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.
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.
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
Fascinating! My dad is realllllly good at math, i had a conversation with him over this and he found this interesting as well. In school i couldn’t learn very well, now im learning math at home to get to the university. Now i can learn in my own time, math is literally amazing!
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
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'.
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.
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
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.
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 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.
Look forward to seeing a Riemann Hypothesis video by you. I believe it will be fantastic. Your insights on such a profound and challenging topic would be incredibly valuable. I've always admired your ability to explain complex mathematical concepts clearly and engagingly. A video on the Riemann Hypothesis would be an excellent addition to your content, and I'm sure many others would benefit from and enjoy it as well. Please do it!
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.
hey saw the thumbnail and title only, I believe that 3x+1 is not a problem, it's a formula. therefore you obviously cant solve it, it's used to solve for x when you have the total already, or to find the total for various different X's. Hope I could help! You're welcome!
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
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.
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.
@@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 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. ❤️❤️❤️
@@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.
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.
Negative numbers are miss understood negative number and positive number are just opposite like-1 is +1 as negatives we don't write +1 because it is implied so the formula for the sequence should be 3x -1 with this the positive and negative value give same result as only-(4,2,1) loop
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.
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.
The principal square root function f ( x ) = x {\displaystyle f(x)={\sqrt {x}}} (usually just referred to as the "square root function") is a function that maps the set of nonnegative real numbers onto itself. In geometrical terms, the square root function maps the area of a square to its side length. The square root of x is rational if and only if x is a rational number that can be represented as a ratio of two perfect squares. (See square root of 2 for proofs that this is an irrational number, and quadratic irrational for a proof for all non-square natural numbers.) The square root function maps rational numbers into algebraic numbers, the latter being a superset of the rational numbers). For all real numbers x, x 2 = | x | = { x, if x≥0 −x, if x
For 15 minutes I was thinking “but what about negative numbers?”. And I got my answer. And now I’m in awe. I’ve been doing it just for fun on my calculator (of course not trying to get something out of it) and i have gone mad already. 😂 Amazing strength and dedication to all the mathematicians trying to actually solve this. 👏
@@stripey7303 on the negatives there’s no specific answer. (At least for the amount of the ones I did). There are many different loops. And what’s more amazing is that there are numbers that look like they always end up higher and then suddenly you go only down and end up in a loop. 😵
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.
I did a survey on 10 random numbers between 1 and 1 Billion. 3 Of the 10 numbers reach 9232. 2 of them reach 341 and the other 4 numbers all reach 22 and the other reaches 70. So this means that if you pick a randomly large number, it has about a 30% chance of reaching exactly 9232 just like 27. That's because it is kind of likely that the random number will reach one of the 14 numbers not divisible by 3 from 1 to 100 that reaches 9232.
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...
@@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.
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.
Here are some axioms I could come up with General: 1. Odd number x Odd number is always results in an Odd number. 2. Adding 1 to an Odd number always makes it an Even number. 3. All Even numbers repeatedly divided by two will eventually turn into a Odd Number. Specific to 3x + 1: 1. In a 3x + 1 sequence the amount Odd numbers will always be less then the amount of Even numbers. 2. There is never two Odd Numbers in a row during a 3x + 1 sequence. 3. As the Even Numbers size increases the amount of divisions by 2 in the sequence increase.
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? 🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🔔🛎️🛎️🔔🛎️🔔🛎️🛎️
The supposed error with the negative numbers is that the negative numbers is like a parallel world to the normal numbers in which all +/- characters are inverted. This must also apply to the formula. Then you get the same strand and the same result just like if you change +/- on the positive side in the formula. Multiplication and division are excluded because they do not interact with +/-. Every Number +/- if devided gets closer to 0 Multiplikation to +/- invinity
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 :)
I understand everything in the beginning as it's simple. But, as the video gets further, I get nothing inside my head. But still, I like to watch these videos😂😂
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.
I am sure the mathematician have already tested it, but I wonder if there is a way to check if all odd numbers will eventually (ergo, after a variable number of iterations) leads to a power of 2. Even numbers are easy: either they are a power of 2, therefore collapse, to 4-2-1, or not, therefore collapse to an odd number. Therefore if we can prove that odd number will eventually lead to an a power of 2, we can prove the conjecture.
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
"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
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.
(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
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. 😅
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.
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 this theory: (3x + 1) : 2 is going to be one if at a point, it is equal to 2^y X is the odd number you choose and y is a random number that can be infinite. I noticed that it will went to one if the number went from odd to 2^y and then it decreased to 1. In conclusion, (3x +1) : 2 = 2^y + a. A is a random number and (2^y + a) : 2b = 1 In which , B is the amount of time it took for 2^y + a to be divided by to and then to 1.
