Incidentally, when we're faced with a "prove or disprove," we're usually better off trying first to disprove with a counterexample, for two reasons: A disproof is potentially easier (we need just one counterexample); and nitpicking arouses our creative juices. Even if the given assertion is true, our search for a counterexample often leads to a proof, as soon as we see why a counterexample is impossible. Besides, it's healthy to be skeptical.
Ronald GrahamAB=1/4((A+B)^2-(A-B)^2) is an amazing identity, and unfortunately, I have to remind my current students how to prove it.
Ronald GrahamSome people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we aren't ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive.
Ronald Graham