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