The Simplest Math Problem No One Can Solve

The Simplest Math Problem No One Can Solve - Collatz Conjecture

Рет қаралды 39,642,314

2 жыл бұрын

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

Пікірлер: 77 000

@Yihtc 2 жыл бұрын

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

@rachelx04 2 жыл бұрын

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

@palindromia130 2 жыл бұрын

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

@ArcFenixDelacroix 2 жыл бұрын

I think Im the only one who chose 7

@vor0g 2 жыл бұрын

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

@samirh2758 2 жыл бұрын

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

@k.pacificnw02134 2 жыл бұрын

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

@TheGreekGodOfWallStreet 2 жыл бұрын

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

@evilkillerwhale7078 2 жыл бұрын

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

@jrbros2371 2 жыл бұрын

I too thought i could solve it :D

@systim30 2 жыл бұрын

What is there to solve? There is nothing to solve

@jrbros2371 2 жыл бұрын

@@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

@user-ik4so3yp2e Ай бұрын

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 25 күн бұрын

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 14 күн бұрын

lol

@user-oq5gn6br1u 3 күн бұрын

😂 lol

@shmuelman 2 ай бұрын

Certainly one of the finest mathematical videos on KZfaq.

@jokes.on.u 2 жыл бұрын

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 жыл бұрын

facts

@lordsiomai 2 жыл бұрын

Imma use this

@scottmurphy248 2 жыл бұрын

@@lordsiomai be honest, no you won't

@compszn 2 жыл бұрын

@@anyaburke6636 its 6

@krisha8430 2 жыл бұрын

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

@grimaffiliations3671 2 жыл бұрын

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

@aashsyed1277 2 жыл бұрын

Noo

@segmentsAndCurves 2 жыл бұрын

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

@srijanpanicker5395 2 жыл бұрын

LMAO🤣🤣🤣

@rana8440 2 жыл бұрын

😝

@Pikachu-Gaming1764 2 жыл бұрын

Lol

@tyagohiee 3 ай бұрын

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 3 ай бұрын

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 2 ай бұрын

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 2 ай бұрын

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

@None-Trick_Pony 2 ай бұрын

@@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 2 ай бұрын

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

@marcuswaterloo 3 ай бұрын

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 2 ай бұрын

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

@jesse406 2 ай бұрын

@@armin3057 dork

@SeanGonzalezMDHEXT 28 күн бұрын

@@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.

@cosmicnomad8575 2 жыл бұрын

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

@soumyadityachakraborty2457 2 жыл бұрын

ridiculous too

@oreziopancrazio3685 2 жыл бұрын

I totally agree. What a waste of time

@christloen4077 2 жыл бұрын

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

@oreziopancrazio3685 2 жыл бұрын

@@christloen4077 No way

@christloen4077 2 жыл бұрын

In your mind

@marcokapusta3843 2 жыл бұрын

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

@JeffMTX 2 жыл бұрын

you too? :)

@luca6819 2 жыл бұрын

I tried to remove the eyelash on the display 🤭

@davidbesant 2 жыл бұрын

There's that damn eyelash on my screen again!

@RetroFuel 2 жыл бұрын

@@luca6819 .same lol

@Hoshino_Channel 2 жыл бұрын

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

@pabescgmail 3 ай бұрын

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 2 ай бұрын

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 2 ай бұрын

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

@eon2330 2 ай бұрын

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 2 ай бұрын

@@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 Ай бұрын

@@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.

@salahsedarous7616 3 ай бұрын

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

@ghostphalanx 2 жыл бұрын

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

@pratanakangsadal521 2 жыл бұрын

Amen.

@gn4sty731 2 жыл бұрын

BR?

@GamingWithTimmy0 2 жыл бұрын

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 жыл бұрын

Math

@cirque1783 2 жыл бұрын

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

@agentkp4574 2 жыл бұрын

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

@davidmedina7721 2 жыл бұрын

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

@apbe2q35 2 жыл бұрын

3 years year old me : what is maltiplikaton?

