The Simplest Math Problem No One Can Solve - Collatz Conjecture

The Collatz Conjecture is the simplest math problem no one can solve - it is easy enough for almost anyone to understand but notoriously difficult to solve. This video is sponsored by Brilliant. The first 200 people to sign up via brilliant.org/veritasium get 20% off a yearly subscription.
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:
Lagarias, J. C. (2006). The 3x+ 1 problem: An annotated bibliography, II (2000-2009). arXiv preprint math/0608208. - ve42.co/Lagarias2006
Lagarias, J. C. (2003). The 3x+ 1 problem: An annotated bibliography (1963-1999). The ultimate challenge: the 3x, 1, 267-341. - ve42.co/Lagarias2003
Tao, T (2020). The Notorious Collatz Conjecture - ve42.co/Tao2020
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.
Tao, T. (2019). Almost all orbits of the Collatz map attain almost bounded values. arXiv preprint arXiv:1909.03562. - ve42.co/Tao2019
Conway, J. H. (1987). Fractran: A simple universal programming language for arithmetic. In Open problems in Communication and Computation (pp. 4-26). Springer, New York, NY. - ve42.co/Conway1987
The Manim Community Developers. (2021). Manim - Mathematical Animation Framework (Version v0.13.1) [Computer software]. www.manim.community/
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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
3d Coral by Vasilis Triantafyllou and Niklas Rosenstein - ve42.co/3DCoral
Coral visualisation by Algoritmarte - ve42.co/Coral

[@k.pacificnw02134]

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

[@TheGreekGodOfWallStreet]

"I could write a computer program to try and solve it". Because I'm sure nobody has tried that before 😪

[@evilkillerwhale7078]

You can actually instantly solve for half of all numbers. If all numbers up to an odd N works, (n+1)/2

[@jrbros2371]

I too thought i could solve it :D

[@systim30]

What is there to solve? There is nothing to solve

[@jrbros2371]

@@rabiebabies7812 0 is not positive but it forms a loop. Its also not negative but no number ends up at zero so it is independent loop of itself

[@Yihtc]

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

[@rachelx04]

I said 4, I usually say 3 but I said 4 😂

[@palindromia130]

He said seven because seven is more likely to be chosen lmao

[@ArcFenixDelacroix]

I think Im the only one who chose 7

[@vor0g]

Only reason I'm not liking is bc tbe lile count is at 69

[@samirh2758]

I didn't choose a number at all because no one can make me do math.

[@user-ik4so3yp2e]

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.

[@JPcommunicates]

Well, that isn't even a person who solve the task. It's a computer programme which tries to explain something what isn't actually relevant.

[@AlbertSatnoianu]

lol

[@user-oq5gn6br1u]

😂 lol

[@shmuelman]

Certainly one of the finest mathematical videos on KZbin.

[@__cypher__]

Wait ... What?!

[@xninja2369]

3Blue1Brwon be like ? 🫥

[@marcokapusta3843]

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

[@JeffMTX]

you too? :)

[@luca6819]

I tried to remove the eyelash on the display 🤭

[@davidbesant]

There's that damn eyelash on my screen again!

[@RetroFuel]

@@luca6819 .same lol

[@Hoshino_Channel]

@@luca6819 You're using youtube in lightmode? ;o

[@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

[@anyaburke6636]

facts

[@lordsiomai]

Imma use this

[@scottmurphy248]

@@lordsiomai be honest, no you won't

[@compszn]

@@anyaburke6636 its 6

[@krisha8430]

@Human Kind its already a 1000 We can make it 2000??

[@tyagohiee]

I was once talking to my math teacher and i asked her "why was Bhaskara so annoying" and she told me "he wasn't, he simplified a lot of things into a single calculus", then my friend said "so mathematicians have to simplify math because humans find it too hard when humans themselves created it" and my teacher said "yes, the point of math is simplifying something we made dificult in the first place". That chat was all i thought about throughout this video.

[@jasondelay2931]

Love this anecdote. Thank you. For the video, it only exist because somebody said “no, you need to divide by 2 if it’s an even number” why? “I don’t have a reason why but it makes it complicated so do it”

[@fletch4231]

As someone who is basically math illiterate, this makes almost no sense… makes me ask why we even made math, how it works, how do things even get figured out like the mathematical theorems and stuff… my confusion in difficult math related thingies makes me want to actually understand it more than my school education 😂

[@chuck1804]

@@fletch4231 My thoughts exactly. Invent problems and then try to solve them. As if we didn't have enough problems!

[@None-Trick_Pony]

​@@fletch4231I'm not very good with math myself, but its origins are very simple. It started as a system of tallies for counting things (typically livestock). That's likely why most counting systems have changes at 5 and/or 10-those are the number of digits on a hand and both hands, the simplest way to tally (cf. Roman V & X, Indo-Arabic 9 to 10, crossing four tally marks, etc.). You probably tally with your fingers subconciously. It evolved into counting more complex things, and you may even have needed to create units of measuring, for parcelling land, weighing grain, and measuring beer. On the note of beer, written language may have developed in the Near East as a medium of accounting, as evidenced by some very early cuneiform tablets mathematically tracking grains and even beer. It slowly got more and more complex as people realized that math is better at describing the universe than it has any right being. Ultimately, it was serendipity that it happened to be our best way of describing the universe, which is absurdly complex. TL;DR: Math started as a way of tallying and became more complex as its applications were discovered. Math is never purposefully obtuse-it's just our best medium of describing the universe. As the universe is absurdly complex, any system describing it must necessarily also be absurdly complex.

