I'm 30 years from high school, and numbers and math still fascinate me. I don't always understand everything in these videos, but I still love watching them.
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.
I noticed that if you take the negative modified version of the sequence it follows a specific pattern. It always returns to one of 3 options: -1, -5/-7 loop or the -17 loop. This pattern holds up to at least -10 million from my tests so far.
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.
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?
@@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
In order to get a mirror image of 3x+1 with negative numbers, you need 3x-1. 3x+1 with negative numbers should be the mirror image of 3x-1 with positive numbers. After all, you're after a scalar of 3 and an offset of 1 away from 0.
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
I have an INSANE coincidence related to this. I discovered this in 2022, and became obsessed, learned a lot about it just because I love math (I'm not even from the exact sciences, I was studying for the ""SAT"" from my country to study psychology). Then, this extremely specialized subject, something a student from high school would have NO business knowing about, ACTUALLY SHOWED UP IN MY "SAT"!!! It was insane, they explained a bit about it and it was kind of just the context for the question they wanted to ask, but everyone I've talked to about it said the question was extremely hard because they had to spend time figuring out what the heck this was. I did it with ease because I was so familiarized with it. Anyway, it was completely crazy and I have this channel to thank because it was what started my interest in the collatz conjecture
@@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.
I came to this channel 2 years ago with no mathematics knowledge. I am here today, intrigued by our universe, I'm going back to college, and I still love Collatz Conjecture and Fibonacci to help calm me down. As a pharmaceutical technician, thank you.
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'.
I think we must approach differently as changing the inputs of the problem. If we do O>5n+1, E>n/2 we find a loop at 13. If we do O>5n+3, E>n/2 we find a loop at 3. But what if we do O>(n^3)+1, E>??? We cannot give a number but 2 to input of even numbers, if we want to divide by. This is their property, indeed this is their definition. For odd numbers, it must not be a quickly-ascelating formula like factorial, but clearly it must not convert the number to odd number neither. Maybe if we can find a connection, we can step further.
@@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.
I love the thought of numerical values plotted out in a visible graph could create images, passing information by nothing more than numbers and understanding of how to multiply and plot them out.
Have you never seen a mathematical equation expressed in a graph before? If not, I assume you are either very young or new to math because it’s common and can be an extremely useful tool.
This is a delightful exploration of the Collatz Conjecture, thank you! I particularly liked just how pretty the visualizations become when you play with adding rotations for evens and odds.
You're videos are great sir I am glad to meet you But just for your kind information sir Almighty the chosen one can solve this problem but he don't have time we have to convince him
Its like somewhere in maths is every organic shape we thought made life somehow special, yet of course, life is biochemistry, its ruled by maths....yet maths is not so regular, so the often made philosophical presumption is that maths produces mechanistic outcomes, when it doesn't. Contingent complexity is one thing though, and hard problems like consciousness are another, but at least philosophically there is some descriptor of aesthetic natural beauty in a way. A way where we can look at the whole like we can a histogram but not make a rule of its parts, like an equation. Such as, those who also presume to quantify art, or say it is relativistic- even from a mathematical pure materialistic sense it has to be neither, but changing quality depending on which level is observed.
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.
This was one of the first programming test I ever made - two players could enter a number and the winner was the one who reached the highest number of steps over 10 rounds.
@@Blind_Ghostling I wrote code that loops through every number possible, the largest number I got "Which was how much numbers were in the loop" was approximately 6300+ but other than that like no luck.
You could say: In order for the conjecture to converge to infinity, it means that there will have to be a limit to which an odd number will be transformed (through 3x+1) to a number of form 2^n (because when a number is in form 2^n, it will always converge to 1, and/or it is the only way to get to 1) so that after you cross that boundary you would not be able to get back to 1 again. Basically at one point you have to land on a 2^n form number. When plotting 3x+1=2^y, we can observe that the function/curve's values after 0 are not undefined, the function it continues infinitely. Therefore we can say that there is no number (seed) that will never stop growing, because the function 3x+1=2^y then has to have a number that does not obey the expression.
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.
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
These types of graphics are the way I always visualized mathematics when in school. Being born in the early 80s, this kind of stuff wasn't available until near the end of my compulsory track. But I always saw the action taking place that the numbers described. Loved loved loved the advent of visual graphics integrated into mathematical teachings. Really shows how dynamic this stuff is.
I'm 7 minutes in, why is the pacing in this video so terrible? This is just a simplified form of: momentum - gravity It's the most basic example of an equation that takes itself into consideration, because gravity continues to decrease the momentum over time. You could think of it as a temporal equation.
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.
@@_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.
In 3x+1 there is no number that stands out / forms a closed loop. It is Mathematics, if 0 isn’t in there and all numbers from 1-9 (1,2,3,4,5,6,7,8,9) obey the law in the first digit/ single digit (Which they do), then all numbers up to infinity follow them. The simple Answer is; 3x+1 is a loop of randomness that at the end solidifies as 4->2->1 and doesn’t contain any abnormalities.
I salute those who genuinely understand this. You have my respect and admiration. I've tried once and I'll try again but I'm just not good at math. But still it's so fundamentally fascinating that I cannot just leave it be. The way in which mathematics describes the very universe is just mind blowingly scary.
I have a question and is like why are we trying to solve a math problem without solution? Instead we have to try to learn more about the space for example. I mean is a problem that have no solution everytime you go n *3 +1 /2 you are going to get a number that you already did so you get to the same conclusion. Even if there is a number this math problem solves nothing, just the problem itselfs. Very good video by the way and is such a cool math problem.
@@Christian2002_ By “solving the problem” what we mean is to find a proof for the question. That being, if you have a function where 3x+1 is applied when odd and x/2 when even, where x is an element of the natural numbers, then all x will be reduced to the repetition of 4,2,1. Is this true or false? The goal is to find a proof for this theorem. That is the goal. The idea behind putting values of x in is to see if we cans find patterns that might lead to an answer. This is very common especially in the case where we see circular patterns as it could hint that Pi is involved. Edit: The other goal is to prove that this is false. The overall goal is to prove or deny the theorem. Edit 2: It was pointed out to me that the question you posed was more of questioning the questions worth and less what the questions is. The answer is why not? A better answer is one from 2 perspectives. One is from the idea that we should try and iron out as many holes in mathematics as humanly possible. We want math to be as consistent and explained as we can make it as it strengthens math overall. Solving specific problems like this is part of how we strengthen math as a science. The other more important reason is that a discovery of a proof for this question might open new doors in mathematics. Maybe someone finds a clever solution that inspires someone else. Maybe we create an entire new mathematical concept to aid in the solving of the problem that then opens the doors for an entire new branch of math. Newton created calculus in his attempts to solve certain specific questions for example. Solutions to specific problems like this can aid in the solving and overall understanding of mathematics as a whole.
