The Simplest Math Problem No One Can Solve - Collatz Conjecture

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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

Опубликовано:

29 июл 2021

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Комментарии : 78 тыс.

@k.pacificnw02134 2 года назад

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

@TheGreekGodOfWallStreet 2 года назад

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

@evilkillerwhale7078 2 года назад

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

@jrbros2371 2 года назад

I too thought i could solve it :D

@systim30 2 года назад

What is there to solve? There is nothing to solve

@jrbros2371 2 года назад

@@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

@marcokapusta3843 2 года назад

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

@JeffMTX 2 года назад

you too? :)

@luca6819 2 года назад

I tried to remove the eyelash on the display 🤭

@davidbesant 2 года назад

There's that damn eyelash on my screen again!

@RetroFuel 2 года назад

@@luca6819 .same lol

@Hoshino_Channel 2 года назад

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

@user-ik4so3yp2e Месяц назад

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 Месяц назад

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 23 дня назад

lol

@user-oq5gn6br1u 12 дней назад

😂 lol

@MathemBrathlem 4 дня назад

W Editor for the humor

@HarmonRAB-hp4nk 17 часов назад

(3x) +1 is correct.. ya cant just do +x they'd require a parathesis so, (3Ax)+1B ... answer is 3AB or 3A 1B ? algebra is killing me lol to long ago .... lol

@shmuelman 2 месяца назад

Certainly one of the finest mathematical videos on RU-vid.

@__cypher__ 7 дней назад

Wait ... What?!

@xninja2369 7 дней назад

3Blue1Brwon be like ? 🫥

@grimaffiliations3671 2 года назад

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

@aashsyed1277 2 года назад

Noo

@segmentsAndCurves 2 года назад

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

@srijanpanicker5395 2 года назад

LMAO🤣🤣🤣

@rana8440 2 года назад

😝

@Pikachu-Gaming1764 2 года назад

Lol

@Naurik 2 года назад

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

@EnriqueLaberintico 2 года назад

History of the entire world, I guess convinces me.

@octaviovilchez3096 2 года назад

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

@alexmangorove 2 года назад

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

@seanallen8828 2 года назад

English, grammar

@benfulford3943 2 года назад

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'.

@CourtneyIsLovely 2 месяца назад

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

@Juggeraufesser 17 часов назад

Same

@salahsedarous7616 3 месяца назад

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

@Yihtc 2 года назад

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

@rachelx04 2 года назад

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

@palindromia130 2 года назад

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

@ArcFenixDelacroix 2 года назад

I think Im the only one who chose 7

@vor0g 2 года назад

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

@samirh2758 2 года назад

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

@cosmicnomad8575 2 года назад

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

@soumyadityachakraborty2457 2 года назад

ridiculous too

@oreziopancrazio3685 2 года назад

I totally agree. What a waste of time

@christloen4077 2 года назад

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

@oreziopancrazio3685 2 года назад

@@christloen4077 No way

@christloen4077 2 года назад

In your mind

@AshenElk 4 дня назад

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.

@richardfellows5041 Месяц назад

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 Месяц назад

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

@jokes.on.u 2 года назад

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 2 года назад

facts

@lordsiomai 2 года назад

Imma use this

@scottmurphy248 2 года назад

@@lordsiomai be honest, no you won't

@compszn 2 года назад

@@anyaburke6636 its 6

@krisha8430 2 года назад

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

@agentkp4574 2 года назад

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

@davidmedina7721 2 года назад

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

@apbe2q35 2 года назад

3 years year old me : what is maltiplikaton?

@Seeker-dx1gj 2 года назад

@BoEatsApples 2 года назад

13 Million*

@Penguins459 2 года назад

@mjh3067 4 дня назад

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

@DeadKarlisAlive 2 месяца назад

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

@shadyceddy6509 2 года назад

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

@amirpakravan4389 2 года назад

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

@justinerek779 2 года назад

ikr

@rayanhaq8552 2 года назад

I am

@motherkhapudang3938 2 года назад

Hmmm

@fnxrz7513 2 года назад

@@amirpakravan4389 shut up u ruin the vibe

@ghostphalanx 2 года назад

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

@pratanakangsadal521 2 года назад

Amen.

