Are not most professional mathematicians spared all trouble incident to income?

The harmony of the universe knows only one musical form - the legato while the symphony of number knows only its opposite - the staccato. All attempts to reconcile this discrepancy are based on the hope that an accelerated staccato may appear to our senses as a legato.

And so matching by itself is incapable of creating an art of reckoning. Without our ability to arrange things in ordered succession little progress could have been made. Correspondence and succession, the two principles that permeate all mathematics - nay, all realms of exact thought - are woven into the very fabric of our number system.