Think of a dentist who has a list of patients, and for each patient, a list of teeth. It makes perfect sense (and plenty of money) to hold the patien… - Douglas Hofstadter

The mathematician's sense of tension is intimately related to his sense of beauty, and is what makes mathematics worthwhile doing.

"In the thirty-first year, however, Godel published his paper, which in some ways utterly demolished Hilbert's program. This paper revealed not only that there were irreparable "holes" in the axiomatic system proposed by Russell and Whitehead, but more generally, that no axiomatic system whatsoever could produce all number-theoretical truths, unless it were an inconsistent system! And finally, the hope of proving the consistency of a system such as that presented in P.M. was shown to be vain: if such a proof could be found using only methods inside P.M., then — and this is one of the most mystifying consequences of Godel's work — P.M. itself would be inconsistent!"

There are shallower aspects of a person and there are deeper aspects, and the deeper aspects are what imbue the shallower ones with genuine meaning.