@@jackbrax7808 i think OCs question was more like "why do the great mathematecians waste time on this?" Instead of using their talents for other causes
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. 😅
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.
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.
Okay, statistically speaking, the average gain it can get is *3-4 and the average loss is /2+1+.5+.25 etc ending up with 4 so the only numbers that go up are numbers where the 3x + 1 and /2 are equal which is only 1 (not including negative numbers) so there are no other positive cycles than 4 2 1
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
As soon as you showed the rules for this, my brain immediately deduced that once you reach a power of two, this cycle is doomed to repeat a loop of 4, 2, 1. In the example at the start, I was surprised that the power of two reached first was as small as 16.
I love how seemingly simple this problem would seem but how it's stumped mathematicians for so long. Makes you appreciate how complicated the mundane can be. Really makes me want to go back to school for a math degree!
Maybe it's just me, but it doesn't seem that interesting. Combined, the sequences shrink, therefore it's no surprise that everything eventually gets back to 1. Why are there no other loops? Because combined... the sequence shrinks, so a closed loop can't exist.
@@cyanrays8177 Because you don't know whether a closed loop exists at a place we can't check yet. I don't think it does - but it's a way less trivial question that you can't just assume your way out of by assuming that you're going to divide by 2 much more frequently than you will multiply by 3 and add 1 - for any starting number.
@@XCC23 Well. A scientist might not make that assumption, but an engineer absolutely would. Point is, it's still not that interesting, because it's hard to really believe that finding a counter example would be anything more than a fun fact.
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.
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 :)
One thing i noticed for any odd number in a given 3x+1 sequence. Ok, this technique is to predict the next odd number in the sequence. We'll assign two roles to the number's we'll take. One will be the initial number of whom we'll predict the next odd number for. The initial number has to always be odd. The other will be the predicted number which will be the next odd number we've predicted. This too has to always be odd. Ok, lets pick 7 as our initial number. Then, we'll do 7×0.53 which is estimated 4 since its closer to 4. Then we'll add 7 to 4 which is equal to 11. This tells us 11 is the predicted number. this ×0.53 trick always works for any given 3×+1 sequence (no even numbers should be applied)
Well I'm about to watch this last thing before going to sleep, so I'll be the test subject for ending the day with brain food... Update: it's now 1am. Feeling extra tired after trying to understand that. Oof.
Here's some more "brain food" for you: There's a much simpler math problem that no one can solve. No one can compute the exact circumference of a circle from a given diameter. Not even the world's most powerful supercomputer can do this. Because, "pi" is an "irrational" number. But as my book explains, "pi" is not irrational; OUR LIMITED 3-DIMENSIONAL PERSPECTIVE IS IRRATIONAL. Math will never be "mature" enough to overcome this irrational world of limitation. But YOU will be. Some day, in some lifetime to come. God's prophet has spoken.
@@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
The Number IS :5 and third, THIS IS the Same as 3n+1, ALL 16 multiples Numbers divided through 3(multiples with forms of 2)= 5 +1/3! And this IS the Same like 3n+1.…5 x 3 =15, +1=16 5 1/3 x 3.=16 too The half x 3 +1:2 and so on ending early or later in 5 too, ALL Numbers have No Chance in ending in 8,4,2,1. Best wishes, Sandra
@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
@@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! ❤️❤️❤️
The whole universe is destined for emptiness, space spread so thin that energy itself can no longer materialize into matter. All of the order which exists will eventually and inevitably return to the chaos of 1
True. Of course, if this conjecture ever gets proven false, we'd get the moral "Someone out there won't go down to 1. Maybe it's you, maybe not. But either way, we won't know until we try." or something...
It's actually quite easy to show that there must be a 1 to 1 correspondence between loops (like 4-2-1-4) and even prime numbers (of which there is only 2), so the 4-2-1-4 loop must be the only loop possible. Now to the second part: are there sequences, that just explode torwards infinity and never loop? For this we need to consider what information must necessarily be a part of the true statement describing the behavior of sequences, which never fall into a loop. Again, its quite easy to show, that any such statement must contain a complete list of all prime numbers. As far as my knowledge goes, no such list can be produced. Nevertheless the set of all prime numbers can be defined without any problems. Which means that there must be a 1 to 1 correspondence between prime numbers which are not in the set of prime numbers (there are none) and sequences that never fall into loops (subsequently there cant be any, because every prime number is in the set of all prime numbers, because it is possible to define a set of natural numbers, which will contain all and only prime numbers), but because the proof of that statement would require a complete list of all prime numbers, which isnt a thing, it ultimately can not be proven nor disproven.
We need to have every high school math teacher put this on the whiteboard for the extra credit exercise and see which previously undiscovered kid makes a breakthrough because they don't know that they aren't supposed to be able to solve it.
Well the first thing anyone is gonna do is look it up online and they'll find it's a well known problem. But yes it sounds like it would make for a fun problem to look at regardless.
Oops, I just realized I conflated the stories of Carl Gauss and George Dantzig in my head. We don't need to do this in schools as extra credit, we need to leave it up on boards in college so that everyone who arrives late thinks it's homework.
I was so inspired when i first saw this video. I’d always think about it. And this year, my math teacher had each student teach their own lesson at the end of the year. I chose this conjecture because of this vid. I used this vid as a source, i watched it like 20 times, and I’m so inspired by your channel. This vid is 2 yrs old as i write this, and will probably get buried in all the comments but i still want to write this for the small chance you see this. so if you are reading this, thank you for inspiring little minds like mine. ❤️❤️❤️
I mean, the difinition of an odd number is 2n+1, so doing the 3x+1 is doing 3(2n+1)+1 that is equal to 6n+4, which not only most of the time that number starts with one, but also could be worked to find the awnser. One way of thinking it is that youre not multipliying by 3 and adding one, your actually adding 2 and then multipliying by 2, which makes it even. And in top of all i think that maybe the awnser is to find a number that when multiplyed by 2 isn't even, which no whole positive number can do. Edit: they can’t 'cuz 2n is the definition of an even number
I noticed that every 3x + 1 is 4 more than a multiple of 6, and now I know why! :) Thanks. Also, I noticed every power of 4 (4, 16, 64, 256, 2014, 4096, etc) is 3x + 1.
@@MikeC2K10 I responded to someone else about the powers of 4 thing, and it is true for every number! If you know some modular arithmetic, I would encourage you to look at the powers of 4, (mod 3) to see why.
I teach programming, and I always have my students write a program to test this conjecture. They really enjoy entering really big numbers and watching how long it takes to get down to one. Also offers a great opportunity to discuss what constitutes a mathematical proof, i.e. just because something works for every number anyone has tried, it doesn't follow for every number.
