The Simplest Math Problem No One Can Solve - Collatz Conjecture

The Collatz Conjecture is the simplest math problem no one can solve - it is easy enough for almost anyone to understand but notoriously difficult to solve. This video is sponsored by Brilliant. The first 200 people to sign up via brilliant.org/veritasium get 20% off a yearly subscription.
Special thanks to Prof. Alex Kontorovich for introducing us to this topic, filming the interview, and consulting on the script and earlier drafts of this video.
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References:
Lagarias, J. C. (2006). The 3x+ 1 problem: An annotated bibliography, II (2000-2009). arXiv preprint math/0608208. - ve42.co/Lagarias2006
Lagarias, J. C. (2003). The 3x+ 1 problem: An annotated bibliography (1963-1999). The ultimate challenge: the 3x, 1, 267-341. - ve42.co/Lagarias2003
Tao, T (2020). The Notorious Collatz Conjecture - ve42.co/Tao2020
A. Kontorovich and Y. Sinai, Structure Theorem for (d,g,h)-Maps, Bulletin of the Brazilian Mathematical Society, New Series 33(2), 2002, pp. 213-224.
A. Kontorovich and S. Miller Benford's Law, values of L-functions and the 3x+1 Problem, Acta Arithmetica 120 (2005), 269-297.
A. Kontorovich and J. Lagarias Stochastic Models for the 3x + 1 and 5x + 1 Problems, in "The Ultimate Challenge: The 3x+1 Problem," AMS 2010.
Tao, T. (2019). Almost all orbits of the Collatz map attain almost bounded values. arXiv preprint arXiv:1909.03562. - ve42.co/Tao2019
Conway, J. H. (1987). Fractran: A simple universal programming language for arithmetic. In Open problems in Communication and Computation (pp. 4-26). Springer, New York, NY. - ve42.co/Conway1987
The Manim Community Developers. (2021). Manim - Mathematical Animation Framework (Version v0.13.1) [Computer software]. www.manim.community/
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Special thanks to Patreon supporters: Alvaro Naranjo, Burt Humburg, Blake Byers, Dumky, Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal
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Written by Derek Muller, Alex Kontorovich and Petr Lebedev
Animation by Ivy Tello, Jonny Hyman, Jesús Enrique Rascón and Mike Radjabov
Filmed by Derek Muller and Emily Zhang
Edited by Derek Muller
SFX by Shaun Clifford
Additional video supplied by Getty Images
Produced by Derek Muller, Petr Lebedev and Emily Zhang
3d Coral by Vasilis Triantafyllou and Niklas Rosenstein - ve42.co/3DCoral
Coral visualisation by Algoritmarte - ve42.co/Coral

[@k.pacificnw02134]

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

[@TheGreekGodOfWallStreet]

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

[@evilkillerwhale7078]

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

[@jrbros2371]

I too thought i could solve it :D

[@systim30]

What is there to solve? There is nothing to solve

[@jrbros2371]

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

[@Yihtc]

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

[@rachelx04]

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

[@palindromia130]

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

[@ArcFenixDelacroix]

I think Im the only one who chose 7

[@vor0g]

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

[@samirh2758]

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

[@user-ik4so3yp2e]

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

[@JPcommunicates]

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

[@AlbertSatnoianu]

lol

[@user-oq5gn6br1u]

😂 lol

[@MathemBrathlem]

W Editor for the humor

[@HarmonRAB-hp4nk]

(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

[@colbycrabtree9469]

The math homework: 1 + 1 = x The math test: 3x + 1

[@56nickrich]

😅👍

[@Adarsha3]

7 😊

[@marcokapusta3843]

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

[@JeffMTX]

you too? :)

[@luca6819]

I tried to remove the eyelash on the display 🤭

[@davidbesant]

There's that damn eyelash on my screen again!

