Both arguments end in correct conclusions, and both arguments hide a lot of facts (empirical, mathematical) that might render one of their premises false. It’s this possibility that we want to avoid. It’s easy to generate wrong arguments for correct conclusions — and such arguments are completely uninformative.

What I would urge is plenty of caution with non-mathematical arguments for mathematical conclusions. I think that in many cases they *can* lead to new insight, and in some cases they do. But my suspicion is this: these non-mathematical tricks are instructive only insofar as they lead to *good* arguments.

For a similar discussion: a “biological proof” of the isoperimetric theorem in 3D.

]]>