not everything is knowable in a world where it seems like artificial intelligence and machine learning can figure out just about anything that might seem like heresy but it is true at least that is the case according to a new international study by a team of mathematicians and ai researchers who discovered that despite the seemingly boundless potential of machine learning even the cleverest algorithms are nonetheless bound by the constraints of mathematics the advantages of mathematics however sometimes come with a cost in a nutshell not everything is provable the researchers led by first author and computer scientist shai ben david from the university of waterloo write in their paper awareness of these mathematical limitations is often tied to the famous austrian mathematician kurt godel who developed in the nineteen thirties what are known as the incompleteness theorems two propositions suggesting that not all mathematical questions can actually be solved now ben davids new research indicates that machine learning is limited by the same unresolvability in this argument a machines ability to actually learn called learnability can be constrained by mathematics that is unprovable in other words it is basically giving an ai an undecidable problem something that is impossible for an algorithm to solve with a true or false response in their research the team investigate a machine learning problem they call estimating the maximum in which a website seeks to display targeted advertising to the visitors that browse the site most frequently although it is not known in advance which visitors will visit the site according to the researchers in this kind of case the mathematical problem to be solved bears similarities to machine learning framework known as probably approximately correct learning but it is also similar to a mathematical paradox called the continuum hypothesis another field of investigation for godel like the incompleteness theorems the continuum hypothesis is concerned with mathematics that cannot ever be proved to be true or untrue and given the conditions of the estimating the maximum example at least machine learning could hypothetically run into the same perpetual stalemate