Just had interesting conversation with chatgpt about this problem, its just ridiculous to ask that question, tell me an odd number which when you multiply it by 3 and add one (which always result in even number) will not at some point result in even number thats not in cycle of power of 2 because if it is then it will collapse on itself, what exactly are you searching for? Lol
@@jankojankic2439 Yes it's SIMPLE. This is not hard to solve.... ALL odd numbers are odd, All odd numbers times 2 are even All odd numbers times 3 are odd All odd numbers times 3 plus 1 are even... Now ALL even numbers divided by 2 are 50/50 even or odd.. So the probability of reaching an even number EACH time you perform an operation is 75%even to 25% odd....the evens get cut in half, so they decrease half their size.... So the odd number formula is actually : "Odd number multiplyed by 3, plus one, then Divided by 2" And the even number formula is just "Even number divided by 2" So we are ALWAYS dividing by 2, and only SOMETIMES 'multiplying by 3 and adding one' before dividing... Am I right? 🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🛎️🔔🛎️🔔🛎️🛎️
At a time back when I didn't know about the collatz conjecture we had this homework assignment. We had to prove that this sequence has a loop. I tried a few starting values and quickly found out that there is a loop of 4, 2, 1. Then I spent the whole day to come up with an inductive proof of the collatz conjecture. Good times.
There is this story about mathematician George Dantzig, who was late to lecture, and couple of days later he solved two statistics problem thinking it was homework.
Imagine being a math teacher and giving the assignment to proof the collatz conjecture just for the lulz and some student shows up with the actual proof.
Me: math is my worst subject. There’s just too many weird rules for me to follow. Also me: uh, wow, that makes sense. Edit; thank you for all the likes. It makes me happy to see ppl relate to my comment’
I have a similar one: take a number example 7,in the spelling of seven there are 5 letters in the spelling of five there are 4 letters and in four there are 4 letters so it is now a loop. you can take any number like thousands and millions. Even the number is less than four for example 1, in one, there are 3 letters and in three there are 5 ,in 5 there are four
When a person (represented by any number) receives the LORD - Father/Son/Holy Spirit, who is The Great Multiplier, and then shares Him with another - (N x 3) + 1 - and then continues on as 2 whole individuals on their own, yet connected paths going forward with Christ, but always remaining in fellowship with all His other children, we see this fully come to life! It’s a representation of LIFE with CHRIST as part of HIS FAMILY. That’s why it’s so incredibly mysterious, because God Himself is a beautiful mystery and life is a miracle happening over and over again on into infinity. The negative numbers represent our disconnect from God when we go down into darkness. Don’t go that way. Abide in Christ, the Living Word of God, The Way, The Truth, The LIFE! Eternal Life! GOD BLESS! ❤️🔥
@@queenj.8i895 Since I am god, I find you trying to explain me insulting. How dare you even try to comprehend what it is I do or why. Never do that again. That is blasphemy to your god Zeus. Go sacrifice a goat to make up for this.
Interesting analogy to associate this conjecture with God. I have to admit that I never thought that this is an approximation with the quest of God. Thank you, I like your comment. A question, are you a member of the mathmaticians that seek to show the greatness of God thru the amazing field of math? @@queenj.8i895
Whoever created all those graph animations is an absolute master in after effects expressions
Amen.
BR?
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
Math
BY "NO ONE" : He meant about Americans cause he himself is a american who dont knows anything about the outside world .
This math problem is actually like my trading portfolio, I can start with any number but end at $ 1
you too? :)
I tried to remove the eyelash on the display 🤭
There's that damn eyelash on my screen again!
@@luca6819 .same lol
@@luca6819 You're using youtube in lightmode? ;o
Everyone here: "...but just a maaaaybe I'll be the one to solve it."
"I could write a computer program to try and solve it". Because I'm sure nobody has tried that before 😪
You can actually instantly solve for half of all numbers. If all numbers up to an odd N works, (n+1)/2
I too thought i could solve it :D
What is there to solve? There is nothing to solve
@@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
I'm 30 years from high school, and numbers and math still fascinate me. I don't always understand everything in these videos, but I still love watching them.
I absolutely love how mathematicians always find the most random things to debate over!
ridiculous too
I totally agree. What a waste of time
Not a waste of time. If you can find this solution, probably there is something you can achieve and get.
@@christloen4077 No way
In your mind
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
facts
Imma use this
@@lordsiomai be honest, no you won't
@@anyaburke6636 its 6
@Human Kind its already a 1000 We can make it 2000??
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.
nerd
Atleast find better ways of procrastination
@Hence Forgot bricks bit to though to bite on man ill rather have alloyed steel
Ez Answer Is 9 I was Doing my math Homework Bruh
You have a great teacher if they motivated you to spend hours on this!
I noticed that if you take the negative modified version of the sequence it follows a specific pattern. It always returns to one of 3 options: -1, -5/-7 loop or the -17 loop. This pattern holds up to at least -10 million from my tests so far.
Yea same here
Same with me
Did bro solve it? (For first 10 million)
@AnVissWno as it says positive interger
Bro is geistig
“Pick a number”
Me:Fou-
“Seven? Good choice”
Me:but I-
I said 4, I usually say 3 but I said 4 😂
He said seven because seven is more likely to be chosen lmao
I think Im the only one who chose 7
Only reason I'm not liking is bc tbe lile count is at 69
I didn't choose a number at all because no one can make me do math.
Nice work Soviets. You got me.
Hitler be like :
@@thishandleisnotavaliable I was watching this video without signing in, but signed in just to like your comment buddy.
The Cold War won't truly be won until the Collatz Conjecture is resolved.
@@akshatvikramsingh8293 thanks mate.
Ngl i hate your facebook page lol
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.
Good pickup!
Wow I did the poll a few seconds before scrolling to the video and this comment, I was wondering what the poll was for
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?
@@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
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??
In order to get a mirror image of 3x+1 with negative numbers, you need 3x-1. 3x+1 with negative numbers should be the mirror image of 3x-1 with positive numbers. After all, you're after a scalar of 3 and an offset of 1 away from 0.
Thats just the exact same as the original problem. It doesn’t help at all
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.
cause you don’t have an exam and your future on it while watching this video, but at school,
yes
@@ultraslanmc That's a very good point! No stress to learn it 😂
Same. Things are so much more interesting when you learn them on your own than when you learn them at school.
The yearn for understanding really seems to increase with age…
Found the mathematical phenomenon A very interesting channel - " Artificial Intelligence plus Lottery"..
The amount of graphic work that had to be done for this video is insane.
Exactly what i was thinking, i was like man props to whoever worked on this video
Try a Captain Disillusion video ... And he does those all himself
Really.. wow. Entropy maybe
@@peterh222 *disillusion
Listen ...don't look
i wrote this comment to appreciate that those graphs were not just random. There were exact and to the scale.