[@dadogdoin1360]

@@jasondelay2931I mean exploring things like that might lead to good discoveries

[@marcuswaterloo]

Here because I have the Collatz Conjecture in a Brilliant coding question. I have found Brilliant the easiest to jump back into when I have time. Great loop back Veritasium.

[@armin3057]

"coding" im always bewildered when people say that. coding is just another notation, nothing more.

[@jesse406]

@@armin3057 dork

[@SeanGonzalezMDHEXT]

​@@armin3057 coding is a verb. It's an action. You code something which is to say you program it to behave in a certain way. What you're referring to is code itself, which is another form of notation. Regardless of the programming language, any mathematical function can be represented in code. What you're saying is out of place in response to this comment as it was not referring to the programming language, but the problem-solving aspect of writing code which in itself has nothing to do with notation.

[@ghostphalanx]

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

[@pratanakangsadal521]

Amen.

[@gn4sty731]

BR?

[@GamingWithTimmy0]

The thumbnail equals 1 cause 3x_ is 3x nothing so if I did that it would be 0 and if I plus the 1 it = 1

[@GamingWithTimmy0]

Math

[@cirque1783]

BY "NO ONE" : He meant about Americans cause he himself is a american who dont knows anything about the outside world .

[@cosmicnomad8575]

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

[@soumyadityachakraborty2457]

ridiculous too

[@oreziopancrazio3685]

I totally agree. What a waste of time

[@christloen4077]

Not a waste of time. If you can find this solution, probably there is something you can achieve and get.

[@oreziopancrazio3685]

@@christloen4077 No way

[@christloen4077]

In your mind

[@pabescgmail]

When negative numbers have 3 different loops, it makes me wonder if I change not only the seed sign but the operand. And turned out that if I apply 3n-1 for negatives (likewise changing the sign of the objectvie function on the concavity on linear programming), the graphical representation is a mirrored one of the positives. This way the whole set can apply the same rules for positives on 3n+1 including a single loop (-4, -2, -1)

[@devangbajpai8608]

If we try the polynomial 3x + 1 for negatives then we will be stuck in a loop of -7 or -1 everytime for any negative integer. Try this too!

[@pabescgmail]

Yes, there are 4 different loops if negatives are used.

[@eon2330]

The +1 is the key tbh. If you go into non whole numbers any .25 .5 or .75 will loop as an odd number infinitely. Because 1 doesn't make it positive and non of these numbers rise a above 1 ever. they keep a 5 at the end. So it only works on numbers because we have no define of 0 as even OR odd, or both, and dividing it is weird, but also because adding 1 is what DEFINES changing from odd to even.

[@DaPoloJay]

@@eon2330 That’s what I was thinking if you start the equation from 0 3x0=0 which is still nothing until u add 1 now we’re positive but u can’t get 2 from 1 so now the loop starts u will never get 0 again

[@lanisilvious7098]

​​@@DaPoloJaywhy did you multiply and add to zero, it's not an odd number. Why do you not divide by 2? 0 divided by 2 is 0. . .and if a previous comment is correct that zero is neither even nor odd, you can't even start at all.

[@HemanthHR-fi5rq]

I’m glad I found this channel. Amazing quality content ❤️🙌

[@Naurik]

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

[@EnriqueLaberintico]

History of the entire world, I guess convinces me.

[@octaviovilchez3096]

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

[@alexmangorove]

School in a form of forced education kills interests and produces stupider people. Coersion always makes things worse.

[@seanallen8828]

English, grammar

[@benfulford3943]

Sorry to hear that you did not have good teachers. I was fortunate to go to a great school that had many good teachers that were able to teach stuff like this in interesting and engaging way. It was the teachers that failed you not the environment where you are 'forced to learn'.

[@grimaffiliations3671]

Me: Where should we eat? Girlfriend: Mathematics is not yet ripe enough for such question

[@aashsyed1277]

Noo

[@segmentsAndCurves]

I love your girlfriend. Wait, no, it's not what you think it is!!!

[@srijanpanicker5395]

LMAO🤣🤣🤣

[@rana8440]

😝

[@Pikachu-Gaming1764]

Lol

[@salahsedarous7616]

You can accelerate the conversion by allowing division by 3 beside 2. I noticed that in my own limited search. Fascinating stuff.

[@kelvinedits9471]

I wanna know who edit his videos.... The hard work ❤ ! We appreciate you bro !!

[@isaacpalmer1195]

Mathway: “Am i a joke to you?” Photomath: “Answer the question.”

[@cryptedmage9739]

Lol wassup homie

[@dino_tokic8884]

Lmaoo

[@WestExplainsBest]

Ugh those programs are virtual math teachers worst nightmare.

[@Hanyamanusiabiasa]

Me : "That's interesting puzzle, maybe I can solve it" Me 22 minutes later : "oh."

[@Dizzy00001]

Lol

[@theultimatetime8029]

Same I was like I'm gonnna guess a random number and try to do it..but 2⁶⁰ is really a big numbers they tried

[@mjzudba5268]

@@theultimatetime8029 well, Derek (the narrator in the video) did say that 2 to the 60 is nothing compared to the other numbers tried in Polya's conjecture. The counterexample which disproved Polya's conjecture was 1.845 × 10^361, an immense number. Still, 2 to the 60 is BIG.

[@theultimatetime8029]

@@mjzudba5268 yes ofcourse

[@khuetranxuan8218]

@@theultimatetime8029 try 70!,it's bigger or even 2^70!