P(reach 1)=1−(0.18) n Summary of the Equation Where:𝑃(reach1)P(reach 1): Probability of reaching 1 from any starting integer. 𝐷=0.82% D=0.82: Probability of a decrease. 𝐼=0.18=0.18: Probability of increase or no change. 𝑛 n: Number of transformations.P(reach 1)=1−(0.18) Summary of the Equation Where: 𝑃(reach1)P(reach 1): Probability of reaching 1 from any starting integer. 𝐷=0.82D=0.82: Probability of a decrease. 𝐼=0.18I=0.18: Probability of increase or no change. 𝑛 n: Number of transformations.
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
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 .
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
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
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!
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
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??
Fascinating! My dad is realllllly good at math, i had a conversation with him over this and he found this interesting as well. In school i couldn’t learn very well, now im learning math at home to get to the university. Now i can learn in my own time, math is literally amazing!
Will you major in math?
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
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 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"..
I appreciate how you simplify even the hardest topics.
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
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
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
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
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'.
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
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"
That's why Number Theory is so fascinating: the proposition is simple, the proof (if any) is very hard...
It's easy if you remember the maths of the past and don't focus on using computers
RUclips gave me the chance to rate your comment
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.
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
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'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.
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.
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 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
Look forward to seeing a Riemann Hypothesis video by you. I believe it will be fantastic. Your insights on such a profound and challenging topic would be incredibly valuable. I've always admired your ability to explain complex mathematical concepts clearly and engagingly. A video on the Riemann Hypothesis would be an excellent addition to your content, and I'm sure many others would benefit from and enjoy it as well. Please do it!
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.
“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.
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
hey saw the thumbnail and title only, I believe that 3x+1 is not a problem, it's a formula. therefore you obviously cant solve it, it's used to solve for x when you have the total already, or to find the total for various different X's. Hope I could help! You're welcome!
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.
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...
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
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??
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
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.
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
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 :)
This really help me and my child with this information
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 😂
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.
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
Negative numbers are miss understood negative number and positive number are just opposite like-1 is +1 as negatives we don't write +1 because it is implied so the formula for the sequence should be 3x -1 with this the positive and negative value give same result as only-(4,2,1) loop
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.
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.
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
The principal square root function
f
(
x
)
=
x
{\displaystyle f(x)={\sqrt {x}}} (usually just referred to as the "square root function") is a function that maps the set of nonnegative real numbers onto itself. In geometrical terms, the square root function maps the area of a square to its side length.
The square root of x is rational if and only if x is a rational number that can be represented as a ratio of two perfect squares. (See square root of 2 for proofs that this is an irrational number, and quadratic irrational for a proof for all non-square natural numbers.) The square root function maps rational numbers into algebraic numbers, the latter being a superset of the rational numbers).
For all real numbers x,
x
2
=
|
x
|
=
{
x,
if
x≥0 −x,
if
x
For 15 minutes I was thinking “but what about negative numbers?”. And I got my answer. And now I’m in awe. I’ve been doing it just for fun on my calculator (of course not trying to get something out of it) and i have gone mad already. 😂
Amazing strength and dedication to all the mathematicians trying to actually solve this. 👏
And what answer did you get? For zero, of course, it's just an endless loop, 0 -> 0 > 0> ...
@@stripey7303 on the negatives there’s no specific answer. (At least for the amount of the ones I did). There are many different loops. And what’s more amazing is that there are numbers that look like they always end up higher and then suddenly you go only down and end up in a loop. 😵
@@stripey7303 you can't have an infinite loop of 0 cause you have +1 or -1 at the end.
@@brotinger_1904 I see, I didn't think about that!
@@brotinger_19040 is even
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 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!
The fact that the first 4-2-1 loop was presented as a 4-2-1 pitch class set was beautiful. Great Easter egg!
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.
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
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
This is my favorite channel for learning new things!
Honestly maths should just grow up and solve its own problems
That's what AI is.
I laughed so hard!😂
Thank you
Yeah that was funny as hell
lol
Good one!
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
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".
I did a survey on 10 random numbers between 1 and 1 Billion. 3 Of the 10 numbers reach 9232. 2 of them reach 341 and the other 4 numbers all reach 22 and the other reaches 70. So this means that if you pick a randomly large number, it has about a 30% chance of reaching exactly 9232 just like 27. That's because it is kind of likely that the random number will reach one of the 14 numbers not divisible by 3 from 1 to 100 that reaches 9232.
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
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!
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
Here are some axioms I could come up with
General:
1. Odd number x Odd number is always results in an Odd number.
2. Adding 1 to an Odd number always makes it an Even number.
3. All Even numbers repeatedly divided by two will eventually turn into a Odd Number.
Specific to 3x + 1:
1. In a 3x + 1 sequence the amount Odd numbers will always be less then the amount of Even numbers.
2. There is never two Odd Numbers in a row during a 3x + 1 sequence.
3. As the Even Numbers size increases the amount of divisions by 2 in the sequence increase.
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
Greatest mathematician in the world....