[@RetroFuel]

@@luca6819 .same lol

[@Hoshino_Channel]

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

[@shadyceddy6509]

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

[@amirpakravan4389]

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

[@justinerek779]

ikr

[@rayanhaq8552]

I am

[@motherkhapudang3938]

Hmmm

[@fnxrz7513]

@@amirpakravan4389 shut up u ruin the vibe

[@AshenElk]

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

[@LadyMysanthrope]

Because maths are the language of the universe.

[@mickodillon1480]

@@LadyMysanthrope Facts.

[@ThatOneKat511]

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

[@jokes.on.u]

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

[@anyaburke6636]

facts

[@lordsiomai]

Imma use this

[@scottmurphy248]

@@lordsiomai be honest, no you won't

[@compszn]

@@anyaburke6636 its 6

[@krisha8430]

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

[@agentkp4574]

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

[@davidmedina7721]

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

[@apbe2q35]

3 years year old me : what is maltiplikaton?

[@Seeker-dx1gj]

Ok

[@BoEatsApples]

13 Million*

[@Penguins459]

more

[@shmuelman]

Certainly one of the finest mathematical videos on KZbin.

[@__cypher__]

Wait ... What?!

[@xninja2369]

3Blue1Brwon be like ? 🫥

[@CourtneyIsLovely]

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

[@Juggeraufesser]

Same

[@michealthekaminoshinagami54]

There's actually studies that show 3 and 7 "feel" the most random to human brains, so they get picked predominantly. If asked to pick randomly from 100, 37 and 73 get picked most often

[@cosmicnomad8575]

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

[@soumyadityachakraborty2457]

ridiculous too

[@oreziopancrazio3685]

I totally agree. What a waste of time

[@christloen4077]

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

[@oreziopancrazio3685]

@@christloen4077 No way

[@christloen4077]

In your mind

[@grimaffiliations3671]

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

[@aashsyed1277]

Noo

[@segmentsAndCurves]

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

[@srijanpanicker5395]

LMAO🤣🤣🤣

[@rana8440]

😝

[@Pikachu-Gaming1764]

Lol

[@DeadKarlisAlive]

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

[@mjh3067]

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

[@elron117]

Because we are fascinated by TRUTH. By its quality of a b s o l u t e n e s s . We are fascinated by Absolutes - by The Absolute - because from there, nothing further needs be 'solved' and we d i s c e r n that very fact. 'Absolvare' means 'to set free'. My 2cts about the why of that.

[@Naurik]

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

[@EnriqueLaberintico]

History of the entire world, I guess convinces me.

[@octaviovilchez3096]

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

[@alexmangorove]

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

[@seanallen8828]

English, grammar

[@benfulford3943]

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

[@Hanyamanusiabiasa]

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

[@Dizzy00001]

Lol

[@theultimatetime8029]

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

[@mjzudba5268]

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

[@theultimatetime8029]

@@mjzudba5268 yes ofcourse

[@khuetranxuan8218]

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

[@adw1z]

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

[@TheGrimReaper67]

4÷2=2=1x3+1 so it's basically being devided by 0. Infinity. Meaning 4÷2=2=1x3+1 ÷ 0 pretty much, that's just my answer though. Since ÷0 ends up as undefined/infinity to most Ai and calculators. It may be almost impossible to solve but you can always have your own answer, keep on working on your own equations, you'll be famous one day I promise.

[@dabolife1]

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

[@risav202]

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

[@therealitygab6074]

@@risav202 please explain. i dont agree

[@segmentsAndCurves]

@@risav202 Nah.

[@mjzudba5268]

I literally just saw you on Nas Daily...

[@TheDarkDresser]

@@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.

[@ghostphalanx]

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

[@pratanakangsadal521]

Amen.

[@gn4sty731]

BR?

[@GamingWithTimmy0]

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

[@GamingWithTimmy0]

Math

[@cirque1783]

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

[@alexanderstohr4198]

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.

