Isaac Newton was made aware of Jean Bernoulli's "brachistochrone" problem #OTD in 1697. He solved it later that evening, showing that the curve of fastest descent between two points was given by a portion of a cycloid.
Newton published his solution anonymously in the Philosophical Transactions of the Royal Society of London. Bernoulli would later say that the identity of the author was obvious; he recognized "the lion by his claw."