@Seeker-dx1gj 2 жыл бұрын

@BoEatsApples 2 жыл бұрын

13 Million*

@Penguins459 2 жыл бұрын

@HemanthHR-fi5rq 2 ай бұрын

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

@gaving.griffon2703 3 ай бұрын

So, here's my observations. 2 to the power of any natural number will fit the conjecture. In addition, if we undo the opperation, we take (2^n)-1 and divide by 3, any output that is an odd, whole number will also fit the conjecture. My idea for solving it would be to see if there was a whole number that *didn't* fit the conjecture but that's just me.

@Hanyamanusiabiasa 2 жыл бұрын

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

@Dizzy00001 2 жыл бұрын

Lol

@theultimatetime8029 2 жыл бұрын

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 жыл бұрын

@@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 жыл бұрын

@@mjzudba5268 yes ofcourse

@khuetranxuan8218 2 жыл бұрын

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

@parkiel54 2 жыл бұрын

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

@CoreDeck 2 жыл бұрын

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

@remenyo 2 жыл бұрын

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

@user-xf6ox6zx4w 2 жыл бұрын

Amajing

@danielrasheedi 2 жыл бұрын

@@remenyo what is it??

@MehtabSinghEdhan 2 жыл бұрын

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

@kelvinedits9471 12 күн бұрын

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

@azhagurajaallinall126 2 ай бұрын

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)

@isaacpalmer1195 2 жыл бұрын

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

@cryptedmage9739 2 жыл бұрын

Lol wassup homie

@dino_tokic8884 2 жыл бұрын

Lmaoo

@WestExplainsBest 2 жыл бұрын

Ugh those programs are virtual math teachers worst nightmare.

@leebydeeby 2 жыл бұрын

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 жыл бұрын

nerd

@livinglogically8180 2 жыл бұрын

Atleast find better ways of procrastination

@r-a-kralphandkoto2413 2 жыл бұрын

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

@Mr.Human69 2 жыл бұрын

Ez Answer Is 9 I was Doing my math Homework Bruh

@sera_makyuri 2 жыл бұрын

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

@priordan80 18 күн бұрын

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.

@norsitoang7714 3 ай бұрын

Found a very cool pattern, I know it doesn't prove and solve anything, which is useless but here, any odd number(represented by Y) multiplied by 3 then added by 1 and divided by 2 will always equal to Y+[(Y-1)/2+1)]. For example "5" since its odd then do 3n+1 which equals 16 and divide it by 2 which gives us 8, and 8 is equals to 5+[(5-1)/2+1)].

@soulsand4287 2 ай бұрын

I found another pattern of odd numbers. 1 takes a single 3x + 1 to get to a multiple of 4. 3 takes two to get to 4x (3, 10, 5, 8), 5 takes 1, 7 takes 3 (7, 22, 11, 34, 17, 52). Basically, an odd number (Y) will take log2(Y + 1) repetitions of 3x + 1, x/2 to get to an even number.

@soulsand4287 2 ай бұрын

Actually, this solves it. Only infinity can go of to infinity. Even with that, (2^31) - 1, for example, will take 61 runs through the function to decrease.

@Sarstan 2 ай бұрын

5 + ((5 - 1) / 2 + 1) does not equal 8. I'm guessing you meant 5 + (((5 - 1) / 2) + 1). But yeah, that's kind of a neat way of compounding the two steps into one.

@aadichinmaysharma4000 2 ай бұрын

@@soulsand4287impressive! Do you gave any idea how to prove this though?

@soulsand4287 2 ай бұрын

@aadichinmaysharma4000 I don't think it's possible to prove. I definitely am not going to be the one to prove it.

@kugelblitz7946 2 жыл бұрын

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

@itismethatguy 2 жыл бұрын

Ikr

@Sintinium 2 жыл бұрын

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 жыл бұрын

@@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 жыл бұрын

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 жыл бұрын

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

@Naurik 2 жыл бұрын

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

@EnriqueLaberintico 2 жыл бұрын

History of the entire world, I guess convinces me.

@octaviovilchez3096 2 жыл бұрын

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

@alexmangorove 2 жыл бұрын

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

@seanallen8828 2 жыл бұрын

English, grammar

@benfulford3943 2 жыл бұрын

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'.

@frtzkng 3 ай бұрын

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?