@gn4sty731 2 года назад

BR?

@GamingWithTimmy0 2 года назад

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 2 года назад

Math

@cirque1783 2 года назад

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

@HemanthHR-fi5rq 2 месяца назад

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

@kelvinedits9471 21 день назад

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

@leebydeeby 2 года назад

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 2 года назад

nerd

@livinglogically8180 2 года назад

Atleast find better ways of procrastination

@r-a-kralphandkoto2413 2 года назад

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

@Mr.Human69 2 года назад

Ez Answer Is 9 I was Doing my math Homework Bruh

@sera_makyuri 2 года назад

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

@Hanyamanusiabiasa 2 года назад

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

@Dizzy00001 2 года назад

Lol

@theultimatetime8029 2 года назад

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 2 года назад

@@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 2 года назад

@@mjzudba5268 yes ofcourse

@khuetranxuan8218 2 года назад

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

@ThatOneKat511 11 дней назад

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.

@priordan80 26 дней назад

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.

@weedy_yeast 2 года назад

I think a lot of us clicked on this video thinking: *”oh it can’t be that hard”* edit: Jesus I didn’t post this comment so ppl could just argue in the replies. It was supposed to be a joke

@mlpfanboy1701 2 года назад

Its only hard to find if you only work with whole numbers, at least assuming thats how mixed numbers would work Never mind a simple search says decimals cant be odd or even only integers, so yes it is that hard

@Auromaxis 2 года назад

@@mlpfanboy1701 i just solved this lol

@zenixx_168 2 года назад

@@Auromaxis what is it?

@EchoYoutube 2 года назад

It’s easy, 0.

@Dragon_Mawce 2 года назад

@@Auromaxis ?

@kugelblitz7946 2 года назад

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

@itismethatguy 2 года назад

Ikr

@Sintinium 2 года назад

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 2 года назад

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

@AxxLAfriku 2 года назад

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 2 года назад

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

@darrenleung3684 2 месяца назад

Schools need more material like this to inspire kids

@aladpresspays 23 дня назад

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.

@walkastray007 2 года назад

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 2 года назад

Good pickup!

@valval4145 2 года назад

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 2 года назад

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 2 года назад

@@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 2 года назад

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??

@javiersolis2993 2 года назад

The animation is everything here.

@milkshake7180 2 года назад

@DON'T stfu

@reallemming1dago..888 2 года назад

@DON'T stfu bi-

@WillCrewMusic 2 года назад

You both just fell for his trap lmfao

@milkshake7180 2 года назад

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

@everywhereman9003 2 года назад

@DON'T IM GONNA SAY THE N WORD

@adw1z Месяц назад

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!

@nikolaifalk803 2 месяца назад

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

@parkiel54 2 года назад

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

@CoreDeck 2 года назад

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

@remenyo 2 года назад

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

@user-xf6ox6zx4w 2 года назад

Amajing

@danielrasheedi 2 года назад

@@remenyo what is it??

@MehtabSinghEdhan 2 года назад

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

@Martdogg3000 2 года назад

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.

@DeadAzz2 2 года назад

You take my words from my mind :))

@ItsMe-gw4kb 2 года назад

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 2 года назад

@hasselbecksucks 2 года назад

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

@GnarlsMSMREAL 2 года назад

It's 4

@wtcodingproductions 2 месяца назад

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 25 дней назад

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

@prasadbhalerao8556 17 дней назад

@@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 16 дней назад

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

@libbydaddy8610 3 дня назад

How'd I miss this program?! Love this stuff

@nimamaster6128 2 года назад

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

@ShatteredCelestial 2 года назад

wait really? lmao

@shibe6181 2 года назад

Wow 4th

@cristianrivas4606 2 года назад

Can we not use decimals?