You got me in the first half, not gonna lie😂😂😂
Every comment getting hearted :v
Ikr lol
?
@@sajayrrrhe is talking about the time in te vid were he just showes a pic of himself and saying the Greatest mathematician in the world....
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
The supposed error with the negative numbers is that the negative numbers is like a parallel world to the normal numbers in which all +/- characters are inverted. This must also apply to the formula. Then you get the same strand and the same result just like if you change +/- on the positive side in the formula. Multiplication and division are excluded because they do not interact with +/-. Every Number +/- if devided gets closer to 0 Multiplikation to +/- invinity
"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.
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
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
I understand everything in the beginning as it's simple. But, as the video gets further, I get nothing inside my head. But still, I like to watch these videos😂😂
Take your age
If it’s even divide by 2
If it’s odd multiply by 3 and add 1
That’s not your age, that’s collatz conjecture
So it’s an endless loop of a series of numbers
@@Jerry__________ No, if finishes at 1 unless you want to go thru the 1,4 loop repeatedly. It can be proven in binary not decimal
my age is 101 and i got 304 for 3x +1
@@ArtyBeans repeat until you get to 1
Take your age and times it by 1 and you’ll get your age that easy
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 ;-)
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
I am sure the mathematician have already tested it, but I wonder if there is a way to check if all odd numbers will eventually (ergo, after a variable number of iterations) leads to a power of 2.
Even numbers are easy: either they are a power of 2, therefore collapse, to 4-2-1, or not, therefore collapse to an odd number. Therefore if we can prove that odd number will eventually lead to an a power of 2, we can prove the conjecture.
The introduction of Terry Tao was top-notch.
Nah I disagree
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
"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
I was laughing a lot xD
Funny
Politician in the making.
Australians be ready 🤣
bait level 2^69
You just wrote down what everyone saw.. lol comments be hella typical these days
If you’re Irish you know “it is what it is” is the actual answer cause that’s life.
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
@@amygdal.a same
And we all click it with a tiny glimmer of hope that we might be able to give it a shot.
Not gonna try to solve it, but I did pick a 7-digit number to try it on, just to make sure it works ya know
What is there to solve? You just keep keep getting random numbers based on where you started until you hit a power of 2.
@The Chosen one I have a proof too, but this comment section is too narrow to contain it..
I actually just figured it out. But its too long to explain in a youtube reply.
@@attchdattchd6036 Dammit Fermat, just write it down!
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.
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.
😂 lol
W Editor for the humor
(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
Thank you for explaining the joke (sarcasm)
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 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
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.
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.
😂😂😂 @ 3:31 lol I’m crying
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*
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 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
I have this theory: (3x + 1) : 2 is going to be one if at a point, it is equal to 2^y X is the odd number you choose and y is a random number that can be infinite. I noticed that it will went to one if the number went from odd to 2^y and then it decreased to 1. In conclusion, (3x +1) : 2 = 2^y + a. A is a random number and (2^y + a) : 2b = 1 In which , B is the amount of time it took for 2^y + a to be divided by to and then to 1.
(3x + 1) : 2 = 2^y + a. (2^y + a) : 2b = 1
Please correct me if i am wrong.
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 RUclips 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 RUclips if you actually noticed trivial things like that.
"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
just imagine how much time it took to make this video, coming up and capture all the right numerical figures, graphs and dynamic illustrations
first reply
What software do people use to me for date graphics videos like this?
@@NotEvenATim first reply
Bruh 3
@@soniah687 wooosh
P(reach 1)=1−(0.18) n
Summary of the Equation
Where:𝑃(reach1)P(reach 1): Probability of reaching 1 from any starting integer. 𝐷=0.82% D=0.82: Probability of a decrease.
𝐼=0.18=0.18: Probability of increase or no change.
𝑛 n: Number of transformations.P(reach 1)=1−(0.18)
Summary of the Equation
Where:
𝑃(reach1)P(reach 1): Probability of reaching 1 from any starting integer. 𝐷=0.82D=0.82: Probability of a decrease. 𝐼=0.18I=0.18: Probability of increase or no change.
𝑛 n: Number of transformations.
This guy is the only guy who doesn’t make my head hurt while explaining math lol
Look up eddie woo, he's a good one too
He is just a presenter trained in NLP and public speaking
A whole team including expert consultants are behind producing this channel.
Wow that’s true
Well, not same
Imagine trying to understand the most diffucult math problem in other language xD (My native language is Spanish)
im learning more than i am in school from this guy rn
Mathway: “Am i a joke to you?”
Photomath: “Answer the question.”
Lol wassup homie
Lmaoo
Ugh those programs are virtual math teachers worst nightmare.