Impurity in contemporary mathematics (Q1981996)

The author argues that, while proof purity -- the requirement that proofs use only the notions of theory they a are part of -- appeals to philosophically minded mathematical logicians or had an appeal in the somewhat distant past to mathematicians, in contemporary mathematics -- for which she chooses the examples of algebraic topology and category theory -- there is not only no concern whatsoever with purity of proofs, but quite the contrary, a much deeper explanatory power is attributed to impure proofs under the banner of \textit{unification}, such as category-theoretic proofs that show why disparate results in different fields of mathematics are true, or algebraic topology proofs that illuminate purely topological phenomena.