@DeadKarlisAlive Ай бұрын

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

@darthenx2585 2 жыл бұрын

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

@chronical 2 жыл бұрын

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

@peterh222 2 жыл бұрын

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

@markjohnson7508 2 жыл бұрын

Really.. wow. Entropy maybe

@josefwakeling7103 2 жыл бұрын

@@peterh222 *disillusion

@birchthebirch4593 2 жыл бұрын

Listen ...don't look

@changolord93 2 жыл бұрын

-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 жыл бұрын

He had me too! Brilliant!

@anonamemous6865 2 жыл бұрын

He had me too

@DrakyHRT 2 жыл бұрын

@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 жыл бұрын

LOL

@lunatik4265 2 жыл бұрын

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

@gokulraj6404 3 ай бұрын

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.

@wtcodingproductions Ай бұрын

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 17 күн бұрын

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

@prasadbhalerao8556 8 күн бұрын

@@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 8 күн бұрын

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

@javiersolis2993 2 жыл бұрын

The animation is everything here.

@milkshake7180 2 жыл бұрын

@DON'T stfu

@reallemming1dago..888 2 жыл бұрын

@DON'T stfu bi-

@WillCrewMusic 2 жыл бұрын

You both just fell for his trap lmfao

@milkshake7180 2 жыл бұрын

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

@everywhereman9003 2 жыл бұрын

@DON'T IM GONNA SAY THE N WORD

@demensclay6419 Жыл бұрын

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

@gniewko123456 Жыл бұрын

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

@josiahjray Жыл бұрын

I really hope this is satire 🤣🤣

@gniewko123456 Жыл бұрын

@@josiahjray baited :D

@josiahjray Жыл бұрын

@@gniewko123456 Hope so lol

@anndyarguedo4453 Жыл бұрын

Ah yes, 999 likes

@Guywiththetypewriter Ай бұрын

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 Ай бұрын

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 Ай бұрын

how long did this take

@Guywiththetypewriter Ай бұрын

@@kinetik9197 how u mean

@jenniferzeng5735 Күн бұрын

Wow …. This is actually really smart

@aladpresspays 15 күн бұрын

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.

@nimamaster6128 2 жыл бұрын

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

@ShatteredCelestial 2 жыл бұрын

wait really? lmao

@shibe6181 2 жыл бұрын

Wow 4th

@cristianrivas4606 2 жыл бұрын

Can we not use decimals?

@Arthurgoldlizard 2 жыл бұрын

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 жыл бұрын

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

@Liur. 2 жыл бұрын

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

@Liur. 2 жыл бұрын

@@Sinaloabricks hypotheses is the plural 🙄

@er00ic 2 жыл бұрын

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

@andrewcramer9200 2 жыл бұрын

Statistician: *does both in bipolarity*

@paxhumana2015 2 жыл бұрын

Is not mathematics merely just a part of science anyway?

@paxhumana2015 2 жыл бұрын

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

@fysics5375 Күн бұрын

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.

@RobertGOrtega-eh9zl 3 ай бұрын

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?

@walkastray007 2 жыл бұрын

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 жыл бұрын

Good pickup!

@valval4145 2 жыл бұрын

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 жыл бұрын

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 жыл бұрын

@@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 жыл бұрын

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??

@shadyceddy6509 2 жыл бұрын

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

@amirpakravan4389 2 жыл бұрын

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

@justinerek779 2 жыл бұрын

ikr

@rayanhaq8552 2 жыл бұрын

I am

@motherkhapudang3938 2 жыл бұрын

Hmmm

@fnxrz7513 2 жыл бұрын

@@amirpakravan4389 shut up u ruin the vibe

@richardfellows5041 Ай бұрын

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 Ай бұрын

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

@thatfuzzypotato1877 3 ай бұрын

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)

@TheMusicalStylingsofBrentBunn 2 жыл бұрын

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

@michagiedrojc5513 2 жыл бұрын

And how much work on calculator.

@isidorregenfu9632 2 жыл бұрын

Looks like 3blue1brown's framework manim at work

@someidiot6067 2 жыл бұрын

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

@quyento9108 2 жыл бұрын

Someone's back is hurtt

@cissedeclercq5567 2 жыл бұрын

we do or best.

@DasSkelett 2 жыл бұрын

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

@lukelively8380 2 жыл бұрын

I was looking for this comment lol

@HungryTacoBoy 2 жыл бұрын

Same here. I thought it was very clever.

