Archive for March 28th, 2008

A Question of Style

March 28, 2008

There’s an interesting discussion going on over at Ars Mathematica about proof styles, beginning with the question, “What makes a well-written proof?” I don’t have a complete answer, but some of the adjectives that come to mind are: understandable, lucid, concise (which can sometimes conflict with “understandable”), motivated, clever (I suspect there might be disagreement on that one). “Correct”, I suppose, ought to be #1, but let’s take that as a given.

A good example of what I think is a well-written proof is Eisenstein’s proof* of the Law of Quadratic Reciprocity.

Head on over and let Walt know what you find well-written.

* G. Eisenstein, Geometrischer Beweis des Fundamentaltheorems für die quadratischen Reste, J. Reine Angew. Math. 28 (1844), 246-248; Math. Werke I, 164-166; Engl. Transl. Quart. J. Math. 1 (1857), 186-191, or A. Cayley: Coll. Math. Papers III, 39-43**

** Found at Proofs of the Quadratic Reciprocity Law