Ikr
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
@@Sintinium of course he wrote a program for it but I expect the developer probably spent at least 2 weeks on making it.
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
@@Sintinium I think he paid some small company to do that, a single person is unlikely to do that
I have an INSANE coincidence related to this. I discovered this in 2022, and became obsessed, learned a lot about it just because I love math (I'm not even from the exact sciences, I was studying for the ""SAT"" from my country to study psychology). Then, this extremely specialized subject, something a student from high school would have NO business knowing about, ACTUALLY SHOWED UP IN MY "SAT"!!! It was insane, they explained a bit about it and it was kind of just the context for the question they wanted to ask, but everyone I've talked to about it said the question was extremely hard because they had to spend time figuring out what the heck this was. I did it with ease because I was so familiarized with it.
Anyway, it was completely crazy and I have this channel to thank because it was what started my interest in the collatz conjecture
Dont get stuck in a loop now!
The animation is everything here.
@DON'T stfu
@DON'T stfu bi-
You both just fell for his trap lmfao
@@WillCrewMusic i didnt even read the pfp the text is too small to see LMAO
@DON'T IM GONNA SAY THE N WORD
Math problem no one can solve: Exists
Me: Finally I'm not the only one who is bad at math.
Not able to do a math problem, doesn't make you bad at math.
@@risav202 please explain. i dont agree
@@risav202 Nah.
I literally just saw you on Nas Daily...
@@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.
The fact that this is the basis to making an organic shaped coral mesmerized me.
wait really? lmao
Wow 4th
Can we not use decimals?
it grows, makes an unpredictable, chaotic but somewhat beautiful image, and then inevitably falls back down to 1. like life and death cycle.
Found the Mathematical Phenomenon A very interesting channel - " Artificial Intelligence plus lottery"
I came to this channel 2 years ago with no mathematics knowledge. I am here today, intrigued by our universe, I'm going back to college, and I still love Collatz Conjecture and Fibonacci to help calm me down. As a pharmaceutical technician, thank you.
Pretty much every subject in school is really interesting if I’m not forced to learn it
History of the entire world, I guess convinces me.
Pretty much every subject in university is really interesting if I"m not forced to learn it
School in a form of forced education kills interests and produces stupider people. Coersion always makes things worse.
English, grammar
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'.
A big shoutout ot the graphics department for making this 100% more understandable!
a big shout down to yoy that you were'nt able to get such a simple equal...
I really hope this is satire 🤣🤣
@@josiahjray baited :D
@@gniewko123456 Hope so lol
Ah yes, 999 likes
Mathematicians: Dont waste your time on this problem
20.7 million people: YES
Just cuz you said that I'm going to code a program that runs through all posible combinations on scratch
3 years year old me : what is maltiplikaton?
Ok
13 Million*
more
I think we must approach differently as changing the inputs of the problem.
If we do O>5n+1, E>n/2 we find a loop at 13.
If we do O>5n+3, E>n/2 we find a loop at 3.
But what if we do O>(n^3)+1, E>???
We cannot give a number but 2 to input of even numbers, if we want to divide by. This is their property, indeed this is their definition. For odd numbers, it must not be a quickly-ascelating formula like factorial, but clearly it must not convert the number to odd number neither. Maybe if we can find a connection, we can step further.
why isnt this comment more liked???
Me : "That's interesting puzzle, maybe I can solve it"
Me 22 minutes later : "oh."
Lol
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
@@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.
@@mjzudba5268 yes ofcourse
@@theultimatetime8029 try 70!,it's bigger or even 2^70!
I love the thought of numerical values plotted out in a visible graph could create images, passing information by nothing more than numbers and understanding of how to multiply and plot them out.
I can't tell if this is sarcasm or not😂
Have you never seen a mathematical equation expressed in a graph before? If not, I assume you are either very young or new to math because it’s common and can be an extremely useful tool.
Uh yes yes very nice
@@IzzyIsIsi its not they are just saying how super basic things can create super cool images
This is a delightful exploration of the Collatz Conjecture, thank you! I particularly liked just how pretty the visualizations become when you play with adding rotations for evens and odds.
You're videos are great sir
I am glad to meet you
But just for your kind information sir
Almighty the chosen one can solve this problem but he don't have time we have to convince him
As did I. Shedding light on a difficult topic is no easy feat.
What about rules like 1x+1 or 2x+1 or 4x+1 etc. Do they form loops?
Its like somewhere in maths is every organic shape we thought made life somehow special, yet of course, life is biochemistry, its ruled by maths....yet maths is not so regular, so the often made philosophical presumption is that maths produces mechanistic outcomes, when it doesn't. Contingent complexity is one thing though, and hard problems like consciousness are another, but at least philosophically there is some descriptor of aesthetic natural beauty in a way. A way where we can look at the whole like we can a histogram but not make a rule of its parts, like an equation. Such as, those who also presume to quantify art, or say it is relativistic- even from a mathematical pure materialistic sense it has to be neither, but changing quality depending on which level is observed.
@@cemgecgel4284 actually not worthy
I tried all of them but 3x+1 do best job
And 3x-1 if you take negative numbers
Thanks!
Thank you!
Mathway: “Am i a joke to you?”
Photomath: “Answer the question.”
Lol wassup homie
Lmaoo
Ugh those programs are virtual math teachers worst nightmare.
Answer:0
Looks like a good formula for generating Mountains in a virtual environment.
Ye
that's how they make roller coaster rides
Perlin noise: am I a joke to you?
not really, mountains aren't created by random processes.
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.
This was one of the first programming test I ever made - two players could enter a number and the winner was the one who reached the highest number of steps over 10 rounds.
Good idea, might practice by doing that...
12:35 Yes, absolutely One of the world's greatest living mathematician 🛐
Me: Where should we eat?
Girlfriend: Mathematics is not yet ripe enough for such question
Noo
I love your girlfriend.
Wait, no, it's not what you think it is!!!
LMAO🤣🤣🤣
😝
Lol
13:55 - my face when started watching this video
18:05 - my face in process of watching
Ooh 16 likes. I bet it will be 2K before 24 hours.
😂🤣 I don't know why I clicked on this video but im glad I did because I saw this comment
I can't stop laughing at this =D
here before this blows up lol
@@jolteoff same
I cant even imagine the amount of work put into the visuals of this video, and of course the research and everything. Thank you so much for this!
I tried solving the 3x+1 in algebra, and.... yeah I wasted a lot of time. I have learned my lesson. Listen to mathematicians 😔
I WASTED 3 HOURS AND 49 MINUTES ON SOLVING A PROBLEM, THAT IS IMPOSSIBLE TO SOLVE.