@Arthurgoldlizard 2 года назад

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

@artificialintelligenceplus1321 2 года назад

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

@demensclay6419 2 года назад

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

@gniewko123456 Год назад

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

@josiahjray Год назад

I really hope this is satire 🤣🤣

@gniewko123456 Год назад

@@josiahjray baited :D

@josiahjray Год назад

@@gniewko123456 Hope so lol

@anndyarguedo4453 Год назад

Ah yes, 999 likes

@AndresFirte 3 месяца назад

Judging from the comments, the Collatz Conjecture could probably have more distinct proofs than the pythagorean theorem! And all of them from engineers, programmers, computer scientists, and amateur physicists with no formal mathematics background! Wonderful!

@jmodified 3 месяца назад

Not so distinct though. At least 80% of the "proofs" are "Over a given number of steps, the odds of the sequence going down is higher than the odds of it going up". Most of the rest are "It has to hit a power of two eventually".

@AndresFirte 3 месяца назад

@@jmodified oh yeah, and let’s not forget the third kind: just look at the last digit, it works for 1,2,3,4, … 8,9. And since every number has those numbers as last digits, it must work for all of them too!

@jmodified 3 месяца назад

@@AndresFirte Yes, I forgot that one. I think those three cover at least 99%.

@XCC23 3 месяца назад

The video: "This seems like a really easy problem which is why a lot of mathematicians are curious about it, since it's actually insanely hard" Laymen watching this video: "Pfft, this seems like a really easy problem" Almost like that was why it was interesting in the first place

@darthenx2585 2 года назад

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

@chronical 2 года назад

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

@peterh222 2 года назад

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

@markjohnson7508 2 года назад

Really.. wow. Entropy maybe

@josefwakeling7103 2 года назад

@@peterh222 *disillusion

@birchthebirch4593 2 года назад

Listen ...don't look

@Drux.i 2 года назад

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 2 года назад

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

@Drux.i 2 года назад

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

@odiltursunov6854 2 года назад

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

@thelocalnecromancer1224 2 года назад

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

@Serpentis666 2 года назад

The yearn for understanding really seems to increase with age…

@borzica 7 дней назад

I’ve actually always thought about this 4-2-1 loop and never knew there was a name for it. I always thought I was too dumb to figure it out.

@devangbajpai8608 3 месяца назад

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!

@Pansotii 2 года назад

This sounds like a problem that we will one day show to a chaotic, but brilliant and creative child/teenager and he will just give us a counterexample in minutes and no one would know how

@owenlee913 2 года назад

Hey what about she it doesn’t need to be a he

@zainelsayed9007 2 года назад

@@owenlee913 i really hope you’re being sarcastic

@stephenhorgan7110 2 года назад

Then he'll solve it and say "how do you like them apples"

@ginger-ale7818 2 года назад

@@owenlee913 Well statistically, that kind of very exciting thinking is found in Savants and autism is more common in men. One could say that almost all savants are he.

@Jelle175 2 года назад

@@owenlee913 Or a non-binary or a trans kid or someone identifying as a AH-64 Apache helicopter. But probably an AI

@isaacpalmer1195 2 года назад

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

@cryptedmage9739 2 года назад

Lol wassup homie

@dino_tokic8884 2 года назад

Lmaoo

@WestExplainsBest 2 года назад

Ugh those programs are virtual math teachers worst nightmare.

@Guywiththetypewriter 2 месяца назад

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 Месяц назад

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 Месяц назад

how long did this take

@Guywiththetypewriter Месяц назад

@@kinetik9197 how u mean

@jenniferzeng5735 9 дней назад

Wow …. This is actually really smart

@BlackHayateMX 3 дня назад

You know, I'm not an expert or anything on mathematics but I'm a programmer so... this sounds like a very solid proof to me

@alexanderstohr4198 2 дня назад

15:50 - the widening of the chart to the right gives a quite interesting pattern of curves that are looking like it were sinus and/or of parabolic definition. also note that it looks like about the left 1/4 width of the area forms a stripe that is more or less avoided by dots.