[@azhagurajaallinall126]

Nice video as far 2:00 i see I have these numbers thoughts since school,goes back to when i learned mathematics to do in mind calculations & once learned formulae,started applied,looked for patterns Though i never formally write those down (maybe in school times,but i lost them) often feel about these, Maybe,maybe i gotta write them down,like some pattern in maths,numbers,look how far they can go,how it can be constant at certain point,arises new etc,,. I often think it may goes huge for calculations(let alone brain thinking) so i doesn't write them down Now i feel like write them down (though anyone sees it in future,see its absurdity) Maybe it helps me do "logical thinking,calculations easy" before i go wild thinking constantly (keep thinking)😅 Instead of avoiding,running over,gotta take care of it,grow myself,train enough to over power it (life hurdles,goals be like) Thank you so far (no time to see fully) Wish all be well 😃🌟✨🙌 21.02.2024 01:31am ist (77k+ comments,871k+ likes,38,625,062+1views)

[@priordan80]

The change of 3x+1 from branches pattern to 3x+1 on the -y axis where the branch pattern changes to a bar chart is reminiscent of the probability scenario on your video about the stock market and demonstrated with your ballbearing prop, also on -y axis 4,3,1 is viewed eventually as a singular number commencing the bar graph pattern.

[@agentkp4574]

Mathematicians: Dont waste your time on this problem 20.7 million people: YES

[@davidmedina7721]

Just cuz you said that I'm going to code a program that runs through all posible combinations on scratch

[@apbe2q35]

3 years year old me : what is maltiplikaton?

[@Seeker-dx1gj]

Ok

[@BoEatsApples]

13 Million*

[@Penguins459]

more

[@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.

[@astronautboynr2018]

nerd

[@livinglogically8180]

Atleast find better ways of procrastination

[@r-a-kralphandkoto2413]

@Hence Forgot bricks bit to though to bite on man ill rather have alloyed steel

[@Mr.Human69]

Ez Answer Is 9 I was Doing my math Homework Bruh

[@sera_makyuri]

You have a great teacher if they motivated you to spend hours on this!

[@aladpresspays]

It always and ultimately comes down to one or shall I say come up to one... the one and only... wherever you'd dig you'll find the one. Just need to open your heart following your eyes opening.

[@wtcodingproductions]

I've created two simple C++ programs that solve the multiplication of binomials such as (3x + 1), and am looking to do more. Thank you for this unique & interesting concept. College Calculus major.

[@adamrozek5782]

Isn't 3x+1 equal to 3x=-1 so X=-1/3 ? Idk what's the problem here btw 😂

[@prasadbhalerao8556]

​@@adamrozek5782Lol this shows the whole video went over your head What they are trying to solve is , They want to find a number which does not go in 4 2 1 loop

[@prasadbhalerao8556]

​@@adamrozek5782Also it's not a 3x+1=0 😂

[@javiersolis2993]

The animation is everything here.

[@milkshake7180]

@DON'T stfu

[@reallemming1dago..888]

@DON'T stfu bi-

[@WillCrewMusic]

You both just fell for his trap lmfao

[@milkshake7180]

@@WillCrewMusic i didnt even read the pfp the text is too small to see LMAO

[@everywhereman9003]

@DON'T IM GONNA SAY THE N WORD

[@nimamaster6128]

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

[@ShatteredCelestial]

wait really? lmao

[@shibe6181]

Wow 4th

[@cristianrivas4606]

Can we not use decimals?

[@Arthurgoldlizard]

it grows, makes an unpredictable, chaotic but somewhat beautiful image, and then inevitably falls back down to 1. like life and death cycle.

[@artificialintelligenceplus1321]

Found the Mathematical Phenomenon A very interesting channel - " Artificial Intelligence plus lottery"

[@matan2924]

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

[@DeadKarlisAlive]

I’ve always wondered why mathematicians only look at the patterns of the ’hailstone integers’ with this problem. Maybe the pattern is found in the numbers that are skipped after doing the equation either with 1 number or after a million numbers

[@Liur.]

Mathematicians: *_cries in proofs_* Scientists: *_laughs in null hypotheses_*

[@Liur.]

@@Sinaloabricks hypotheses is the plural 🙄

[@er00ic]

@@Sinaloabricks Who says that we have only the one hypothesis?

[@andrewcramer9200]

Statistician: *does both in bipolarity*

[@paxhumana2015]

Is not mathematics merely just a part of science anyway?

[@paxhumana2015]

@@andrewcramer9200 Bipolar Person: "Finally, someone DOES understand me"!

[@changolord93]

-showing his own face “One of the greatest mathematicians” Dudes pops out of nowhere “Mr. Tao” Lol you had me at the first half not gonna lie

[@veramentestanco]

He had me too! Brilliant!

[@anonamemous6865]

He had me too

[@DrakyHRT]

@samridh sood infinity is a number, any number, or all numbers should i say, and no, this is not the problem with this conjecture.

[@irenegold3969]

LOL

[@lunatik4265]

@samridh sood I think you´re on to something. The Fields Medal is in reach!

[@Guywiththetypewriter]

Old video but heres recontextulistion thats pretty neat. Dividing by 2 bit shifts binary numbers to the right. The 4,2,1 pattern is 100 010 001 Hence, a hamming weight (number of non 0 bits in binary number ) of 1 will lead to the 4,2 ,1 pattern, no matter how large the number is. This is the same as the any number of 2^n observation but bear with me. Multiplying by 3 in binary is the same as adding the binary value of itself but bit shifted left by 1(and hence you have this beautiful thing where the bit shift left is the odd process, the bit shift right is the even process). E.g 101 (5) multiplied by 3 is 0101 + 1010 1111 An odd multiple 3 added to by 1 will always either leave the hamming number the same (if the least significant run of ones is size 1 : e.g 010001 + 1 = 010010 Or Will reduce the hamming weight by n-1 where n is the size of rhe least significsnt run of 1s. E.g 011(hamming weight of 2) + 1 / = 100 (hamming weight of 1, hence 2-1 reduction has occured). New runs of 1's in a 3 multiplication will be isolated with size 1 max. Dividing an odd number by 2 will move the least significant run of ones to the least significant bit. This will trigger a termination eventually (with delays only guranteeing a larger reduction in hamming weight) ( not proven) any individual 1s end up in a run of ones before the +1 termination step. Hence, whilst hamming weight may increase temporarily, the overall pattern caused by the +1 termination and the limitation of of new 1 bits tending towards runs of ones, the overall hamming weight will reduce during iteration of the colletz conjecture processes. Hence, the hamming weight tends to 1... guranteeing the 4,2,1 loop. Its not quite a proof. But christ i feel like its close 😅