[@priordan80]

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

[@RiderGeats]

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

[@BrianHartman]

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

[@brokenwingbird2552]

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]

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]

Smart in class: *Gets 10pts*

[@davidyansky6605]

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

[@MrScientific]

Nice work Soviets. You got me.

[@HottestBrownMan]

Hitler be like :

[@akshatvikramsingh8293]

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

[@vigilantcosmicpenguin8721]

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

[@HottestBrownMan]

@@akshatvikramsingh8293 thanks mate.

[@ultramb6206]

Ngl i hate your facebook page lol

[@aussieraver7182]

3:01 Thats what scares me the most. Graphically representing a number that dramatically goes so high, the animation/graph becomes incomphrehensible and you have a mini panic. I get thay alot working in 3D game engines. There must be a phobia for it. Such as using Google Earth, and zooming out all the way. Ahhhhhhhhhh!

[@jayetabhattacharya5420]

Yes,I get it too.

[@jayetabhattacharya5420]

Yes,I get it too.

[@kelvinedits9471]

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

[@parvizsattorov2411]

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

[@SparinglyIsDumb]

Ye

[@kalucardable]

that's how they make roller coaster rides

[@mosab_faozi]

Perlin noise: am I a joke to you?

[@-morrow]

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

[@bmwheel1263]

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

[@kugelblitz7946]

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

[@itismethatguy]

Ikr

[@Sintinium]

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

[@EpicVideos2]

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

[@AxxLAfriku]

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

[@kugelblitz7946]

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

[@HemanthHR-fi5rq]

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

[@oriongurtner7293]

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 🙂

[@leebydeeby]

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

[@astronautboynr2018]

nerd

[@livinglogically8180]

Atleast find better ways of procrastination

[@r-a-kralphandkoto2413]

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

[@Mr.Human69]

Ez Answer Is 9 I was Doing my math Homework Bruh

[@sera_makyuri]

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

[@colebrew]

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

[@JosephAR513]

BRO😂😂

[@Fixis]

Everyone chooses 7 cause 7 wins everytime lol

[@Byokie1]

SAME

[@DaisyCoreXD]

Lol same

[@sunset_anything1875]

I think it’s 3

[@libbydaddy8610]

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

[@Guywiththetypewriter]

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

[@clutchmatic]

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

[@kinetik9197]

how long did this take

[@Guywiththetypewriter]

@@kinetik9197 how u mean

[@jenniferzeng5735]

Wow …. This is actually really smart

[@BlackHayateMX]

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

[@DasSkelett]

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

[@lukelively8380]

I was looking for this comment lol

[@HungryTacoBoy]

Same here. I thought it was very clever.

[@cortnetisjustbetter]

* You're , btw I am better than you

[@MightyHashBrown]

@@cortnetisjustbetter not you’re but ok

[@Sleepy_Joe]

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

[@weedy_yeast]

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]

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]

@@mlpfanboy1701 i just solved this lol

[@zenixx_168]

@@Auromaxis what is it?

[@EchoYoutube]

It’s easy, 0.

[@Dragon_Mawce]

@@Auromaxis ?

[@nikolaifalk803]

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

[@wtcodingproductions]

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

[@adamrozek5782]

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

[@prasadbhalerao8556]

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

[@prasadbhalerao8556]

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

[@isaacpalmer1195]

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

[@cryptedmage9739]

Lol wassup homie

[@dino_tokic8884]

Lmaoo

[@WestExplainsBest]

Ugh those programs are virtual math teachers worst nightmare.

[@parkiel54]

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

[@CoreDeck]

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

[@remenyo]

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

[@user-xf6ox6zx4w]

Amajing

[@danielrasheedi]

@@remenyo what is it??

[@MehtabSinghEdhan]

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

[@keepsakecube]

Mathematicians are already nuts, so when they say something is nuts, you know that guy has really got somethin up with him

[@changolord93]

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

[@veramentestanco]

He had me too! Brilliant!

