SERENDIPITY

n.
coined (c. 1754) by Horace Walpole after The Three Princes of Serendip (i.e., Sri Lanka), a Pers fairy tale in which the princes make such discoveries
1 a seeming gift for finding something good accidentally
2 luck, or good fortune, in finding something good accidentally

serendipitous
adj.

They say, (though it may hurt man's ego), that 80% of scientific advances have occurred because of serendipity. James Watt was doing something else, when the idea of a steam engine struck him. Similarly, the Apple-Newton legend occurred just like that, not that Isaac Newton deliberately sat under a tree to find out how/why an apple falls!

But then, pressures of modern life are such that we cannot solely rely on serendipity to yield solutions. You would love to read books by Edward de bono on Thinking.

Serendipity also advocates man's subconscious mind is always at play, thus what seems accidental discovery, might be lots of background processing by our mind.