@changolord93 2 года назад

-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 2 года назад

He had me too! Brilliant!

@anonamemous6865 2 года назад

He had me too

@DrakyHRT 2 года назад

@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 2 года назад

LOL

@lunatik4265 2 года назад

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

@MrScientific 2 года назад

Nice work Soviets. You got me.

@HottestBrownMan 2 года назад

Hitler be like :

@akshatvikramsingh8293 2 года назад

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

@vigilantcosmicpenguin8721 2 года назад

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

@HottestBrownMan 2 года назад

@@akshatvikramsingh8293 thanks mate.

@ultramb6206 2 года назад

Ngl i hate your facebook page lol

@nobody-fe4gn День назад

I hate math when i was in school and college, but suddenly i found this channel and… i’m start to like math

@oinvestigard Месяц назад

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

@cryofrostrs3856 2 года назад

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

@toolaazy 2 года назад

I go to Confucius

@YOUNOTSMART 2 года назад

@@toolaazy And Confucius says

@anmoldeepsingh9281 2 года назад

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

@YOUNOTSMART 2 года назад

@@anmoldeepsingh9281 😭😂🤣😭😂🤣

@johnjonjhonjonathanjohnson3559 2 года назад

@@YOUNOTSMART no more numbers jumping on the graph

@CrimsonRegalia 2 года назад

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

@anunknownperson4018 2 года назад

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

@vector1213 2 года назад

Big maffs

@fanaticjay3825 2 года назад

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

@Floorlicker2000 2 года назад

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

@HaaKaaf 2 года назад

@@fanaticjay3825 bruh what

@OptimusPhillip День назад

I feel like there's a broader point that's missing here: every number that leads to the 1-2-4 loop must be a power of 2. Of the three numbers in the loop, only 4 can be reached by 3x+1, and that requires x to be 1. Any other way to reach any of those numbers requires an approach from x/2. So this conjecture can be restated from "...must go to the 1-2-4 loop" to "...must go to a power of 2". I don't know how much that helps, but I feel like the shift in perspective should be useful.

@residentenigma7141 Месяц назад

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

@adityaagarwal6719 2 года назад

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

@chriswebster24 2 года назад

*there

@adityaagarwal6719 2 года назад

@@chriswebster24 thanks.. Noted!

@mistersunny3636 2 года назад

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

@emilpysenisoncrack420 2 года назад

Could I get some clarification?

@emilpysenisoncrack420 2 года назад

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

@Liur. 2 года назад

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

@Liur. 2 года назад

@@Sinaloabricks hypotheses is the plural 🙄

@er00ic 2 года назад

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

@andrewcramer9200 2 года назад

Statistician: *does both in bipolarity*

@paxhumana2015 2 года назад

Is not mathematics merely just a part of science anyway?

@paxhumana2015 2 года назад

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

@oriongurtner7293 3 дня назад

I did a bit of mind-numbing study into this problem and the Twin Prime Conjecture and found some surprising intersections, mostly in how prime numbers interact with each other to disperse composite numbers throughout the number line Sadly it doesn’t answer either problem, but it does provide some insight into how both conjectures might be solved, or at least how they both can’t be solved And it’s really not all that confusing, it all comes down to primes greater than 3 (and their respective composites) are all +/-1 of all the multiples of 6, and how the composites are all in a +/-1 position based on whether their factors were the same polarity or opposite of each other And, well, the non-triple evens do exactly the same thing, they just also include the p>3 group in the factors, which is where the 3n+1 comes into play, as those are the numbers you encounter upon using that function (and the n/2 part as well) Notably: that does NOT include triples, as those cannot be +/-1 of each other, and as such the only triples you’ll encounter are the ones you start with in the case of odd triples, or the initial halving-chain for even triples Fun stuff, very little use in it but boy is it fascinating 🙂

@someonegreat_ Месяц назад

All of Veritasium's videos prove that if you find a subject boring or cumbersome it's your teacher's fault

@DasSkelett 2 года назад

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

@lukelively8380 2 года назад

I was looking for this comment lol

@HungryTacoBoy 2 года назад

Same here. I thought it was very clever.