@@Blind_Ghostling I wrote code that loops through every number possible, the largest number I got "Which was how much numbers were in the loop" was approximately 6300+ but other than that like no luck.
@@Blind_Ghostling But what is it that they are trying to solve for? That all numbers come back down to 1?
Or what?
@@epsteinsghost7247 i've got no idea 😂
You could say: In order for the conjecture to converge to infinity, it means that there will have to be a limit to which an odd number will be transformed (through 3x+1) to a number of form 2^n (because when a number is in form 2^n, it will always converge to 1, and/or it is the only way to get to 1) so that after you cross that boundary you would not be able to get back to 1 again. Basically at one point you have to land on a 2^n form number. When plotting 3x+1=2^y, we can observe that the function/curve's values after 0 are not undefined, the function it continues infinitely. Therefore we can say that there is no number (seed) that will never stop growing, because the function 3x+1=2^y then has to have a number that does not obey the expression.
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.
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.
12
The video is 20 minutes. LoL. Of course they not going to watch it.
It's 4
There is actually two ways to solve that and I put money u would lose if u tried to guess the other way
Oh my god, this poor animator. That is a serious amount of dedication. Looks fantastic!
i was just gonna say that! Amazing work by the editor.
It seems like it is made by the same software that 3b1b uses.
Amajing
@@remenyo what is it??
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
Your way of Explaining through Graphics is beautiful sir.
@@icantlivewithoutnesquik2032 109 likes :/
Now its 321 likes lmao, You thought you could Make a good point there but you couldn't LOL
These types of graphics are the way I always visualized mathematics when in school. Being born in the early 80s, this kind of stuff wasn't available until near the end of my compulsory track. But I always saw the action taking place that the numbers described. Loved loved loved the advent of visual graphics integrated into mathematical teachings. Really shows how dynamic this stuff is.
@@icantlivewithoutnesquik2032 the lowest number is 1 meanwhile me learning more complex math that have negative numbers be like: bruhhhh
3blue1brown: "Pff...."
I'm 7 minutes in, why is the pacing in this video so terrible?
This is just a simplified form of: momentum - gravity
It's the most basic example of an equation that takes itself into consideration, because gravity continues to decrease the momentum over time.
You could think of it as a temporal equation.
I appreciate how you simplify even the hardest topics.
I'm not a mathematician but found this fascinating enough to watch the entire video.
Same
Fr bro also me
Sam3
everyone is a mathematician whether they know it or not
ew wtf just happened
Yep, so did 99.9% of viewers that watched
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.
ahhhhh
i guess the adage that the average person is an idiot is true then
The only thing I honestly understood
@@_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.
@@_ikako_ proud even = red gang
Mad respect to the animators here. That must've been a lot of work.
And how much work on calculator.
Looks like 3blue1brown's framework manim at work
i agree, but there are other people that have animators do even more like haminations (he's a story time animator)
Someone's back is hurtt
we do or best.
In 3x+1 there is no number that stands out / forms a closed loop. It is Mathematics, if 0 isn’t in there and all numbers from 1-9 (1,2,3,4,5,6,7,8,9) obey the law in the first digit/ single digit (Which they do), then all numbers up to infinity follow them.
The simple Answer is;
3x+1 is a loop of randomness that at the end solidifies as 4->2->1 and doesn’t contain any abnormalities.
I salute those who genuinely understand this. You have my respect and admiration. I've tried once and I'll try again but I'm just not good at math. But still it's so fundamentally fascinating that I cannot just leave it be. The way in which mathematics describes the very universe is just mind blowingly scary.
Just stay curious and I promise you things will get clearer the more you dig into it.
Not scary, enigmatic. And the enigma is beautiful and haunting whether or not you understand it or not.
8x8*2
Can I just take a moment to applaud the animations created for the visual representation of the concepts?
3blue1brown animations
Thought exactly the same while watching
yes you can.
Found the Mathematical phenomenon A very interesting channel - " Artificial Intelligence plus lottery".
"Worlds Greatest living Mathematician"
I see what you did there.
*there
@@chriswebster24 thanks.. Noted!
Ahaha! That sequence took me a second. Nice one! (12:33)
Could I get some clarification?
@Chinmaye Last name Well now it's obvious. Thanks
Whoever did those mind-blowingly intricate and utterly beautiful graphics deserves the highest accolade.
I have a question and is like why are we trying to solve a math problem without solution? Instead we have to try to learn more about the space for example. I mean is a problem that have no solution everytime you go n *3 +1 /2 you are going to get a number that you already did so you get to the same conclusion. Even if there is a number this math problem solves nothing, just the problem itselfs. Very good video by the way and is such a cool math problem.
I’d love to know what visualisation tools were used in the production.
@@Christian2002_ By “solving the problem” what we mean is to find a proof for the question. That being, if you have a function where 3x+1 is applied when odd and x/2 when even, where x is an element of the natural numbers, then all x will be reduced to the repetition of 4,2,1. Is this true or false? The goal is to find a proof for this theorem. That is the goal.
The idea behind putting values of x in is to see if we cans find patterns that might lead to an answer. This is very common especially in the case where we see circular patterns as it could hint that Pi is involved.
Edit: The other goal is to prove that this is false. The overall goal is to prove or deny the theorem.
Edit 2: It was pointed out to me that the question you posed was more of questioning the questions worth and less what the questions is.
The answer is why not? A better answer is one from 2 perspectives. One is from the idea that we should try and iron out as many holes in mathematics as humanly possible. We want math to be as consistent and explained as we can make it as it strengthens math overall. Solving specific problems like this is part of how we strengthen math as a science.
The other more important reason is that a discovery of a proof for this question might open new doors in mathematics. Maybe someone finds a clever solution that inspires someone else. Maybe we create an entire new mathematical concept to aid in the solving of the problem that then opens the doors for an entire new branch of math. Newton created calculus in his attempts to solve certain specific questions for example. Solutions to specific problems like this can aid in the solving and overall understanding of mathematics as a whole.
@@jackbrax7808 i think OCs question was more like "why do the great mathematecians waste time on this?" Instead of using their talents for other causes
@@Feisty123 Ah I see. I will make an edit for correction thank you.
I laughed when he said "one of the greatest mathematicians" and showed his his grinning into the camera
?
@@VERSACE.1X 12:36
@@John-el5sv i see. thought he meant the guy frm the beginning.
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. 😅
"Why 3x+1 is famous"
"May be its not famous but infamous"
Lmao
Fun fact: We are not mathematicians but we got interested by this.
People that know math are are mathematicians and also if thay do math they are mathematicians
ikr
I am
Hmmm
@@amirpakravan4389 shut up u ruin the vibe
The transition at 12.33 "World's greatest living mathematician ..." was so hilarious.
Well played sir.. well played.
