A computational no-coincidence principle

In a recent paper in Annals of Mathematics and Philosophy, Fields medalist Timothy Gowers asks why mathematicians sometimes believe that unproved statements are likely to be true. For example, it is unknown whether \(\pi\) is a normal number (which, roughly speaking, means that every digit appears in \(\pi\) with equal frequency), yet this is widely believed. Gowers proposes that there is no sign of any reason for \(\pi\) to be non-normal -- especially not one that would fail to reveal itself in...