[@anonamemous6865]

He had me too

[@DrakyHRT]

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

[@irenegold3969]

LOL

[@lunatik4265]

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

[@CrimsonRegalia]

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

[@anunknownperson4018]

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

[@vector1213]

Big maffs

[@fanaticjay3825]

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

[@Floorlicker2000]

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

[@HaaKaaf]

@@fanaticjay3825 bruh what

[@koreanstallion]

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

[@oinvestigard]

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

[@haxexd2830]

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

[@LaniPlayzRoblox]

*choice

[@keenjoaquin847]

@@LaniPlayzRoblox *choise

[@mrcrunch4635]

@@keenjoaquin847 *chuse

[@Uranium_chewer]

@@LaniPlayzRoblox choes

[@ahhblehh]

@@mrcrunch4635 *cheese

[@Liur.]

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

[@Liur.]

@@Sinaloabricks hypotheses is the plural 🙄

[@er00ic]

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

[@andrewcramer9200]

Statistician: *does both in bipolarity*

[@paxhumana2015]

Is not mathematics merely just a part of science anyway?

[@paxhumana2015]

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

[@Texas75023]

7:46 Neglecting the "+1" is a source of error that should not be dismissed. Discovery of a cycle is critically dependent on the accumulation of *EVERY* contribution of "+1" in the sequence.

[@frantisekvrana3902]

16:00 I find it very interesting that the number of perfect squares within the first n numbers seems to be square root of n. As a way to prove or disprove it, I did only a bit of thinking. In order to escape the Collatz conjecture, a number's descendants would have to never be a power of 2. On reaching a power of 2, the numbers slide back down to 1. Additionally, in order to appear on another number's sequence, a number needs to either be even and 3n+1, or be whole and (3n+1)/2

[@BioniclesaurKing4t2]

Derek: "Pick a number." Me: "Four." Derek: "…He's too dangerous to be left alive."

[@John-AEC]

heheh Good one ;)

[@keldrean]

Four is my lucky number

[@justajobro1266]

Mista: ....

[@ndjs]

@@justajobro1266 I was waiting for that

[@cenaytopaloglu2779]

He got me at 7 tho :/

[@FullMetalOptimusPrime]

Honestly maths should just grow up and solve its own problems

[@EvenFive]

That's what AI is.

[@divyanshusingh7767]

I laughed so hard!😂 Thank you

[@jasonspades5628]

Yeah that was funny as hell

[@shsjjhsh]

lol

[@ttoo1830]

Good one!

[@ParBas-in1op]

Kind of interesting how if you start with 7, the next number is 22. And 22/7 is a famous approximation of pi. It's like the ratio of term 1 and term 2 approximates pi when N=7.

[@darrenleung3684]

Schools need more material like this to inspire kids

[@whosnico4669]

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

[@sarahsanchez150]

5... 😭😭

[@KratonWolf]

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

[@savathunthewitchqueen8299]

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

[@adcgdsin9320]

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

[@iteratedofficial]

Ikr... I picked 4...

[@javiersolis2993]

The animation is everything here.

[@milkshake7180]

@DON'T stfu

[@reallemming1dago..888]

@DON'T stfu bi-

[@WillCrewMusic]

You both just fell for his trap lmfao

[@milkshake7180]

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

[@everywhereman9003]

@DON'T IM GONNA SAY THE N WORD

[@joshberna5801]

I like the conclusion, well done. As I've often said (and probably heard somewhere else before), humanity did not invent mathematics, no. Humanity is in the process of discovering mathematics...

[@crzykev11]

At 8:44 your data points at the top are exactly what a tape measure looks like I just thought it was funny

[@ishanpujari2171]

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

[@SienaaBee]

Perfect.

[@tina5833]

Yes.

[@joehadari7315]

Fitting

[@shrirangbondale8711]

And this comment is just like last piece of jigsaw puzzle

[@raoutsigueddoura3859]

I like your style

[@darthenx2585]

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

[@chronical]

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

[@peterh222]

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

[@markjohnson7508]

Really.. wow. Entropy maybe

[@josefwakeling7103]

@@peterh222 *disillusion

[@birchthebirch4593]

Listen ...don't look

[@dewaard3301]

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

[@borzica]

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.