[@clutchmatic]

I like this one. My version was to argue that despite how large the number gets, application of the process results in the number going back to previously checked numbers and everything goes down to 4-2-1, so the conjecture must be true for any natural number

[@kinetik9197]

how long did this take

[@Guywiththetypewriter]

@@kinetik9197 how u mean

[@jenniferzeng5735]

Wow …. This is actually really smart

[@CourtneyIsLovely]

“Pick a number, any number” Uhh… 7? “7? Good choice!”

[@kugelblitz7946]

i wrote this comment to appreciate that those graphs were not just random. There were exact and to the scale.

[@itismethatguy]

Ikr

[@Sintinium]

Ikr I wonder how many days or months it took to build all of those. Unless he wrote a program for it then maybe a day or two

[@EpicVideos2]

@@Sintinium of course he wrote a program for it but I expect the developer probably spent at least 2 weeks on making it.

[@AxxLAfriku]

You dislike the stuff that gets uploaded by my fingers clicking upload? Are you just a h8er boi? I say see you l8er boi. Don't watch the stuff that gets uploaded by my fingers clicking upload anymore. Your dislikes are damaging my good good GOOD reputation. I am a superstar, dear kd

[@kugelblitz7946]

@@Sintinium I think he paid some small company to do that, a single person is unlikely to do that

[@walkastray007]

A couple of days ago he had a poll on what colour would evens and odds would be if they had a colour. The poll decided blue as even and red as odd. In this video, he has the evens as blues and the odds as reds. I love how much he cares about his community and the little details.

[@InsideOutAnus]

Good pickup!

[@valval4145]

Wow I did the poll a few seconds before scrolling to the video and this comment, I was wondering what the poll was for

[@NandR]

Good catch. I like the social experiment that is in itself. That is such an arbitrary question that it should be close to 50/50. But it seems something is tilting us one way. Is it nature or society?

[@valval4145]

@@NandR I was also thinking the same. Maybe people who prefer the color blue also prefer even numbers, or people who prefer the color red also prefer odds? Just a thought

[@JS-jh4cy]

What about color blind people, there choices may be just a valid, pick any of the two, for maybe they are different shades of the same color??

[@richardfellows5041]

Consider the following. 1. there are an infinite number of 2^n numbers. 2. Consider an algorithm that selects a random number and tests it against whether it is a 2^n number. And if so applies the second half of the 3n+1 problem, in which case it will always collapse to the 4 -2-1 sequence. 3. What is the probability that the random number generator will never hit on one of the 2^n numbers. 4. I contend that the probability is zero.

[@jmodified]

It's not a random process. Consider that 3x-1 has identical statistics but multiple loops.

[@Fraber87]

I have noticed that the numbers that have the most difficulty in going down to 1 are those that precede an even number with the characteristic of repeatedly decaying into an even number many times in a row (i.e. those that get to 1 more easily). Example, the even number below decays several times repeatedly into an even number, easily arriving at the number 1 (as do all the numbers belonging to the group 2x2x2x2x2x2x2): 64 ---> 32, 16, 8, 4, 2, 1 Both the number 63 (the previous one) and 62 (the even number before 64) both have extreme difficulty going down to 1, so the numbers preceding 64 are in the opposite condition to that of 64 (which instead decays very easily to 1, without ever rising upwards). So, if I choose the number 2048 ( = 2x2x2x2x2x2x2x2x2x2), I assume, based on the above, that 2047 and 2046 decay to 1 very slowly (having many ups and downs).

[@darthenx2585]

The amount of graphic work that had to be done for this video is insane.

[@chronical]

Exactly what i was thinking, i was like man props to whoever worked on this video

[@peterh222]

Try a Captain Disillusion video ... And he does those all himself

[@markjohnson7508]

Really.. wow. Entropy maybe

[@josefwakeling7103]

@@peterh222 *disillusion

[@birchthebirch4593]

Listen ...don't look

[@parkiel54]

Oh my god, this poor animator. That is a serious amount of dedication. Looks fantastic!

[@CoreDeck]

i was just gonna say that! Amazing work by the editor.

[@remenyo]

It seems like it is made by the same software that 3b1b uses.

[@user-xf6ox6zx4w]

Amajing

[@danielrasheedi]

@@remenyo what is it??

[@MehtabSinghEdhan]

i generated these graphs with python matplotlib, and then save the changing graphs for value of x, in an image sequence, then played them in premiere pro, voila..no animation needed for graphs and bar graphs 😁you can generate graphs with python

[@Alexa-dt8fm]

Pascal triangle is an example of directed tree It is used to show how much fluctuation carbon shows in a spectrum in chemistry

[@Alexa-dt8fm]

Or rather it predicts how many fluctuations carbon can shows in its bonding with hydrogen

[@adw1z]

For those wondering, Alex K. is the narrator and voice behind the Quanta Magazine’s stunning video on the Riemann Hypothesis. This is like a collab of dreams!

[@Yextiny]

"This math is weird because of math. We can't do enough math to solve the math - there's just too much math!"

