I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces."
Paul HalmosA good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, I make it my first job to build one.
Paul HalmosI read once that the true mark of a pro - at anything - is that he understands, loves, and is good at even the drudgery of his profession.
Paul Halmos[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing - one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.
Paul Halmos