After a long pause I have been reading more in Julian Havil’s Gamma, which I mentioned a couple months ago.
On the bus going home tonight I worked through Euler’s original solution of the Basel problem. I was just stunned by how clever that was.
This original solution was somewhat lacking in mathematical rigor–more like the sort of thing a physicist would do :-)> So I appreciated it all the more. Euler later went back and produced a rigorous version.