[@holdontoyourwig]

You could start by calling it MATHS

[@user-lg9cf4sw4x]

my dumbass brain is quaking

[@001100AAAEA]

Pretty much lol

[@babydriver8134]

Weapons of Math Instruction?

[@bujharvard9313]

@@holdontoyourwig Unless he's British, why should he?

[@colebrew]

"Pick a number" -"Uh seven?" "Seven? Good choise!" -"WHAT THE-"

[@JosephAR513]

BRO😂😂

[@Fixis]

Everyone chooses 7 cause 7 wins everytime lol

[@Byokie1]

SAME

[@DaisyCoreXD]

Lol same

[@sunset_anything1875]

I think it’s 3

[@gokulraj6404]

I would say that 3n+1 is trying to reach the number to the sequence of 2^n and the division of 2 is used to say "You are coming close to join my family ,but try with someone else". what do you think about. maybe binary representations could make it easier to understand.

[@demensclay6419]

A big shoutout ot the graphics department for making this 100% more understandable!

[@gniewko123456]

a big shout down to yoy that you were'nt able to get such a simple equal...

[@josiahjray]

I really hope this is satire 🤣🤣

[@gniewko123456]

@@josiahjray baited :D

[@josiahjray]

@@gniewko123456 Hope so lol

[@anndyarguedo4453]

Ah yes, 999 likes

[@DasSkelett]

Your "one of the world's greatest living mathematicians" joke totally killed me.

[@lukelively8380]

I was looking for this comment lol

[@HungryTacoBoy]

Same here. I thought it was very clever.

[@cortnetisjustbetter]

* You're , btw I am better than you

[@MightyHashBrown]

@@cortnetisjustbetter not you’re but ok

[@Sleepy_Joe]

I immediately knew this would be in the comments as well lol.

[@frtzkng]

My first thought is, since all numbers which are a power of 2, so 2^n, end up as 1, wouldn't it be easier to rephrase the problem and try to prove (or disprove) that by applying 3n+1 if odd and n/2 if even, all primes eventually give a result that is 2^n?

[@austinvanderveer213]

This reminds me of the Philosophy Wikipedia page, where if you click on the first link in any Wikipedia entry you'll eventually get to Philosophy.

[@tobiandobito3736]

I looked up a train. I ended up at philosophy...

[@CrimsonRegalia]

"What do you do for a living?" Mathematician: "I am studying 3x+1."

[@anunknownperson4018]

havent watch the whole video but 3x+1 is impossible to solve bc it has infinite solutions??

[@vector1213]

Big maffs

[@fanaticjay3825]

no one not even no one me: 3x+1 equals 1 because 3x nothing is 0 amd + 1 is 1

[@Floorlicker2000]

When I saw that picture I was like it’s obviously 4x I disagree

[@HaaKaaf]

@@fanaticjay3825 bruh what

[@Martdogg3000]

I like the amount of people who didn't watch the video for even a moment, and are just here talking about how easy it is to solve 3x+1.

[@HakunaMatata688]

You take my words from my mind :))

[@ItsMe-gw4kb]

I watched it up to 20:57, and had a couple of thoughts along the way. First off, I hit the loop quickly because my chosen number is 4. My thoughts were that this could be considered an exercise in looking at every possible angle of a situation, which both has practical applications, and seems likely to sharpen the analytical way of thinking -- or likely to be frustrating because there is no clear answer other than the loop, without finding an alternate path. A good brain exercise, no question. Second, while looking at the visual ways to consider this, since I'm an occasional artist, I thought mapping it would be a great way to create some drawings or paintings and either add to them, based on what I saw, or call them finished. Either way, it's great for stimulating the mind. And if anyone chose to read all this, it's also fun to think about.

[@beauxsmith674]

12

[@hasselbecksucks]

The video is 20 minutes. LoL. Of course they not going to watch it.

[@GnarlsMSMREAL]

It's 4

[@05DarkSaint]

1,2,4,8,16,32,64,128,256 So long as 3x+1 solves for a multiple of doubling, which will also go on to infinity, then so too must the equation

[@Guywiththetypewriter]

Hey all. If ur seeing this 2024 I have a treat for ya all. The sum of 4^n with limits k=0 to n, calculated via geometric series.... is equal to (4^(n+1) -1)/3 -1 and then /3 . So any odd number in form of a sum of the powers of 4 is equal to a power of 4 when 3x+1... Powers of 4 then immediatly reduce to the 4 2 1 pattern... The pattern at the end of the conjecture is a side effect of the 2 actual proveable parts of collatz. Any sum of the powers of 4 multiplied by 3 and adding 1 leads to a power of 4. A power of 4 divided by 2 will only become odd when it reaches 1. 1 is the sum of the powers of 4... i.e 4^0... The loop is caused by the coincidence of 1 being the only odd number that is both a power of 4 and a sum of powers of 4 at the same time.

[@Drux.i]

I have never been someone who liked math during school, but for some reason I find it so completely interesting to learn about on my own time.

[@ultraslanmc4619]

cause you don’t have an exam and your future on it while watching this video, but at school, yes

[@Drux.i]

@@ultraslanmc4619 That's a very good point! No stress to learn it 😂

[@odiltursunov6854]

Actually i liked it at school. But it annoys me at school

[@thelocalnecromancer1224]

Same. Things are so much more interesting when you learn them on your own than when you learn them at school.

[@Serpentis666]

The yearn for understanding really seems to increase with age…

[@shadyceddy6509]

Fun fact: We are not mathematicians but we got interested by this.