[@TheMusicalStylingsofBrentBunn]

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

[@michagiedrojc5513]

And how much work on calculator.

[@isidorregenfu9632]

Looks like 3blue1brown's framework manim at work

[@someidiot6067]

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

[@quyento9108]

Someone's back is hurtt

[@cissedeclercq5567]

we do or best.

[@demensclay6419]

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

[@gniewko123456]

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

[@josiahjray]

I really hope this is satire 🤣🤣

[@gniewko123456]

@@josiahjray baited :D

[@josiahjray]

@@gniewko123456 Hope so lol

[@anndyarguedo4453]

Ah yes, 999 likes

[@user-cp8dg6uq2j]

By the way, the difference between the numbers we've calculated for the 3x+1 conjecture and haselgrove who solved the Pólya conjecture is the same as the difference between a planck length and 1.837869×10^231 Universes

[@05DarkSaint]

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

[@Yextiny]

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

[@holdontoyourwig]

You could start by calling it MATHS

[@user-lg9cf4sw4x]

my dumbass brain is quaking

[@001100AAAEA]

Pretty much lol

[@babydriver8134]

Weapons of Math Instruction?

[@bujharvard9313]

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

[@danielwitham1791]

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

[@ujjwal2473]

next they'll invent another law for you to follow

[@jackrobinson9403]

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

[@von...]

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

[@von...]

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

[@shamsandharia123]

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

[@nobody-fe4gn]

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

[@Aryae_Sakura]

Somebody should have told me in school that math can be this interesting 🤔 great visualization :D

[@nimamaster6128]

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

[@ShatteredCelestial]

wait really? lmao

[@shibe6181]

Wow 4th

[@cristianrivas4606]

Can we not use decimals?

[@Arthurgoldlizard]

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

[@artificialintelligenceplus1321]

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

[@adityaagarwal6719]

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

[@chriswebster24]

*there

[@adityaagarwal6719]

@@chriswebster24 thanks.. Noted!

[@mistersunny3636]

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

[@emilpysenisoncrack420]

Could I get some clarification?

[@emilpysenisoncrack420]

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

[@residentenigma7141]

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

[@lamtungbenny6214]

If only decimals were allowed 😢

[@EpicGamer-69]

Bro is onto nothing🔥🔥🔥

[@jetstreamsam9580]

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

[@drawingtutorials7296]

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

[@kassimasinia3314]

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

[@Smdday._]

Homework equals 6🕺🏾

[@HorrorGirl-tb2yo]

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

[@krayon1034]

The answer is six

[@Martdogg3000]

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

[@DeadAzz2]

You take my words from my mind :))

[@ItsMe-gw4kb]

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

[@beauxsmith674]

12

[@hasselbecksucks]

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

[@GnarlsMSMREAL]

It's 4

[@someonegreat_]

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

[@walkastray007]

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

[@InsideOutAnus]

Good pickup!

[@valval4145]

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

[@NandR]

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

[@valval4145]

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

[@JS-jh4cy]

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

[@shadaabansari6654]

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

[@segmentsAndCurves]

exponential*

[@joriskylie6857]

What exactly is the problem?

[@felosrg1266]

The classic "To big to fail" problem

[@patricknez7258]

Nice!

[@qwerty11111122]

sunk cost fallacy

[@fysics5375]

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

[@cryofrostrs3856]

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

[@toolaazy]

I go to Confucius

[@YOUNOTSMART]

@@toolaazy And Confucius says

[@anmoldeepsingh9281]

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

[@YOUNOTSMART]

@@anmoldeepsingh9281 😭😂🤣😭😂🤣

[@johnjonjhonjonathanjohnson3559]

@@YOUNOTSMART no more numbers jumping on the graph

[@cattail73]

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

[@cgduude]

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

[@filam7371]

I picked 4 as well...😅

[@tacoballsUS]

omg same thing happened to me!!

