Mathematical Refactoring
My functional analysis course has included work by guys like Lebesgue and Hausdorff. Much of the motivation for their work seems to be a desire to clean up existing ideas, to repair/simplify/unify concepts, to formalize abstractions, and then to extend capabilities in new directions taking advantage of their much improved frameworks. According to Professor Demkowicz's inclass historical anecdotes, these software refactoringlike activities were all the rage in the late 19th and early 20th century mathematics. Call it mathematical refactoring.
I wish I could claim the phrase mathematical refactoring as my own, but Arnold deVos coined it five years ago. Well done sir.
As of now, Google only shows "mathematical" and "refactoring" appearing adjacent to each other four times in all of the Internet:
 1. A Framework for Automated Software Design Optimization (PDF) by Dr. John Murphy (2002)

In this way each transformation will be "mathematical", refactoring being a very well defined codelevel transformation.
 2. A forum posting on TestDriven Development by Arnold deVos (4 Dec 2002)

Imagine a case where a refactoring affects just two collaborators A and B. A "mathematical" refactoring can be performed quickly and reliably. But if there are tests on A and on B and associated test cases there is a lot more work to do.
 3. A listserv posting by Mathieu Bouchard (15 Sept 2006)

AFAIK, String Theory is still baffling itself; it's more of a mathematical refactoring of previous theories, than a scientific theory, due to the lack of experiments to test the theory.
 4. An IBM Global Services presentation on Electronic Batch Records (PDF) (December 2006)

Use a mathematical Refactoring Model to determine the optimal sequence of actions to mitigate this risk for these products, technologies, and sites over the preset horizon and within the constraints.
Neither Murphy nor the IBM presentation used mathematical refactoring as a compound phrase in the sense that I am, but both deVos and Bouchard both did. deVos easily predates Bouchard.
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