Where this gets interesting is that you can say, what if this axiom was not true? Let's assume it's not. And then possibly come up with a whole new system of mathematics (like non-euclidean geometry) which may turn out to have actual use in previously unsolvable problems.
>A scientific theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment. Such fact-supported theories are not "guesses" but reliable accounts of the real world.[2]
[1]: https://en.wikipedia.org/wiki/Scientific_theory
[2]: http://www.aaas.org/news/press_room/evolution/qanda.shtml
But you could falsify the theory by finding characteristics incompatible with being exothermic. Finding the dinosaurs with feathers and other characteristics of the (warm-blooded) birds probably helped, too.
Some of the "incorrect facts" are really theories that were substantiated to the best degree possible at the time, and no falsifying evidence existed at the time.
I suspect some, like "non-functional junk DNA", is a case of scientific qualifiers being ignored in the mainstream media and forgotten.
Humans like "facts", but we inevitably drop the error bars that originally accompanied each new "fact".