As other commenters have alluded to , this question is answerable to the same degree as this question is answerable Are numbers made up ? I love math , and part of the reason I love math is that we have taken patterns of our consciousness and cultivated a system that , for all intents and purposes , is based on nothing more than our thoughts . We have then built this whole empire of Mathematics on those first building blocks of Number . A question I ' ve wondered , and would love if someone contributed some thoughts to Would pi as an infinite number exist if how we first thought about math was different ? I know that simply having a different base system would not change the fact that pi is a mathematical constant , but what if our understanding of math was so different that pi would be a finite number ? What would that system look like ?