Why is the Mazur swindle named so?

Question

Often results or techniques in mathematics are called 'theorems'. Sometimes they are called 'tricks'. In no other context have I seen a result called a 'swindle'. Is there a historical reason for this trick being called a swindle?

Answer 1

The earliest use of the term ‘swindle’ for this little ploy, this ruse, appears to be in H. Bass. Big Projective Modules Are Free, Illinois J. Math. 7(1) (1963), 24–31. He writes:

Our method relies on two basic tools. … The second is an elegant little swindle, observed several years ago by Eilenberg, and which might well have sprung from the brow of Barry Mazur.

This is in reference to the 1959 and 1961 papers of B. Mazur, namely On the structure of certain semi-groups of spherical knot classes, Publications Mathématiques de l'IHÉS 3 (1959), 19–27, and On embeddings of spheres, Acta Mathematica 105(1–2) (1961), 1–17.

As for why Bass chose the term ‘swindle’… Well, the trick does appear to be quite the swindle, quite the sham, and maybe almost a scandal indeed! For surely you would feel cheated if someone told you something like $$1=1+(-1+1)+(-1+1)+\dots=(1-1)+(1-1)+\dots=0.$$