@cortnetisjustbetter 2 года назад

* You're , btw I am better than you

@MightyHashBrown 2 года назад

@@cortnetisjustbetter not you’re but ok

@Sleepy_Joe 2 года назад

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

@colebrew 2 года назад

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

@JosephAR513 2 года назад

BRO😂😂

@Fixis 2 года назад

Everyone chooses 7 cause 7 wins everytime lol

@Byokie1 2 года назад

SAME

@DaisyCoreXD 2 года назад

Lol same

@sunset_anything1875 2 года назад

I think it’s 3

@dewaard3301 Месяц назад

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.

@koreanstallion 20 дней назад

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!

@Yextiny 2 года назад

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

@holdontoyourwig 2 года назад

You could start by calling it MATHS

@user-lg9cf4sw4x 2 года назад

my dumbass brain is quaking

@001100AAAEA 2 года назад

Pretty much lol

@babydriver8134 2 года назад

Weapons of Math Instruction?

@bujharvard9313 2 года назад

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

@TheMusicalStylingsofBrentBunn 2 года назад

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

@michagiedrojc5513 2 года назад

And how much work on calculator.

@isidorregenfu9632 2 года назад

Looks like 3blue1brown's framework manim at work

@someidiot6067 2 года назад

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

@quyento9108 2 года назад

Someone's back is hurtt

@cissedeclercq5567 2 года назад

we do or best.

@rjkhatri6920 4 дня назад

This problem is very simple actually X+1 (X+1)*3 = 3X+ 3 (3x+4)/2 = 1.5x+ 0.75x+1 As long as “X” can be divided by 3 the loop doesn’t end

@Ali-Mhsn 2 года назад

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

@jAYROCCS1x 2 года назад

@John-el5sv 2 года назад

@@jAYROCCS1x 12:36

@jAYROCCS1x 2 года назад

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

@bill6687 2 года назад

"The world's greatest mathematician: myself"

@PureMagma 2 года назад

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. 😅

@FullMetalOptimusPrime 2 года назад

Honestly maths should just grow up and solve its own problems

@EvenFive 2 года назад

That's what AI is.

@divyanshusingh7767 2 года назад

I laughed so hard!😂 Thank you

@jasonspades5628 2 года назад

Yeah that was funny as hell

@shsjjhsh 2 года назад

lol

@ttoo1830 2 года назад

Good one!

@lamtungbenny6214 Месяц назад

If only decimals were allowed 😢

@EpicGamer-69 13 дней назад

Bro is onto nothing🔥🔥🔥

@TheButtflyEffectAnimator 23 дня назад

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

@AlbertSatnoianu 23 дня назад

*37*

@xTANNA3 2 года назад

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

@xTANNA3 2 года назад

@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 2 года назад

True

@Mango-rl2yg 2 года назад

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 2 года назад

@@Mango-rl2yg huh?

@annac.6863 2 года назад

@@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! ❤️❤️❤️

@parvizsattorov2411 2 года назад

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

@SparinglyIsDumb 2 года назад

@kalucardable 2 года назад

that's how they make roller coaster rides

@mosab_faozi 2 года назад

Perlin noise: am I a joke to you?

@-morrow 2 года назад

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

@bmwheel1263 2 года назад

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.

@Fraber87 14 дней назад

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).

@frtzkng 3 месяца назад

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?

@gopiharwani5765 2 года назад

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

@MrAshtute 2 года назад

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

@AMP_7 2 года назад

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 2 года назад

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

@MrAshtute 2 года назад

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

@KokeBeast23 2 года назад

Obviously not all on this one problem

@kg4wwn 2 года назад

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 2 года назад

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 2 года назад

Can’t wait for Matt Damon to solve it!