[@svatisingh1]

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

[@BryceCorbitt]

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

[@zevnikov]

It is like a youtube algorhitm. At the end it always like this with your views.

[@bleethan6809]

"One of the worlds greatest mathematicians..." (shows a picture of himself) "...Terry Tao" (Extends photo.) Edit: How is my best comment on a Math video xD

[@AYAyayayaya987]

I was laughing a lot xD

[@uwuowo4856]

Funny

[@SJ-cl4wq]

Politician in the making. Australians be ready 🤣

[@ShouvikMukherjee0-_-0]

bait level 2^69

[@floramiller1133]

You just wrote down what everyone saw.. lol comments be hella typical these days

[@dimethebloodwolf3034]

“Pick a number, any number.” Me: “seven.” Him: “seven? Good choice.” Me: *quaking* Edit: I made this post yesterday what the hell

[@cofftea]

Same I was shocked

[@TylerMcVicar]

me too LMAOOO

[@minskghoul]

7 is the most common choice of 'random' number by human when asked to chose from 1 to 10.

[@Kirkdi]

But i pick 4

[@salvatoregetlostii334]

Same

[@Fraber87]

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

[@dustymiller65]

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

[@NurMars]

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

[@phucminhnguyenle250]

I laughed hard that.

[@umavasu766]

Man has some humour

[@ClaytonSummers]

This is the comment I came looking for lol

[@SlimShady-gs8pl]

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

[@abdurrafi9318]

@@SlimShady-gs8pl 12:36

[@saifuusuri]

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

[@Link-12]

me to :p

[@AnAnonymousMan]

1k square miles ?

[@king_james_official]

@@AnAnonymousMan three, take it or leave it

[@maxwellsequation4887]

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

[@saifuusuri]

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

[@JD_Mortal]

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

[@jmodified]

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

[@extravagantpanda7962]

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

[@johnnyp6202]

If I had to guess my intuition would say that just like the odd number of factors that ultimately this conjecture will also turn out to be wrong. The reason I think this is that the relationship between prime numbers and a composite number becomes much more complex at very high numbers and their hooks to each other become more and more disconnected and at some point the "inevitability" to come upon a composite number that will reduce fully to 1 becomes statistically less and less probable.

[@Drux.i]

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

[@ultraslanmc4619]

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

[@Drux.i]

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

[@odiltursunov6854]

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

[@thelocalnecromancer1224]

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

[@Serpentis666]

The yearn for understanding really seems to increase with age…

[@Ali-Mhsn]

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

[@jAYROCCS1x]

?

[@John-el5sv]

@@jAYROCCS1x 12:36

[@jAYROCCS1x]

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

[@bill6687]

"The world's greatest mathematician: myself"

[@PureMagma]

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

[@Vinicisxhf]

Imagine that the reason why we can't solve or prove some of these questions on mathematics it's because there is something missing at the base of our knowledge, like for example, another digit in our system. I think it's, supposedly, only possible to find a solution if we start to think in another basic way.

[@user-qg1kp3yy8o]

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

[@kushagrawal8307]

That is just wrong? Even for x = 3, 3x+1 = 10 which has factors 5,2 and 1 and is thus not a prime.

[@sammcdonald4]

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

[@GummieI]

Yeah that was so good

[@syedfaisal9544]

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

[@dreamer097]

12:33

[@Cube_Box]

@@dreamer097 thanks

[@rgmjr]

Haha. I came to look for this. Haha.

[@gopiharwani5765]

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

[@MrAshtute]

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

[@AMP_7]

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

[@novatime3214]

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

[@MrAshtute]

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

[@KokeBeast23]

Obviously not all on this one problem

[@goblinking8510]

Alright following the sequence of pi, take the highest number we've test and just keep testing pi til the heat death of the universe

[@matan2924]

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