If you stumble across something or stumble on it, you find it or discover it unexpectedly. I stumbled across an extremely simple but very exact method for understanding where my money went History relates that they stumbled on a magnificent waterfall. = come across
[ 'st&m-b&l ] (verb.) 14th century. Middle English, probably of Scandinavian origin; akin to Norwegian dialect stumle to stumble; akin to Old Norse stemma to hinder; more at STEM.