@technomage6736 2 года назад

Solve what though? 3x + 1??

@kg4wwn 2 года назад

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 2 года назад

Its on d worldwide blackboard called footube

@fysics5375 10 дней назад

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.

@05DarkSaint Месяц назад

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

@lovepuma6625 2 года назад

".....that not even the world's best mathematicians have been able to solve. " Me : "Alright, tell what it is, maybe i can solve it. "

@captaincool9636 2 года назад

I think it's just 10

@MP-ut6eb 2 года назад

@@captaincool9636 42. The answer is 42.

@NamidaCho 2 года назад

@@MP-ut6eb no not at all

@gbsantana9679 2 года назад

@@MP-ut6eb no, you don't know the answer if the best mathematicians don't know it. You're not that guy buddy

@MP-ut6eb 2 года назад

@@gbsantana9679 its meme my friend. Its a meme.

@Free2Flay 2 года назад

Two things I learned from this video: 1. Mathematicians smile gratuitously in front of cameras. 2. Boring subjects become interesting when they're accompanied by animated graphs.

@DGill48 2 года назад

Two to the 68 power?? lots of time on their hands

@manswind3417 2 года назад

@@DGill48 Or maybe lots of mathematicians and machines in the world's hands?

@Matthewjames1016 2 года назад

Wait til you find out .9 and 1 are equal

@JaseHDX 2 года назад

3. wHy DoNt PeOpLe GiVe Me A cHaNcE oN yOuTuBe????!!???!!

@oxanamikki3326 2 года назад

are u saying math is boring

@seroujghazarian6343 Месяц назад

I think the reason why this works is if we start with 1 and then apply the inverses of both rules and only leaving the integers, eventually, we can get all positive integers one way or another

@Sangeet794 Месяц назад

Dude ive solved this kinda problem once my friend asked me to do so during my JEE preparation , it was as easy as cherry of cake 💀

@TheSheep1 15 часов назад

“But any loop (other than the 4-2-1) needed at least 186,000 numbers” The number 0:

@sammcdonald4 2 года назад

Shows a picture of himself. “One of the world’s greatest mathematicians…Terry Tao” Then includes Terry. Lol

@GummieI 2 года назад

Yeah that was so good

@syedfaisal9544 2 года назад

😂, That's was funny , He's also good scientist tooo

@dreamer097 2 года назад

12:33

@Cube_Box 2 года назад

@@dreamer097 thanks

@rgmjr 2 года назад

Haha. I came to look for this. Haha.

@saifuusuri 2 года назад

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 2 года назад

me to :p

@AnAnonymousMan 2 года назад

1k square miles ?

@king_james_official 2 года назад

@@AnAnonymousMan three, take it or leave it

@maxwellsequation4887 2 года назад

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

@saifuusuri 2 года назад

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

@IHaveInfinityGaming 22 дня назад

It feels like I’ve learnt everything and nothing at the same time

@alexanderstohr4198 2 дня назад

15:55 - number of perfect squares in a base set: 100: 10% 1000: 3.1% - but we are talking on squares and their likeliness shrinks quadratically... so for a honest comparison lets do this: 3.1*3.1 = 9.61 - the fraction difference is supposed to be caused by the finite nature of integer value granularity. counter check: square root of 10 = 3,16227766...

@shadaabansari6654 2 года назад

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

@segmentsAndCurves 2 года назад

exponential*

@joriskylie6857 2 года назад

What exactly is the problem?

@felosrg1266 2 года назад

The classic "To big to fail" problem

@patricknez7258 2 года назад

Nice!

@qwerty11111122 2 года назад

sunk cost fallacy

@jetstreamsam9580 2 года назад

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

@drawingtutorials7296 2 года назад

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

@kassimasinia3314 2 года назад

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._ 2 года назад

Homework equals 6🕺🏾

@HorrorGirl-tb2yo 2 года назад

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

@krayon1034 2 года назад

The answer is six

@Symbioticism 5 дней назад

That ending really gave me chills

@dany_fg 12 часов назад

he chose 7 at the beginning of the video. it's 37 all over again.