@cortnetisjustbetter 2 жыл бұрын

* You're , btw I am better than you

@MightyHashBrown 2 жыл бұрын

@@cortnetisjustbetter not you’re but ok

@Sleepy_Joe 2 жыл бұрын

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

@Fraber87 5 күн бұрын

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).

@austinvanderveer213 3 ай бұрын

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 2 ай бұрын

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

@CrimsonRegalia 2 жыл бұрын

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

@anunknownperson4018 2 жыл бұрын

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

@vector1213 2 жыл бұрын

Big maffs

@fanaticjay3825 2 жыл бұрын

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

@Floorlicker2000 2 жыл бұрын

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

@HaaKaaf 2 жыл бұрын

@@fanaticjay3825 bruh what

@Yextiny 2 жыл бұрын

"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 жыл бұрын

You could start by calling it MATHS

@user-lg9cf4sw4x 2 жыл бұрын

my dumbass brain is quaking

@001100AAAEA 2 жыл бұрын

Pretty much lol

@babydriver8134 2 жыл бұрын

Weapons of Math Instruction?

@bujharvard9313 2 жыл бұрын

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

@darrenleung3684 Ай бұрын

Schools need more material like this to inspire kids

@devangbajpai8608 2 ай бұрын

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!

@parvizsattorov2411 2 жыл бұрын

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

@SparinglyIsDumb 2 жыл бұрын

@kalucardable 2 жыл бұрын

that's how they make roller coaster rides

@mosab_faozi 2 жыл бұрын

Perlin noise: am I a joke to you?

@-morrow 2 жыл бұрын

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

@bmwheel1263 2 жыл бұрын

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.

@RiderGeats 2 жыл бұрын

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

@BrianHartman 2 жыл бұрын

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

@brokenwingbird2552 2 жыл бұрын

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 жыл бұрын

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 жыл бұрын

Smart in class: *Gets 10pts*

@davidyansky6605 2 жыл бұрын

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

@adw1z Ай бұрын

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!

@Drux.i 2 жыл бұрын

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 жыл бұрын

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

@Drux.i 2 жыл бұрын

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

@odiltursunov6854 2 жыл бұрын

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

@thelocalnecromancer1224 2 жыл бұрын

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

@Serpentis666 2 жыл бұрын

The yearn for understanding really seems to increase with age…

@Ali-Mhsn 2 жыл бұрын

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

@jAYROCCS1x 2 жыл бұрын

@John-el5sv 2 жыл бұрын

@@jAYROCCS1x 12:36

@jAYROCCS1x 2 жыл бұрын

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

@bill6687 2 жыл бұрын

"The world's greatest mathematician: myself"

@PureMagma 2 жыл бұрын

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. 😅

@starforge5663 2 ай бұрын

When it comes to the 3x+1 conjecture, what are we solving for? Sure we could try and prove it true or false but, what are we solving the conjecture for? What are we looking for in the equation?

@ahmedkhafage7783 Ай бұрын

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 Ай бұрын

What are yo talking about exactly?

@dabolife1 2 жыл бұрын

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

@risav202 2 жыл бұрын

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

@therealitygab6074 2 жыл бұрын

@@risav202 please explain. i dont agree

@segmentsAndCurves 2 жыл бұрын

@@risav202 Nah.

@mjzudba5268 2 жыл бұрын

I literally just saw you on Nas Daily...

@TheDarkDresser 2 жыл бұрын

@@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.

@Martdogg3000 2 жыл бұрын

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 2 жыл бұрын

You take my words from my mind :))

@ItsMe-gw4kb 2 жыл бұрын

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 жыл бұрын

@hasselbecksucks 2 жыл бұрын

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

@GnarlsMSMREAL 2 жыл бұрын

It's 4

@dewaard3301 26 күн бұрын

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.

@colebrew 2 жыл бұрын

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

@JosephAR513 2 жыл бұрын

BRO😂😂

@Fixis 2 жыл бұрын

Everyone chooses 7 cause 7 wins everytime lol

@Byokie1 2 жыл бұрын

SAME

@DaisyCoreXD 2 жыл бұрын

Lol same

@sunset_anything1875 2 жыл бұрын

I think it’s 3

@whosnico4669 2 жыл бұрын

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

@sarahsanchez150 2 жыл бұрын

5... 😭😭

@KratonWolf 2 жыл бұрын

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

@savathunthewitchqueen8299 2 жыл бұрын

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

@adcgdsin9320 2 жыл бұрын

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

@iteratedofficial 2 жыл бұрын

Ikr... I picked 4...

