One of my good buddies is named Dakota and even I didn ' t realize Dak was supposed to be short for Dakota <| sep |> Well , it won ' t be as clearcut as the higherlevel examples but even something like the dimension of a vector space is problematic to think of as being invented . I ' m fine with we invent the definition of a vector space and the definition of a basis . But if the theorems about vector spaces are discovered then when we discover the theorem that any basis of a space has the same cardinality , it makes no sense to turn around and say we invented the definition of dimension . What happened is we discovered that there is a property of vector spaces a posteriori and all we invented was the name dimension .