

Teacher: Why did you not answer the questions on your test.
Me: Because the Math is not ripe enough for me to answer these questions

[ThatOneKat]

15:02 why negative numbers have three loops? Well, use positive numbers but change the function from 3x+1 to 3x-1 and you’ll get the same three loops.

[mjh]

I am not great at math, but I have no idea why I am so fascinated by these videos and topics

[Naurik]

Pretty much every subject in school is really interesting if I’m not forced to learn it

[stevebuttner]

I teach programming, and I always have my students write a program to test this conjecture. They really enjoy entering really big numbers and watching how long it takes to get down to one. Also offers a great opportunity to discuss what constitutes a mathematical proof, i.e. just because something works for every number anyone has tried, it doesn't follow for every number.

[matan]

At this point it just looks like mathematicians are creating problems for the heck of it

[leebydeeby]

My calculus professor just introduced this conjecture to us last week, and ever since then I've been shamelessly addicted to just bringing up a random number generator for a starting point and wasting away the hours.

[aussieraver]

3:01
Thats what scares me the most.

Graphically representing a number that dramatically goes so high, the animation/graph becomes incomphrehensible and you have a mini panic.

I get thay alot working in 3D game engines.

There must be a phobia for it.
Such as using Google Earth, and zooming out all the way.

[cajunag]

What's interesting to me about this problem is, that if there is a number that does not result in reaching the 4, 2, 1 loop (let's call that number R), then there are actually an infinite number of other numbers that also do not result in reaching the 4, 2, 1 loop. So that means either there is no number that doesn't reach this loop, or there is an infinite number of numbers that don't reach this loop.

This is the case because if R does not reach this loop, then R multiplied by any power of 2 also does not reach this loop. Because any number that is the product of R and any power of 2 would eventually reach R by repeatedly dividing by 2 and therefore, never reach the 4, 2, 1 loop.

[nimamaster]

The fact that this is the basis to making an organic shaped coral mesmerized me.

[grimaffiliations]

Me: Where should we eat?

Girlfriend: Mathematics is not yet ripe enough for such question