World’s Trickiest Math Problem.

mathematics is an amazing science that sometimes makes us feel as if we are standing before the gates of a secret Temple but instead of mysterious doors and hidden traps we are met with equations endless rows of numbers and sometimes problems that seem to have been written by a crazy mathematician in his spare time today we will dive into a world where one of these Mysteries Reigns a problem that has haunted great minds for centuries to be more precise we will talk about the oldest unsolved mathematical problem and the collat fractal this mathematical Riddle That can break even the most resilient brain let us make a reservation right away if you are not afraid of nightmares associated with numbers if you like riddles that make people suffer in University corridors then this problem is for you we present to your attention the colat conjecture is a 90 plusy old puzzle and its solution still seems like a find a needle in a galaxy of needles puzzle before we dive into that mathematical hell let's start with something simple so in 1937 Katz posed a question that goes something like this what happens if you take any natural number and following Simple Rules continue to do math on it the rules are if the number is even divide it by two if it's odd multiply by three and add one now repeat this process on the result seems easy right there's just one small detail the conjecture states that no matter what number you start with you will always end up up with a number one that's it the challenge is to prove that this is true for any number how does this work with an example let's take the number six and see for ourselves [Music] [Music] it seems simple after a few steps we arrive at the coveted unit but don't be fooled when you start with some large numbers real chaos will begin for example if you take 27 the number of steps to one will be impressively large and along the way you will get numbers much larger than those with which you started where is the complexity at first glance this is an elementary school level problem but it hides a depth comparable to an infinite number of mathematical nervous breakdowns the problem is that despite all attempts no one has yet been able to prove that any natural number really always leads to one moreover no one has found an example of a number that does not every mathematician Who falls captive to the collap conjecture immediately thinks now I'll quickly prove it and send the article to Times magazine but it was not so after all for decades no one has been able to prove that the conjecture is true for all numbers it's like solving a sodoku puzzle that changes the rules at every step imagine that the collat conjecture is a giant mathematical Labyrinth where the walls suddenly turn into even narrower corridors and at the exit you will find not a magic prize but simply a big number one during the time where working on this problem many mathematicians managed to immerse themselves in its simple Infinity some even began to believe that the colat number is some kind of hidden revenge of mathematics on Humanity for all the witches burned at the stake in the Middle Ages but if you think that all this is boring let's take a look at the colot fractal what could be better than turning a mathematical problem into a work of art we can visualize numbers by following the rules of the conjecture and as a result we get an amazingly beautiful and crazy fractal these fractals look like complex patterns that can be observed in nature they are somewhat reminiscent of the structure of snowflakes or the tree like patterns of lightning mathematical Elegance here is opposed to the complete chaos of the problem itself and what's interesting some Daredevils even tried to hear the collapse numbers translating these mysterious sequences into music the result is something between jazz and the sounds of your computer crashing when it can't handle the calculation of the giant sequences [Music] [Music] [Music] how to avoid going crazy from collapse there is a simple answer you can't many great minds have tried to solve the problem but so far this problem remains unsolved although to be fair no number has been able to escape to Infinity any known number sooner or later returns to one however this is not a strict proof of the hypothesis because Infinity as we know is a dimensionless thing to fully appreciate the Absurd complexity of the colat problem let's look at it from the other side the many problems in mathematics begin to look more difficult if you involve large numbers as soon as the numbers become multi-digit our intuition weakens and with it any hopes for quick answers it would seem that the collapse conjecture is a simple almost childish problem in essence take a number divide or multiply depending on its parity and voila but as soon as you start working with large numbers everything becomes to put it mildly devilishly complex let's say you start with 27 at first glance that doesn't seem like a big number but the collat sequence for it has wait for it 111 steps steps 111 steps before it returns to the magic one the process becomes insanely long 27 turns into 82 then 41 then 124 and so on as if collat had found a way to torture you with each digit remotely numbers over a thousand start to behave even worse the sequence can increase hundreds of times before collapsing back to the coveted one the process is like a marathon in which every time you almost reach the Finish Line it gets moved forward a few kilometers now comes the scariest part there are examples in mathematics of how numbers can escape to Infinity Like Pirates who never return home for example there are famous sequences such as the Fibonacci sequence or prime numbers which grow without any limits people have been looking for proof that the collat conjecture works for all numbers but no official proof has been found what does this mean it means that there is always a chance that somewhere out there in the Labyrinth of numbers there is such a mischievous number that does not obey the rule turning into an endless race where it will increase and decrease but will never reach the number one it is like The collat Runaway Universe in which numbers try to cheat the laws of arithmetic mathematics is a science that works with iron logic each formula each law is built like bricks that create a building of knowledge and yet despite this Logic the colat conjecture eludes us like a shadow rabbit in a clearing jumping from one formula to another without being caught but will anyone ever solve it the big question many great mathematicians have spent years of their lives on it and no one has been rewarded with success on the other hand perhaps someday someone even a school boy with a notebook will accidentally discover the key to the solution and Shock the World by proving that all the numbers in the world are truly submissive to their digital selves and always return to one or he will find a rebel a number that is decided that it does not care what colat says but while we wait for an answer colat remains something of a ma matical Twin Peaks a Riddle That captivates with its absurdity and genius at the same time it's unlikely that there's another problem that's so simple at first glance and so difficult when you try to get to the bottom of it the cads fractal is a reflection not only of the beauty of mathematical sequences but also of their chaos mystery and let's be honest complete illogicality for our ordinary non-numerical thinking so if you're suddenly bored or want to feel like a real mathematician take any number start factoring it out using colassa rules and who knows maybe you'll be the one to solve one of the greatest mathematical mysteries of all time but remember once you enter this world there may be no way out [Music] [Applause] [Music] [Music] [Music]