[@amirpakravan4389]

People that know math are are mathematicians and also if thay do math they are mathematicians

[@justinerek779]

ikr

[@rayanhaq8552]

I am

[@motherkhapudang3938]

Hmmm

[@fnxrz7513]

@@amirpakravan4389 shut up u ruin the vibe

[@thatfuzzypotato1877]

I would place my bet on if there IS an exception, it's a new loop not a number that shoots off to infinity (in which case that number in itself would have to be proven to shoot off to infinity and not get into some other insane loop at numbers too high to comprehend)

[@fysics5375]

You can say that y=2^x is a true solution, since that will always divide down to 1. Take all the whole answers to y=2^x, then try to find any numbers that lead into those using 3x+1. Then continue to extrapolate that out. Figure out if there are any excluded values. Working from the solution back I think would be faster.

[@adityaagarwal6719]

"Worlds Greatest living Mathematician" I see what you did there.

[@chriswebster24]

*there

[@adityaagarwal6719]

@@chriswebster24 thanks.. Noted!

[@mistersunny3636]

Ahaha! That sequence took me a second. Nice one! (12:33)

[@emilpysenisoncrack420]

Could I get some clarification?

[@emilpysenisoncrack420]

@Chinmaye Last name Well now it's obvious. Thanks

[@TheMusicalStylingsofBrentBunn]

Mad respect to the animators here. That must've been a lot of work.

[@michagiedrojc5513]

And how much work on calculator.

[@isidorregenfu9632]

Looks like 3blue1brown's framework manim at work

[@someidiot6067]

i agree, but there are other people that have animators do even more like haminations (he's a story time animator)

[@quyento9108]

Someone's back is hurtt

[@cissedeclercq5567]

we do or best.

[@ThatOneKat511]

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.

[@dewaard3301]

I feel that the answer lies in a different representation of the natural numbers that kind of represent 'power of 2'-ness, and showing that that can never increase under the operations described.

[@parvizsattorov2411]

Looks like a good formula for generating Mountains in a virtual environment.

[@SparinglyIsDumb]

Ye

[@kalucardable]

that's how they make roller coaster rides

[@mosab_faozi]

Perlin noise: am I a joke to you?

[@-morrow]

not really, mountains aren't created by random processes.

[@bmwheel1263]

If you use a decimal the number will go for ever as eg: 1.23 you would x3+1 =4.69 4.69x3+1 = 15.7 the decimal number will always be multiplied by 3 leavening you with a always odd decimal. If you start with an even decimal the decimal will keep getting divided by 2 until the decimal meets 1 then it’s will continue to rise. Adding a decimal is a way to bypass the number having to turn even every time you times the number by 3 and add 1. You are welcome for me solving it.

[@Ali-Mhsn]

I laughed when he said "one of the greatest mathematicians" and showed his his grinning into the camera

[@jAYROCCS1x]

?

[@John-el5sv]

@@jAYROCCS1x 12:36

[@jAYROCCS1x]

@@John-el5sv i see. thought he meant the guy frm the beginning.

[@bill6687]

"The world's greatest mathematician: myself"

[@PureMagma]

Humble-bragging or else it's a better way to subvert expectations before revealing truth! Terry Tao looks like someone who would appreciate the joke. 😅

[@devangbajpai8608]

If we try the polynomial 3x + 1 for negatives then we will be stuck in a loop of -7 or -1 everytime for any negative integer. Try this too!

[@dustymiller65]

★ I love this math problem, it's like my life--difficult and unsolvable yet easy to live with if i purposely close my eyes. ❤️

[@WeloTwelve]

"Pick a number, any number" Me: 42 "Picks 7 anyways"

[@peytenwalden8652]

Yes I always do thst

[@smolsoul1796]

Ah, the answer to life and everything.

[@thanos4784]

Ah yes, let me just adjust my super microphone so I can hear you through videos

[@LisaOnRoids]

Yup

[@wassuphoomanimyourlocalali3784]

I picked nine, not seven >:(

[@shiteshchourasia]

The transition at 12.33 "World's greatest living mathematician ..." was so hilarious. Well played sir.. well played.

[@karlmarx828]

12:33

[@blue_slime5776]

Yeah It Got Me Laughing

[@adityakrishnamalhotra1]

@@karlmarx828 i love you 😩😩 My favourite capitalist

[@dhruvalvyas3924]

He said “ONE OF THE world’s greatest living Mathematician".

[@giornogiovanna4602]

It seriously doesn't take effort to write 12:33 But seeing your pfp it makes sense since its shikamaru

[@NexusMatematica]

❤ A matemática é realmente encantadora 😮😮🎉 estou apaixonada!!

[@darrenleung3684]

Schools need more material like this to inspire kids

[@haxexd2830]

"Pick a number" "- Seven?" "Seven? Good choise!" "- Looks Back Carefully"

[@LaniPlayzRoblox]

*choice

[@keenjoaquin847]

@@LaniPlayzRoblox *choise

[@mrcrunch4635]

@@keenjoaquin847 *chuse

[@Uranium_chewer]

@@LaniPlayzRoblox choes

[@ahhblehh]

@@mrcrunch4635 *cheese

[@danielwitham1791]

"use Benford's law for tax evasion" Got it

[@ujjwal2473]

next they'll invent another law for you to follow

[@jackrobinson9403]

Ffs even when you break the law you gotta follow other laws, huh? ):

[@von...]

@Soul Seeker appropriate name for someone who works at the IRS or on some other auditing team lmao

[@von...]

@@jackrobinson9403 I guess "only break one law at a time" spans between the laws of our society & the laws of mathematics lmao don't try to divide by 0 while smoking weed kids

[@shamsandharia123]

Most tax verification algorithms are having the same function in the root file patch 🤞

[@ahmedkhafage7783]

nice work man i love your explanation but i have only one question what about the x because we are saying 3x which means it has power one and to add or subtract numbers they need to have the same power

[@user-pk9qo1gd6r]

What are yo talking about exactly?

