In a recent visit to the National Aquarium in Baltimore, we saw a dolphin show. I really enjoyed it 'cause dolphins are awesome, but there's one thing the announcer said that really bugged me: "Dolphins swim faster than they should be able to."
It's sort of like the old myth that according to the laws of aerodynamics, bumblebees can't fly. The basic concept here is that people have a complete understanding of laws of motion (flight, swimming, etc), and these doggone animals are violating our laws.
The truth is, the animals have it right and we've got it wrong. When our math indicates one thing and observation reveals something else, um, that means our math is wrong. Rather than saying things like "Bumblebees shouldn't be able to fly" or "dolphins shouldn't be able to swim that fast," we should go with something like "Our understanding of physics is wrong / incomplete / etc." But let's not blame the animals when their behavior doesn't comply with our "laws."
In the case of dolphins' speed, the discrepancy is known as Gray's Paradox, posed in 1936 by biologist James Gray. He basically thought dolphins couldn't be strong enough to overcome the force of drag as they swim through the water. He was wrong, but that wasn't proven until 2008.
So, when there's a mismatch between our model and reality, don't criticize reality. Fix the model. When a theory is "mathematically correct but operationally wrong," it's wrong and needs to be modified... no matter how rigorous the math appears to be.
And yeah, this has something to do with project leadership. It's all well and good to have theories and guesses about how much a project should cost, how long it should take or how people should behave in certain situations. But when reality diverges from expectations, it's time to adjust the expectations.