12:33
Yeah It Got Me Laughing
@@karlmarx828 i love you 😩😩
My favourite capitalist
He said “ONE OF THE world’s greatest living Mathematician".
It seriously doesn't take effort to write 12:33
But seeing your pfp it makes sense since its shikamaru
3x+1 is easily solvable when you rearrange the numbers into 3x1+ which spells out “exit”, therefore you won’t need to worry about the problem.
Ngl I audibly giggled
take a note of this guy over here, lmao!
You want a field medal mate?
Found the Mathematical phenomenon A very interesting channel - " Artificial Intelligence plus lottery".
"This math is weird because of math. We can't do enough math to solve the math - there's just too much math!"
You could start by calling it MATHS
my dumbass brain is quaking
Pretty much lol
Weapons of Math Instruction?
@@holdontoyourwig Unless he's British, why should he?
The fact that the first 4-2-1 loop was presented as a 4-2-1 pitch class set was beautiful. Great Easter egg!
"One of the world's greatest living mathematitians" with your photo that is then uncovered is genius
Yeah, that part was hilarious
Yeah, it cracked me up! :D
i’m an english teacher and you didn’t pass the test
@ttrouble’s animations I can appreciate the thinking, it’s an interesting path to explore
@ttrouble’s animations why should 1.0 be classified as even? I can't understand your thinking honestly.
Imagine being a Math Teacher and you gave an entire class an activity
1. Solve Collatz Conjecture 3x+1 (10 pts.)
The issue isn't solving it but proving it. :)
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.
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.
Smart in class: *Gets 10pts*
He/She would be barred from further teaching due to academic cruelty beyond comprehension.
12:34 "one of the world's greatest living mathematicians..." the editing really got me laughing. Nicely done.
lol😂🤣🤣
369th like :)
Same lol I was looking for the comment
Got me too, 😂
@@michgroy1427 Lol ! Me too
Okay, statistically speaking, the average gain it can get is *3-4 and the average loss is /2+1+.5+.25 etc ending up with 4 so the only numbers that go up are numbers where the 3x + 1 and /2 are equal which is only 1 (not including negative numbers) so there are no other positive cycles than 4 2 1
Mathematicians: *_cries in proofs_*
Scientists: *_laughs in null hypotheses_*
@@Sinaloabricks hypotheses is the plural 🙄
@@Sinaloabricks Who says that we have only the one hypothesis?
Statistician: *does both in bipolarity*
Is not mathematics merely just a part of science anyway?
@@andrewcramer9200 Bipolar Person: "Finally, someone DOES understand me"!
"The simplest math problem no one can solve"
My math professor: oh, looks perfect for the exam!
🤗
congrats on 300 likes
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
@@Phantom-el6oe ?
@@Phantom-el6oe He's not doing an exam, are u dumb?
@@Phantom-el6oe but u cant actually do that
The urge to solve this problem is directly proportional to the amount of work already in hand.
exponential*
What exactly is the problem?
The classic "To big to fail" problem
Nice!
sunk cost fallacy
As soon as you showed the rules for this, my brain immediately deduced that once you reach a power of two, this cycle is doomed to repeat a loop of 4, 2, 1. In the example at the start, I was surprised that the power of two reached first was as small as 16.
"What do you do for a living?"
Mathematician: "I am studying 3x+1."
havent watch the whole video but 3x+1 is impossible to solve bc it has infinite solutions??
Big maffs
no one
not even no one
me: 3x+1 equals 1 because 3x nothing is 0 amd + 1 is 1
When I saw that picture I was like it’s obviously 4x
I disagree
@@fanaticjay3825 bruh what
I don't care about math whatsoever but this was incredibly interesting.
Amazingly presented, dude!
Hello Sunset Shimmer! What's up in
Canterlot High School? :D
@@Haxior5506 The usual, ehe ;)
Maybe we should tell Sci-Twi about it, she might crack this case!
If you found this incredibly interesting, I think you do care about math, just not in the way one might normally define "math" in everyday life
Enjoyed being the 200th person to like this comment!!
@@Aerma maths NOT math
I love how seemingly simple this problem would seem but how it's stumped mathematicians for so long. Makes you appreciate how complicated the mundane can be. Really makes me want to go back to school for a math degree!
Can someone explain what is there to solve?
Maybe it's just me, but it doesn't seem that interesting. Combined, the sequences shrink, therefore it's no surprise that everything eventually gets back to 1. Why are there no other loops? Because combined... the sequence shrinks, so a closed loop can't exist.
@@elliott8596 Same with me, it's just the nature of it and what else is there to explain - we can already understand why it goes back to 1
@@cyanrays8177 Because you don't know whether a closed loop exists at a place we can't check yet. I don't think it does - but it's a way less trivial question that you can't just assume your way out of by assuming that you're going to divide by 2 much more frequently than you will multiply by 3 and add 1 - for any starting number.
@@XCC23 Well. A scientist might not make that assumption, but an engineer absolutely would.
Point is, it's still not that interesting, because it's hard to really believe that finding a counter example would be anything more than a fun fact.
12:35 😂That's good
I laughed too 😂😂😂😂😂
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.
Because maths are the language of the universe.
@@LadyMysanthrope Facts.
Why did the math book look sad?
Because it had too many problems!
😂😂😂😂😂😂😂😂😂😂😂😂😂
@@pasaamvmaker5251 LOL
How is it a problem if there's no equation.?
No = symbol.
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.
me to :p
1k square miles ?
@@AnAnonymousMan three, take it or leave it
It makes me feel better when I realise that. Maybe you just have way too much undeserved ego.
@@maxwellsequation4887 When did I ever say it didn't do the same for me?
I feel better too.
You could see the pain in the eyes of prof. Alex. He spends 20 years on this problem. 20 YEARS.
There's a man in dire need of a life.....
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 :)
in 20 years he realised his wife had left him, and he had wasted his life
@@novatime3214 it wasn't an entire waste...his wife left him 😁
Obviously not all on this one problem
One thing i noticed for any odd number in a given 3x+1 sequence. Ok, this technique is to predict the next odd number in the sequence. We'll assign two roles to the number's we'll take. One will be the initial number of whom we'll predict the next odd number for. The initial number has to always be odd. The other will be the predicted number which will be the next odd number we've predicted. This too has to always be odd. Ok, lets pick 7 as our initial number. Then, we'll do 7×0.53 which is estimated 4 since its closer to 4. Then we'll add 7 to 4 which is equal to 11. This tells us 11 is the predicted number. this ×0.53 trick always works for any given 3×+1 sequence (no even numbers should be applied)
I love on how people immediately pointed their fingers to the Soviets for an unsolvable problem
I go to Confucius
@@toolaazy And Confucius says
@@KENDRICKREVIEWZ I am confusion, this is kansas, why this arkansoo, america eggsplain
@@anmoldeepsingh9281 😭😂🤣😭😂🤣
@@KENDRICKREVIEWZ no more numbers jumping on the graph
The introduction of Terry Tao was top-notch.