[@dgaubin]

Two thoughts for me. 1) If 100% of any number we've tried eventually gets back to the 4-2-1 loop, why should any other number behave any differently? Any bigger number is still a number with the previous numbers as factors. The predictabity of 100% suggests every number will resolve to the 4-2-1 loop and no one has yet to prove otherwise. 2) Every exercise produces even numbers which, after dividing by two, continues the exercise at half the "altitude" of numbers, pulling our next step back down to within the range that we have already proven will resolve to 4-2-1. So, in terms of what a number "is" (eg, not 0, or not infinity), all numbers, by all available evidences thus far, will resolve to the 4-2-1 loop. 3x+1 vs x/2 could be just part of the nature of numbers.

[@saifuusuri]

This problem makes all my life problems seem like child's play. Kinda like having existential dread when you realize how large the universe is.

[@Link-12]

me to :p

[@AnAnonymousMan]

1k square miles ?

[@king_james_official]

@@AnAnonymousMan three, take it or leave it

[@maxwellsequation4887]

It makes me feel better when I realise that. Maybe you just have way too much undeserved ego.

[@saifuusuri]

@@maxwellsequation4887 When did I ever say it didn't do the same for me? I feel better too.

[@theseculartheist3239]

The introduction of Terry Tao was top-notch.

[@rishabhkumarparashar1045]

Nah I disagree

[@koreanstallion]

I 've been waiting to get struck by a lightening and receive the answers in my singed head. I will let yo u know. Great video!

[@JD_Mortal]

It's a quirk of base-10. Do it in base-8, base-3, base-40... and you get different, but similar results. It is the (division) and (+1), which is the secret to the quirk... Because (1/3) * (3) != 1... Go back to your "remainders", where they loop down to 1, with powers and +1. 4 + 2 + 1 = 7, which goes Even, Even, Odd, which cancels out the formula of halves and +1 by 3 units. Also, 4=3+1, and 2+1=3, (It's starting to look like the math formula itself.)

[@jmodified]

It's the same in any number base or representation. You can use Roman Numerals if you want.

[@extravagantpanda7962]

Base is irrelevant here. It is just the way we represent numbers in writing, but the actual relations between the numbers does not depend on the base. Think of the base as a language (e.g. German). If we translate a statement in German to, say, French, we are changing the representation we use to write the statement (the language), but the semantic meaning stays the same. Similarly, if we have some arithmetic expression written in base 10, then changing to base 2 only changes the written representation of the numbers and not the meaning of the expression.

[@xTANNA3]

Me: “tries to do it in negative” “Gets in a loop anyways”

[@xTANNA3]

@UC-cuXojkaoATvG21be0s25w 0 x 3 + 1 = 1 And 1 x 3 + 1 = 4 then divide 4 by 2 it’s 2 then divide it again it’s 1 And yeah we’re stuck no matter how you try it

[@One-Trick-Pony2]

True

[@Mango-rl2yg]

This is really dumb 3x+1=3 because u plus the 0 with the 1 = 3x1 I hate math and dont know anything about it but i still clicked on this vid

[@frightenedsoul]

@@Mango-rl2yg huh?

[@annac.6863]

@@Mango-rl2yg if you meant 3x+1 where x=0, the result would, indeed be zero. Anything times zero is zero, meaning 3•0=0 From there, you add the one, giving you 1 as a result. My apologies if I misunderstood what you were trying to say! ❤️❤️❤️

[@whosnico4669]

him: "pick a number, any number." me: "eight.." him: "seven? good choice!"

[@sarahsanchez150]

5... 😭😭

[@KratonWolf]

Me: 0. Him: ok, if it's odd, × 3 + 1, if even, ÷ 2 Me: I think you just broke your calculator.

[@savathunthewitchqueen8299]

@@KratonWolf yeah. 0 really isn’t even or odd, so your just stuck

[@adcgdsin9320]

@@savathunthewitchqueen8299 and even if you do plug in zero to 3n+1, you go back to one.

[@iteratedofficial]

Ikr... I picked 4...

[@TheButtflyEffectAnimator]

i have watched this *37* times. its too good.

[@AlbertSatnoianu]

*37*

[@nikolaifalk803]

I was tought more maths from this video than any of my classes

[@cryofrostrs3856]

I love on how people immediately pointed their fingers to the Soviets for an unsolvable problem

[@toolaazy]

I go to Confucius

[@YOUNOTSMART]

@@toolaazy And Confucius says

[@anmoldeepsingh9281]

@@YOUNOTSMART I am confusion, this is kansas, why this arkansoo, america eggsplain

[@YOUNOTSMART]

@@anmoldeepsingh9281 😭😂🤣😭😂🤣

[@johnjonjhonjonathanjohnson3559]

@@YOUNOTSMART no more numbers jumping on the graph

[@volcarona.]

I'm proud of myself for voluntarily watching a video about Math

[@presidentfresh448]

big brain moment

[@andrewjessicahersh9466]

Haha my sentiments exactly!

[@ultimatemonster5987]

This is an epic gamer moment

[@ultimatemonster5987]

This is an epic gamer moment

[@Griffin12536]

Every journey to the couch begins with a single step.

[@residentenigma7141]

These people have too much time on their hands... And the power to them !

[@oinvestigard]

All these numbers are beautiful, but nothing, but this one is weird, but possibily valuable.

[@gopiharwani5765]

You could see the pain in the eyes of prof. Alex. He spends 20 years on this problem. 20 YEARS.

[@MrAshtute]

There's a man in dire need of a life.....