@05DarkSaint Ай бұрын

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

@user-qg1kp3yy8o Ай бұрын

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?

@adityaagarwal6719 2 жыл бұрын

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

@chriswebster24 2 жыл бұрын

*there

@adityaagarwal6719 2 жыл бұрын

@@chriswebster24 thanks.. Noted!

@mistersunny3636 2 жыл бұрын

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

@emilpysenisoncrack420 2 жыл бұрын

Could I get some clarification?

@emilpysenisoncrack420 2 жыл бұрын

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

@emay4r 2 жыл бұрын

I like how you asked us what colors would represent odd and even numbers before making this video. And according to the results for most people the odd numbers would be red and even numbers would be blue just like they are in this video.

@babyyoda5074 2 жыл бұрын

ahhhhh

@_ikako_ 2 жыл бұрын

i guess the adage that the average person is an idiot is true then

@julesgenrev6574 2 жыл бұрын

The only thing I honestly understood

@tonydai782 2 жыл бұрын

@@_ikako_ I mean it doesn’t really prove anything does it? Color as experienced by us is purely qualitative, numbers don’t really have innate color, but we can also designate such a property if we are asked to, it doesn’t make us idiots.

@_wetwillyinc 2 жыл бұрын

@@_ikako_ proud even = red gang

@doyltruddy902 2 ай бұрын

your video was such great content that when you started talking about your sponsor I actually didn't skip it and listened to what you had to say.

@CourtneyIsLovely 2 ай бұрын

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

@0oJMPo0 2 жыл бұрын

"The simplest math problem no one can solve" My math professor: oh, looks perfect for the exam!

@rohangupta3363 2 жыл бұрын

🤗 congrats on 300 likes

@Phantom-el6oe 2 жыл бұрын

It can be solved. Edit: So apparently this is an algorithm, so in this case: f(x)={1;2;3;4} or f(x)=[4;1] (those are random numbers, not a solution). This is the correct way to solve problem like this, which is what you learn in algebra classes There is always a solution in math, except you need to write it differently than x=7. Also, if there isn't any possible solution (like delta of an angle being less than zero), then you simply write "no answer" and close the case

@destros6576 2 жыл бұрын

@@Phantom-el6oe ?

@organizedmicrowave4414 2 жыл бұрын

@@Phantom-el6oe He's not doing an exam, are u dumb?

@salimkibria6955 2 жыл бұрын

@@Phantom-el6oe but u cant actually do that

@jetstreamsam9580 2 жыл бұрын

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

@drawingtutorials7296 2 жыл бұрын

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

@kassimasinia3314 2 жыл бұрын

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 жыл бұрын

Homework equals 6🕺🏾

@HorrorGirl-tb2yo 2 жыл бұрын

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

@krayon1034 2 жыл бұрын

The answer is six

@user-zu4ft8yw9e 12 күн бұрын

The Collatz Conjecture, also known as the 3n + 1 problem, is a mathematical problem that has remained unsolved since its proposal in the 1930s. It involves a simple sequence of operations on a positive integer. Here's how it works: 1. Start with any positive integer, n. 2. If n is even, divide it by 2 (n/2). 3. If n is odd, multiply it by 3 and add 1 (3n + 1). 4. Repeat steps 2 and 3 until the sequence reaches 1. The Collatz Conjecture states that no matter which positive integer you start with, the sequence will always end at 1. Despite extensive research and numerous attempts, the conjecture has not been proven or disproven, making it one of the most intriguing unsolved problems in mathematics.

@ikwenmusic 7 күн бұрын

yes... yes, we watched the video?

@ishanpujari2171 2 жыл бұрын

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

@SienaaBee 2 жыл бұрын

Perfect.

@tina5833 2 жыл бұрын

Yes.

