Robert Brown (1773–1858) was a Scottish botanist — not a mathematician at all — which makes it wonderfully odd that one of the deepest objects in modern mathematics is named after him. In 1827, squinting through a microscope at pollen grains floating in water, he noticed they would not sit still: they twitched and jiggled and wandered, ceaselessly, for no reason he could see.

Not the spark of life

Brown's first guess was the romantic one — perhaps the dance was the pollen being alive, some vital "life force" at work. Being a careful scientist, he tested it: he looked at dust, at soot, at ground-up rock, even at a chip of stone said to be from the Sphinx. Dead matter jiggled in exactly the same restless way. Whatever was going on, it plainly wasn't life. He described the motion meticulously and, wisely, left the why to someone else.

The answer, eighty years later

The jiggle is water molecules — far too small to see — hammering the grain from every side, a few more from the left this instant, a few more from the right the next. Einstein turned that picture into hard proof, in 1905, that atoms are real; Norbert Wiener later turned it into rigorous mathematics, the Brownian motion that now powers every option price. A puzzled botanist's footnote became the random engine at the heart of modern finance.

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The full story (with far fewer jokes) is on Wikipedia: Robert Brown — Wikipedia.