Nah I disagree
This is kind of video I need to watch first thing in morning to get started with some brain food! You rock veritasium ! Love your channel
Lol for real first vid i watched at 8:30am 😱 after my tea lol
Well I'm about to watch this last thing before going to sleep, so I'll be the test subject for ending the day with brain food...
Update: it's now 1am. Feeling extra tired after trying to understand that. Oof.
Veratasium - Real food for thought . Thanks Ve Team
Here's some more "brain food" for you: There's a much simpler math problem that no one can solve. No one can compute the exact circumference of a circle from a given diameter. Not even the world's most powerful supercomputer can do this. Because, "pi" is an "irrational" number. But as my book explains, "pi" is not irrational; OUR LIMITED 3-DIMENSIONAL PERSPECTIVE IS IRRATIONAL. Math will never be "mature" enough to overcome this irrational world of limitation. But YOU will be. Some day, in some lifetime to come. God's prophet has spoken.
i told this to my professor and we skipped the whole period trying to solve the problem
Lucky you
That is actually lucky for skipping a whole period
Thanks for the idea I wil use it
Ur definitely a person that I wish I have in math class
I should try that
Your "one of the world's greatest living mathematicians" joke totally killed me.
I was looking for this comment lol
Same here. I thought it was very clever.
* You're , btw I am better than you
@@JamesAccountStuff not you’re but ok
I immediately knew this would be in the comments as well lol.
"use Benford's law for tax evasion"
Got it
next they'll invent another law for you to follow
Ffs even when you break the law you gotta follow other laws, huh? ):
@Soul Seeker appropriate name for someone who works at the IRS or on some other auditing team lmao
@@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
Most tax verification algorithms are having the same function in the root file patch 🤞
0:01 We did this in my differential equations lab as an example of chaos, and here it is in my recommended 3 years after publishing.
I brought this up to my algebra teacher. She spent half the class trying to find a number that missed the pattern. To no avail.
Legend
In soviet classroom, student schools teacher!
maybe consider relocating
@@daxpaxton5986 how? its just a guy telling his/her teacher a math equation he doesnt know the answer him self
She's only a middle school teacher. And what a great lesson for the students!
"It's a simple spell, but quite unbreakable" ~ Dr. Strange
Perfect.
Yes.
Fitting
And this comment is just like last piece of jigsaw puzzle
I like your style
him: "pick a number, any number."
me: "eight.."
him: "seven? good choice!"
5... 😭😭
Me: 0.
Him: ok, if it's odd, × 3 + 1, if even, ÷ 2
Me: I think you just broke your calculator.
@@KratonWolf yeah. 0 really isn’t even or odd, so your just stuck
@@savathunthewitchqueen8299 and even if you do plug in zero to 3n+1, you go back to one.
Ikr... I picked 4...
The Number IS :5 and third, THIS IS the Same as 3n+1, ALL 16 multiples Numbers divided through
3(multiples with forms of 2)=
5 +1/3! And this IS the Same like 3n+1.…5 x 3 =15, +1=16
5 1/3 x 3.=16 too
The half x 3 +1:2 and so on ending early or later in 5 too,
ALL Numbers have No Chance in ending in 8,4,2,1. Best wishes,
Sandra
This channel has single handedly made me interested in maths again.
You might like numberphile
You’re british
BRITISH DETECTED
@@pegleg759 Australian actually
@@KaneSoulbreaker Stop saying maths Aussie
Me: “tries to do it in negative”
“Gets in a loop anyways”
@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
True
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
@@Mango-rl2yg huh?
@@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!
❤️❤️❤️
No matter how big or small, we all eventually come back to 1.
I have no idea what this means, but it’s provocative.
Ball so hard!
The whole universe is destined for emptiness, space spread so thin that energy itself can no longer materialize into matter. All of the order which exists will eventually and inevitably return to the chaos of 1
“You know, you come from nothing, you're going back to nothing. What have you lost? Nothing!”
True. Of course, if this conjecture ever gets proven false, we'd get the moral "Someone out there won't go down to 1. Maybe it's you, maybe not. But either way, we won't know until we try." or something...
@@MattAsherMusicisn’t that meant to be zero. I’d say 1 is singularity
It's actually quite easy to show that there must be a 1 to 1 correspondence between loops (like 4-2-1-4) and even prime numbers (of which there is only 2), so the 4-2-1-4 loop must be the only loop possible.
Now to the second part: are there sequences, that just explode torwards infinity and never loop? For this we need to consider what information must necessarily be a part of the true statement describing the behavior of sequences, which never fall into a loop. Again, its quite easy to show, that any such statement must contain a complete list of all prime numbers. As far as my knowledge goes, no such list can be produced. Nevertheless the set of all prime numbers can be defined without any problems. Which means that there must be a 1 to 1 correspondence between prime numbers which are not in the set of prime numbers (there are none) and sequences that never fall into loops (subsequently there cant be any, because every prime number is in the set of all prime numbers, because it is possible to define a set of natural numbers, which will contain all and only prime numbers), but because the proof of that statement would require a complete list of all prime numbers, which isnt a thing, it ultimately can not be proven nor disproven.
We need to have every high school math teacher put this on the whiteboard for the extra credit exercise and see which previously undiscovered kid makes a breakthrough because they don't know that they aren't supposed to be able to solve it.
Well the first thing anyone is gonna do is look it up online and they'll find it's a well known problem. But yes it sounds like it would make for a fun problem to look at regardless.
Can’t wait for Matt Damon to solve it!
Solve what though? 3x + 1??
Oops, I just realized I conflated the stories of Carl Gauss and George Dantzig in my head. We don't need to do this in schools as extra credit, we need to leave it up on boards in college so that everyone who arrives late thinks it's homework.
Its on d worldwide blackboard called footube
I was so inspired when i first saw this video. I’d always think about it. And this year, my math teacher had each student teach their own lesson at the end of the year. I chose this conjecture because of this vid. I used this vid as a source, i watched it like 20 times, and I’m so inspired by your channel. This vid is 2 yrs old as i write this, and will probably get buried in all the comments but i still want to write this for the small chance you see this. so if you are reading this, thank you for inspiring little minds like mine. ❤️❤️❤️
I’m reading this
Me too lol
Cool
We'll be liking your comment until it reaches him.
Fun fact, I was the first like :)
The Animation level of this Channel , unlike Collatz Conjecture, is going up everytime !
I know right? I hope the animators get decently paid, these graphs can be a pain in the brain to animate.
