Sometimes the most amazing discoveries emerge from a mundane attempt to make two columns of numbers sum to the same thing. Neutrinos, those famously elusive subatomic particles, were invented to keep from losing track of energy and momentum in nuclear weak interactions. Cliff Stoll's discovery of international computer crime (cf. The Cuckoo's Egg) grew out of a mismatch between a pair of billing accounts. James Clerk Maxwell had to insert new terms into his equations of electromagnetism so that moving a coil of wire over a magnet would induce the same current as moving a magnet through a coil of wire. Likewise for Albert Einstein's connections between space, time, and matter.
Other examples?
(cf. EdgeOfTheUniverse (8 June 1999), CherishedBeliefs (19 Apr 2000), Key Problems (11 Oct 2003), ...)
TopicScience - 2006-07-16
(correlates: PlusUltra, NewYorkNewYork, LightningRods, ...)