The Most Controversial Idea In Math

[Music] there is a rule in mathematics that is so simple you would think it obviously must be true but if you accept it you find there are now some line segments that have no length a sphere without adding anything to it can be turned into two identical spheres 100 plus years of mathematics has been built on this Axiom it seems intuitive and it works but it also creates ridiculous paradoxes so is it right well it all starts with the issue of choice try this choose a number I can just pluck a random number from my head like 37 or 42 but that is the human brain at work not a mathematical process in math you can't truly pick things at random because formulas always give the same result which is why computers don't have true random number generators instead they usually run an algorithm on your current local time to generate numbers that appear random so if we can't pick randomly how do we select anything in math well the only way is to follow a rule of some sort so a rule could be always choose the smallest thing for example if we're looking at whole positive integers the smallest is one for prime numbers it would be two easy but what about the real numbers that's any number positive negative whole fraction even irrational like Pi or the Square < t of two now try to choose the smallest one it's impossible the real numbers stretch off to negative infinity even if we try to fix our rule by making it super specific like choose the smallest number after one we still get stuck there's 1.01 and then 1.001 then 1.001 and so on so really what number comes after one if we can't begin to specify the order of the real numbers next in previous first and last we're stuck the ridiculous part is we know we have infinite options but despite that we can't figure out how to just pick one the mission to resolve this began with one man in 1870 he took on the task of putting the real numbers in a definitive order even if it killed him and it nearly did gorg Cantor was a talented German mathematician who found himself at the center of a firestorm after publishing one of his very first papers at the ...