A hipótese de Riemann explicada

when you look at this what do you see to me this is one of the most beautiful fascinating and frustrating things I've ever seen that's because I'm a mathematician and these hypnotizing curly cues have haunted people like me for 150 years what we're looking at is a glimpse of the Riemann hypothesis it's one of the most important if not the most important unsolved problems in all of mathematics you may have heard about the Riemann hypothesis because it's one of the Millennium Problems of the clay Institute what that means is that the person who solves it not only achieves immortality in mathematics but also wins a one million dollar prize but there are other reasons to care about the Enigma that is the Riemann hypothesis if the hypothesis is true it would solve a mystery as old as math itself that is the mystery of the prime numbers countless theorems in Fields as far apart as cryptography and quantum physics assume that the Riemann hypothesis is true which means that we have a lot riding on this single so what is it what is the Riemann hypothesis why has the search for a proof become something of a holy grail for mathematicians and what do these strange curly cues have to do with all of this my name is Alex katarovich and I'm a professor of mathematics I'll serve as your guide as we explore the Riemann hypothesis in order to build a somewhat sophisticated understanding of this hypothesis what I'm going to try to do is mention some slightly advanced concepts now you don't need an advanced degree in mathematics to go on this journey with me what I'm going to do is try to lay the groundwork step by step in a visual and intuitive way so to begin let's Venture into the chaotic and Elusive Universe of prime numbers this is Factor city where the primes are literally the building blocks of all numbers now every whole number is a building and it's been constructed out of its Primes the one-story houses are exactly the Primes now thanks to the ancient Greek Euclid of Alexandria we know that the one-story buildings keep going on forever if you can walk that far but depending on where you're standing you might want to know how many one-story buildings do you see around you this is what we want to understand about the prime numbers and what we currently don't you see the prime numbers seem to just pop up randomly among the natural numbers all the way out to Infinity [Music] in the late 1700s mathematicians were really starting to wonder whether it was possible to predict the places where primes would appear now a teenage boy named Carl Friedrich daus was especially obsessed with taming the primes he calculated massive tables of primes going all the way up to 3 million and looked for patterns we can see the data that Gauss collected on the prime numbers by using something we'll call the prime counting function the graph of that function will show us exactly where the prime numbers appear as the numbers get bigger and bigger so the graph stays flat until you hit a