[@AMP_7]

Yet... It would be nice to have a unchangeable objective for 20 years, something to dedicate your life on, something to challenge you daily, keep you intrigued, engaged, energized ! It's, in fact, a good thing. Painful, yes, but good thing :)

[@novatime3214]

in 20 years he realised his wife had left him, and he had wasted his life

[@MrAshtute]

@@novatime3214 it wasn't an entire waste...his wife left him 😁

[@KokeBeast23]

Obviously not all on this one problem

[@shadaabansari6654]

The urge to solve this problem is directly proportional to the amount of work already in hand.

[@segmentsAndCurves]

exponential*

[@joriskylie6857]

What exactly is the problem?

[@felosrg1266]

The classic "To big to fail" problem

[@patricknez7258]

Nice!

[@qwerty11111122]

sunk cost fallacy

[@Colour_beaks]

0:26 Seven is the most common number to pick, it's also has an interesting sequence

[@vgrants1717]

In theory, all times that the # will go down to the 4,2,1 loop is when the number is 2^x. Using that as a starting point, you could find a trend in how long it takes the number to hit 2^x. Smaller even # have an advantage because the numbers from 2^x are more concentrated there. Another thing is that the +1 is the only thing that makes sure that you don’t get into a different loop. The blend of addition and multiplication creates an annoying “randomness”.

[@fos1451]

Without the +1 it will keep being an odd number

[@RobertGOrtega-eh9zl]

Since I see no = sign, I'd assume the answer would be equal to - 1/3 but that equals zero. A trick question like no want wants to see that 2 to the x = 9 as x equal pi because round off a number does not give a true statement if you are only using a two decimal situation, but some are afraid to expand beyond for digits because it is to much mind set usage?

[@kg4wwn]

We need to have every high school math teacher put this on the whiteboard for the extra credit exercise and see which previously undiscovered kid makes a breakthrough because they don't know that they aren't supposed to be able to solve it.

[@legitvone4575]

Well the first thing anyone is gonna do is look it up online and they'll find it's a well known problem. But yes it sounds like it would make for a fun problem to look at regardless.

[@Duplicitousthoughtformentity]

Can’t wait for Matt Damon to solve it!

[@technomage6736]

Solve what though? 3x + 1??

[@kg4wwn]

Oops, I just realized I conflated the stories of Carl Gauss and George Dantzig in my head. We don't need to do this in schools as extra credit, we need to leave it up on boards in college so that everyone who arrives late thinks it's homework.

[@alexokin6819]

Its on d worldwide blackboard called footube

[@FullMetalOptimusPrime]

Honestly maths should just grow up and solve its own problems

[@EvenFive]

That's what AI is.

[@divyanshusingh7767]

I laughed so hard!😂 Thank you

[@jasonspades5628]

Yeah that was funny as hell

[@shsjjhsh]

lol

[@ttoo1830]

Good one!

[@basje_b]

15:09 - if you count 3x-1 on the negative side you do get the same 'tree' (mirrored) as the one on the positive side...

[@danmcconnell5941]

It’s a nonlinear dynamical system with a point attractor. It perhaps even describes the heat death of the universe. Conway’s game of life is a simple example.

[@ishanpujari2171]

"It's a simple spell, but quite unbreakable" ~ Dr. Strange

[@SienaaBee]

Perfect.

[@tina5833]

Yes.

[@joehadari7315]

Fitting

[@shrirangbondale8711]

And this comment is just like last piece of jigsaw puzzle

[@raoutsigueddoura3859]

I like your style

[@MrScientific]

Nice work Soviets. You got me.

[@HottestBrownMan]

Hitler be like :

[@akshatvikramsingh8293]

@@HottestBrownMan I was watching this video without signing in, but signed in just to like your comment buddy.

[@vigilantcosmicpenguin8721]

The Cold War won't truly be won until the Collatz Conjecture is resolved.

[@HottestBrownMan]

@@akshatvikramsingh8293 thanks mate.

[@ultramb6206]

Ngl i hate your facebook page lol

[@foliostarbi5744]

You know mathematicians are lost when they brutforce not just to visualise but also try to prove something first and then make the logical calculation after.

[@ryantownsend2730]

I fail to see how this is a math problem, but kudos for the work and the views

[@XCC23]

Because math problems once you get beyond middle school (sometimes beyond high school) are much less about "calculate the length of this triangle side" and much more things like "prove that triangles with identical angles are similar (can be scaled and rotated to be identical to each other)

[@Christopher-of-Columbus]

I'm not a mathematician but found this fascinating enough to watch the entire video.

[@jplaguee88]

Same

[@Yxnte]

Fr bro also me

[@laurenpowers2100]

Sam3

[@bee14.]

everyone is a mathematician whether they know it or not ew wtf just happened

[@user-xw4mu6nz4t]

Yep, so did 99.9% of viewers that watched

[@jetstreamsam9580]

The class: 3+5 The homework: 3 times the square root of 4 The exam:

[@drawingtutorials7296]

Exactly we go over short division then the exam is like (2a+1b)/10 the times by 10

[@kassimasinia3314]

For real the homework and class work are like 3 x 2 and the test is like calculate the diameter of the sun and multiply it by the amount of water molecules are in a single bottle of water.

[@Smdday._]

Homework equals 6🕺🏾

[@HorrorGirl-tb2yo]

@@Smdday._ Dang it! I was gonna say that!😂

[@krayon1034]

The answer is six

[@RINO_POACHERPATRIOT]

Such a great video.

[@user-qg1kp3yy8o]

In algebra, if a expression like 3x+1 does not have a Greatest Common Factor except 1, It's prime, so regardless you would get the same result?