@joehadari7315 2 жыл бұрын

Fitting

@shrirangbondale8711 2 жыл бұрын

And this comment is just like last piece of jigsaw puzzle

@raoutsigueddoura3859 2 жыл бұрын

I like your style

@shiteshchourasia 2 жыл бұрын

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

@karlmarx828 2 жыл бұрын

12:33

@blue_slime5776 2 жыл бұрын

Yeah It Got Me Laughing

@adityakrishnamalhotra1 2 жыл бұрын

@@karlmarx828 i love you 😩😩 My favourite capitalist

@dhruvalvyas3924 2 жыл бұрын

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

@giornogiovanna4602 2 жыл бұрын

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

@Alexa-dt8fm 3 ай бұрын

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 3 ай бұрын

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

@user-hw4de2vi3r 3 ай бұрын

can any one help me out with a similar math problem putting it really simplified is it possible for us to prove that a limit tending to infinity is actually odd or even can we even prove if limn->infinity 2n+1 is odd and we can then there is a limit that we can prove to be odd or even hence proving that the 3n+1 can shoot to inifnity or not regards please help!

@MrScientific 2 жыл бұрын

Nice work Soviets. You got me.

@HottestBrownMan 2 жыл бұрын

Hitler be like :

@akshatvikramsingh8293 2 жыл бұрын

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

@vigilantcosmicpenguin8721 2 жыл бұрын

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

@HottestBrownMan 2 жыл бұрын

@@akshatvikramsingh8293 thanks mate.

@ultramb6206 2 жыл бұрын

Ngl i hate your facebook page lol

@danielwitham1791 2 жыл бұрын

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

@ujjwal2473 2 жыл бұрын

next they'll invent another law for you to follow

@jackrobinson9403 2 жыл бұрын

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

@von... 2 жыл бұрын

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

@von... 2 жыл бұрын

@@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 2 жыл бұрын

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

@Alex_192. 3 күн бұрын

If any increasing function can be used to exclude numbers, every positive number can be excluded, meaning all loops must not include positive numbers.

@user-vb3tm9tx8i Ай бұрын

what if there's a relationship between 3x+1 and cancer? perhaps there is a correlation between 3x+1 and biology or genetics that would help identify gene sequences which lead to cancer.

@xTANNA3 2 жыл бұрын

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

@xTANNA3 2 жыл бұрын

@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 жыл бұрын

True

@Mango-rl2yg 2 жыл бұрын

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 жыл бұрын

@@Mango-rl2yg huh?

@annac.6863 2 жыл бұрын

@@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! ❤️❤️❤️

@sammcdonald4 2 жыл бұрын

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

@GummieI 2 жыл бұрын

Yeah that was so good

@syedfaisal9544 2 жыл бұрын

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

@dreamer097 2 жыл бұрын

12:33

@Cube_Box 2 жыл бұрын

@@dreamer097 thanks

@rgmjr 2 жыл бұрын

Haha. I came to look for this. Haha.

@RicThai63 10 күн бұрын

Well, that makes quite sense: any even number divided by 2, eventually - keeping adding 1 to any odd result and dividing it again by two - becomes 1. Despite the 3x or not. Multiplying it by an odd number would just makes the process longer, but eventually it goes to 1. No way out. I would say it is quite intuitive.

@XCC23 9 күн бұрын

The most obvious issue for your intuition is that it stops being true if you, for example, ask about 3x-1 or 5x+1 instead. Like, we can all agree that it seems pretty clear that almost all numbers reach 1. But it's *very* hard to show that it's all numbers.

@RicThai63 8 күн бұрын

@@XCC23 - you may be correct, or you may be not. It would takes hours and hours of logic and calculations to know it. And I won't. For the time being, I am happy with the stimulation of this video. Thanks anyway for the comment.

@XCC23 8 күн бұрын

@RicThai63 I am correct, because your reasoning doesn't predict that for 3x-1, the sequence 5, 14, 7, 20, 10, 5 exists. The hard part is ruling out that sequences like these can exist.

@dustymiller65 10 күн бұрын

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

@NurMars 2 жыл бұрын

"One of the world's greatest mathematicians... " *Proceeds to show himself*

@phucminhnguyenle250 2 жыл бұрын

I laughed hard that.

