Platonism, Mathematical | Internet Encyclopedia of Philosophy # Mathematical Platonism Mathematical platonism is any metaphysical account of mathematics that implies mathematical entities exist, that they are abstract, and that they are independent of all our rational activities. For example, a platonist might assert that the number pi exists outside of space and time and has the characteristics it does regardless of any mental or physical activities of human beings. Mathematical platonists are often called “realists,” although, strictly speaking, there can be realists who are not platonists because they do not accept the platonist requirement that mathematical entities be abstract. Mathematical platonism enjoys widespread support and is frequently considered the default metaphysical position with respect to mathematics. This is unsurprising given its extremely natural interpretation of mathematical practice. In particular, mathematical platonism takes at face-value such well known truths as that “there exist” an infinite number of prime numbers, and it provides straightforward explanations of mathematical objectivity and of the differences between mathematical and spatio-tempor