Nassim Taleb is full of one-liners good for maxims, mottoes, and mantras. Just read his book "The Bed of Procrustes." This particular advice, however, comes from his book "The Black Swan."
For example, he tells the story of a painter, Apelles, who couldn't perfect the foam around a horse's mouth and in frustration threw the sponge at the canvas, which made the perfect foam.
Serendipity is a fickle friend. I cannot think of any instances in my life where I've encountered serendipity, but that could be because I haven't been looking for it. I'm not a very spontaneous person, and probably wouldn't have thrown the sponge.
Anyways, here's to maximizing serendipity!
P.S. Apparently, the opposite of serendipity is zemblanity: "making unhappy, unlucky and unexpected discoveries occurring by design."