@umavasu766 2 жыл бұрын

Man has some humour

@ClaytonSummers 2 жыл бұрын

This is the comment I came looking for lol

@SlimShady-gs8pl 2 жыл бұрын

What's the timestamp for this? I just finished watching but I must not have caught that lol

@abdurrafi9318 2 жыл бұрын

@@SlimShady-gs8pl 12:36

@cryofrostrs3856 2 жыл бұрын

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

@toolaazy 2 жыл бұрын

I go to Confucius

@YOUNOTSMART 2 жыл бұрын

@@toolaazy And Confucius says

@anmoldeepsingh9281 2 жыл бұрын

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

@YOUNOTSMART 2 жыл бұрын

@@anmoldeepsingh9281 😭😂🤣😭😂🤣

@johnjonjhonjonathanjohnson3559 2 жыл бұрын

@@YOUNOTSMART no more numbers jumping on the graph

@silencecasserole Ай бұрын

Choosing random numbers and applying the rules until you get caught in the loop is a great way to kill time in class, I do it all the time

@AndresFirte 2 ай бұрын

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 2 ай бұрын

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 2 ай бұрын

@@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 2 ай бұрын

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

@XCC23 2 ай бұрын

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

@Free2Flay 2 жыл бұрын

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 жыл бұрын

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

@manswind3417 2 жыл бұрын

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

@Matthewjames1016 2 жыл бұрын

Wait til you find out .9 and 1 are equal

@JaseHDX 2 жыл бұрын

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

@oxanamikki3326 2 жыл бұрын

are u saying math is boring

@lovepuma6625 2 жыл бұрын

".....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 жыл бұрын

I think it's just 10

@MP-ut6eb 2 жыл бұрын

@@captaincool9636 42. The answer is 42.

@NamidaCho 2 жыл бұрын

@@MP-ut6eb no not at all

@gbsantana9679 2 жыл бұрын

@@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 жыл бұрын

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

@theorangereacher1213 Ай бұрын

I wanna know what doing the reverse(?) would add to the conversation; 3x+1 for evens, divide by 2 for odds. I know that pulls in decimals, resulting in an asymptote, so how does this play into the question?

@XCC23 Ай бұрын

odd numbers immediately break the system, because then the next step is meaningless (rational numbers and their worse cousin, real numbers, aren't odd or even at all, so you immediately run into nonsense). Even numbers now produce an odd number and proceed to break the system.

@koreanstallion 11 күн бұрын

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!

@Christopher-of-Columbus 2 жыл бұрын

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

@jplaguee88 2 жыл бұрын

Same

@Yxnte 2 жыл бұрын

Fr bro also me

@laurenpowers2100 2 жыл бұрын

Sam3

@bee14. 2 жыл бұрын

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

@user-xw4mu6nz4t 2 жыл бұрын

Yep, so did 99.9% of viewers that watched

@franzpattison 2 жыл бұрын

Can I just take a moment to applaud the animations created for the visual representation of the concepts?

@markshiman5690 2 жыл бұрын

3blue1brown animations

@putrycydes 2 жыл бұрын

Thought exactly the same while watching

@sincicalpvp9252 2 жыл бұрын

yes you can.

@artificialintelligenceplus1321 2 жыл бұрын

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

@oinvestigard Ай бұрын

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

@cattail73 2 жыл бұрын

“Pick a number, any number.” Me: “Fou-“ “Seven? Good choice.”

@cgduude 2 жыл бұрын

Haha, 4 would be a horrible/great intro to this problem

@filam7371 2 жыл бұрын

I picked 4 as well...😅

@tacoballsUS 2 жыл бұрын

omg same thing happened to me!!

@svatisingh1 2 жыл бұрын

Same! Apparently 4 denotes stability... :))

@BryceCorbitt 2 жыл бұрын

I picked Zero... Wasn't until later in the video that "Positive Integer" was specified

@Pansotii 2 жыл бұрын

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 жыл бұрын

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

@zainelsayed9007 2 жыл бұрын

@@owenlee913 i really hope you’re being sarcastic

@stephenhorgan7110 2 жыл бұрын

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

@ginger-ale7818 2 жыл бұрын

@@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 жыл бұрын

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

@seroujghazarian6343 27 күн бұрын

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

@user-ei7vm4lw1h 25 күн бұрын

I have a question about the terry tao part pls. Why does it matter if its arbitarily small? Isn't it sufficient to just be smaller than the seed? Like why does it matter that its smaller than any function?