Why is the Mazur swindle named so? 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?

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 $$1=1+(-1+1)+(-1+1)+\dots=(1-1)+(1-1)+\dots=0.$$