Literally you are still alive ,scrub
Infinity episode animations flashback
@@Shinkajo Thanks...Yea I am Alive and really happy to see scrub who calls others scrub !
@@abhinandanmalhotra8519 I'm definitely a scrub too.r
Takes one to know one😜
I mean, the difinition of an odd number is 2n+1, so doing the 3x+1 is doing 3(2n+1)+1 that is equal to 6n+4, which not only most of the time that number starts with one, but also could be worked to find the awnser. One way of thinking it is that youre not multipliying by 3 and adding one, your actually adding 2 and then multipliying by 2, which makes it even.
And in top of all i think that maybe the awnser is to find a number that when multiplyed by 2 isn't even, which no whole positive number can do.
Edit: they can’t 'cuz 2n is the definition of an even number
I noticed that every 3x + 1 is 4 more than a multiple of 6, and now I know why! :) Thanks.
Also, I noticed every power of 4 (4, 16, 64, 256, 2014, 4096, etc) is 3x + 1.
@@MikeC2K10 I responded to someone else about the powers of 4 thing, and it is true for every number! If you know some modular arithmetic, I would encourage you to look at the powers of 4, (mod 3) to see why.
I teach programming, and I always have my students write a program to test this conjecture. They really enjoy entering really big numbers and watching how long it takes to get down to one. Also offers a great opportunity to discuss what constitutes a mathematical proof, i.e. just because something works for every number anyone has tried, it doesn't follow for every number.
You are a goated teacher
Just had interesting conversation with chatgpt about this problem, its just ridiculous to ask that question, tell me an odd number which when you multiply it by 3 and add one (which always result in even number) will not at some point result in even number thats not in cycle of power of 2 because if it is then it will collapse on itself, what exactly are you searching for? Lol
@@jankojankic2439
Yes it's SIMPLE. This is not hard to solve....
ALL odd numbers are odd,
All odd numbers times 2 are even
All odd numbers times 3 are odd
All odd numbers times 3 plus 1 are even...
Now ALL even numbers divided by 2 are 50/50 even or odd..
So the probability of reaching an even number EACH time you perform an operation is 75%even to 25% odd....the evens get cut in half, so they decrease half their size....
So the odd number formula is actually : "Odd number multiplyed by 3, plus one, then Divided by 2"
And the even number formula is just "Even number divided by 2"
So we are ALWAYS dividing by 2, and only SOMETIMES 'multiplying by 3 and adding one' before dividing...
Am I right?
🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🛎️🔔🛎️🔔🛎️🛎️
Oh wow, now that I think about it, that's really easy to program, I might try this
Right when he ended with the 4 loop I said “ I’m gonna right this all down and see how my rude teacher likes being outsmarted “
right? worng!
*write🤦♂️🤦♂️
And what did they think
I was gonna do this-but my teacher is super nice!
Write*
At a time back when I didn't know about the collatz conjecture we had this homework assignment. We had to prove that this sequence has a loop. I tried a few starting values and quickly found out that there is a loop of 4, 2, 1. Then I spent the whole day to come up with an inductive proof of the collatz conjecture. Good times.
I thought about induction too as he was talking about the video...curious, if you have your notes, what step in inductive process does one get stuck ?
They did you bad mate, sympathies
There is this story about mathematician George Dantzig, who was late to lecture, and couple of days later he solved two statistics problem thinking it was homework.
Imagine being a math teacher and giving the assignment to proof the collatz conjecture just for the lulz and some student shows up with the actual proof.
@@mintoo2cool very likely it is the induction step, where one gets stuck ;-)
😂😂😂 @ 3:31 lol I’m crying
I can only imagine how difficult and time consuming it was doing the math for everything here, connecting it, AND animating every bit.
Is this a joke
Kj
@@jhtsurvival ?
well that sucks i guess
Okkkknknono
"Pick a number"
"- Seven?"
"Seven? Good choise!"
"- Looks Back Carefully"
*choice
@@LaniPlayzLPS *choise
@@keenjoaquin847 *chuse
@@LaniPlayzLPS choes
@@mrcrunch4635 *cheese
Me: math is my worst subject. There’s just too many weird rules for me to follow.
Also me: uh, wow, that makes sense.
Edit; thank you for all the likes. It makes me happy to see ppl relate to my comment’
Hehe same
@Dylan Brokaw ???
@@mikaylawilliams1651 ???
Samr
@Krishkrash14 ???
I have a similar one:
take a number example 7,in the spelling of seven there are 5 letters
in the spelling of five there are 4 letters and in four there are 4 letters so it is now a loop.
you can take any number like thousands and millions. Even the number is less than four for example 1,
in one, there are 3 letters and in three there are 5 ,in 5 there are four
That's interesting... Nice problem over there... I might think about it in the next days...
Amazing presentation for those of us who are not experts on math, but love to explore it.
Yes but I have a very simple but hard...not really a question is it? It is math related.
When a person (represented by any number) receives the LORD - Father/Son/Holy Spirit, who is The Great Multiplier, and then shares Him with another - (N x 3) + 1 - and then continues on as 2 whole individuals on their own, yet connected paths going forward with Christ, but always remaining in fellowship with all His other children, we see this fully come to life!
It’s a representation of LIFE with CHRIST as part of HIS FAMILY. That’s why it’s so incredibly mysterious, because God Himself is a beautiful mystery and life is a miracle happening over and over again on into infinity.
The negative numbers represent our disconnect from God when we go down into darkness. Don’t go that way. Abide in Christ, the Living Word of God, The Way, The Truth, The LIFE! Eternal Life!
GOD BLESS! ❤️🔥
@@queenj.8i895 Since I am god, I find you trying to explain me insulting. How dare you even try to comprehend what it is I do or why.
Never do that again. That is blasphemy to your god Zeus. Go sacrifice a goat to make up for this.
Interesting analogy to associate this conjecture with God. I have to admit that I never thought that this is an approximation with the quest of God. Thank you, I like your comment. A question, are you a member of the mathmaticians that seek to show the greatness of God thru the amazing field of math? @@queenj.8i895
It always goes to even from odd going up or down and odd from even going down and up
Shows a picture of himself.
“One of the world’s greatest mathematicians…Terry Tao”
Then includes Terry. Lol
Yeah that was so good
😂, That's was funny , He's also good scientist tooo
12:33
@@dreamer097 thanks
Haha. I came to look for this. Haha.
That guys beaming smile while he talks about math is so wholesome
Yeah, he's got a great camera presence and clearly cares about what he's saying
Why has everyone adopted the word wholesome into their UA-cam vocabulary. Weird
@@Scott-got-caught Reddit users prob
Yes, he is healthy food for a math canibal. Wholesome. What else?
@@Scott-got-caught I think you spend too much time on UA-cam if you actually noticed trivial things like that.