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Purity in Practice Einstein on Purity in Geometry Purity in Number Theory: Jacobi’s Four Squares Theorem Summing up the Case Studies Purity of Proof vs. Purity of Definition Looking Ahead A Brief History of Purity Types of Purity Geographical Purity Topical Purity Syntactic Purity Logical Purity Elemental Purity Values of Purity Purity and Rigor Purity, Understanding and Explanation Geographical Purity and Local Knowledge Topical Purity and the Stability of Knowledge The Simplicity of Purity and Impurity Conclusions References