@whosnico4669 2 года назад

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

@sarahsanchez150 2 года назад

5... 😭😭

@KratonWolf 2 года назад

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

@savathunthewitchqueen8299 2 года назад

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

@adcgdsin9320 2 года назад

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

@iteratedofficial 2 года назад

Ikr... I picked 4...

@dabolife1 2 года назад

Math problem no one can solve: Exists Me: Finally I'm not the only one who is bad at math.

@risav202 2 года назад

Not able to do a math problem, doesn't make you bad at math.

@therealitygab6074 2 года назад

@@risav202 please explain. i dont agree

@segmentsAndCurves 2 года назад

@@risav202 Nah.

@mjzudba5268 2 года назад

I literally just saw you on Nas Daily...

@TheDarkDresser 2 года назад

@@risav202 I assume that you're not referring to math in general, just a specific math problem. Those of us with dyscalculia find even basic math challenging, to say the least.

@SHADOWBANE369 2 месяца назад

That we need we we need is math that makes us curious

@orsonewe3893 Месяц назад

This is actually an interesting concept, the moment the number reaches a number that is a power of 2,it falls all the way down to the 4-2-1 loop.

@kittycat0143 Месяц назад

This is why I believe this conjecture is true for all numbers. The probability is almost certain for a chain to hit a power of two somewhere. But I mean I haven't dealt with numbers quite that high yeeeeet. Maybe someone in the future will prove my thinking wrong

@orsonewe3893 Месяц назад

@@kittycat0143 there isn’t meant to be a number that doesn’t hit a power of 2 with this cycle, other than infinity, as we don’t know if it’s odd or even or even a number, but infinity is the only number that can follow this concept WITHOUT entering the 4,2,1 cycle

@kittycat0143 Месяц назад

@@orsonewe3893 the problem is infinity will never exist as a definite number as we can just keep adding 0s at the end and making bigger numbers... therefore this conjecture will never be proven false but theres no possible way to test all natural numbers

@fos1451 Месяц назад

@@kittycat0143the problem is really if the number itself hit a loop of itself. 5x+1 for example doesn’t always come back to 1, 13 is already a counter example that it will come back to itself

@Christopher-of-Columbus 2 года назад

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

@jplaguee88 2 года назад

Same

@Yxnte 2 года назад

Fr bro also me

@laurenpowers2100 2 года назад

Sam3

@bee14. 2 года назад

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

@user-xw4mu6nz4t 2 года назад

Yep, so did 99.9% of viewers that watched

@RiderGeats 2 года назад

Imagine being a Math Teacher and you gave an entire class an activity 1. Solve Collatz Conjecture 3x+1 (10 pts.)

@BrianHartman 2 года назад

The issue isn't solving it but proving it. :)

@brokenwingbird2552 2 года назад

It's not a problem, it is a pattern. There is no solution. This is literally the formula for how all life grows, 124875 this sequence repeats infinitely, with alternating "branches" of 36363636 also repeating infinitely.

@peregrina7701 2 года назад

I once had a professor set the proof of the Boltzmann equation on a midterm. That proof exists but for a nonmathematician/nonphysicist (I was studying materials science) it was a beast. The equation is s = k * ln (m). Looks simple doesn't it? That was twenty years ago and I'm still traumatized. Mad props to mathematicians.

@ItsSchwifty 2 года назад

Smart in class: *Gets 10pts*

@davidyansky6605 2 года назад

He/She would be barred from further teaching due to academic cruelty beyond comprehension.

@roby_fan2018 4 дня назад

2000 = 2 × 103 = 20 × 102 = 200 × 10 but also 2000 = 0.2 × 104 = 0.02 × 105 = 0.002 × 106. Once the basic concept is understood, practice does the rest. we want to calculate the square root of 0.01: √0.01 =√10−2.