The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.
Dijkstra argues that mathematical elegance is more than an attractive quality added to otherwise sound work. He treats it as part of what makes reasoning genuinely mathematical. A clumsy argument may reach a correct conclusion, but unnecessary complication can obscure structure, make verification harder and weaken the economy of the reasoning.
His position reflects a broader concern with simplicity and effectiveness. Elegant mathematics, in this sense, expresses an idea with enough structure to make the reasoning clear while avoiding machinery that does not contribute to the result. The standard is therefore practical as well as aesthetic.
The remark is deliberately uncompromising: Dijkstra does not merely praise elegant mathematics but makes elegance a criterion of the discipline itself. Applied more broadly, it encourages mathematicians to improve proofs not only by checking correctness, but by asking whether their reasoning can be made clearer, shorter and more revealing.