"Heavier-than-air flying machines are impossible."
- Lord Kelvin, ca. 1895, British mathematician and physicist

Lord Kelvin was not only mistaken, he had already been proven wrong, thousands of years earlier.

Birds and bats and insects are heavier-than-air machines, and by Lord Kelvin's time it had already been known for several hundred years that they could fly strictly as a result of natural, mechanical processes. I'e.,
he knew perfectly well that birds were not using magic or god's grace to fly. So his comment was incorrect even by the knowledge of his time.

I think this is a very important distinction to bring up, because this sort of issue arises today all the time. According to our science, faster-than light-travel is impossible, and although we have no guarantee that our science will never be proven wrong, the impossibility of FTL is a very different kind of statement than say, "Fusion-powered rockets will never work".

We know fusion occurs in the stars, and we know we can reproduce it in reactors and H-bombs. Perhaps there are good engineering reasons why fusion propulsion will never be possible, but we don't know that for certain yet. Like Kelvin's mechanical birds, the science is feasible, so the engineering may soon catch up.

Keep your fingers crossed.