My favorite math mistake is the flying wing design.

In the 50's they asked the question, "What plane design would get the maximum range?" They set up their equations, solved for all of the partials being 0, and came up with the flying wing. Then they built it at the cost of billions, tried it, and it sucked.

Turns out that if they had checked the second derivative, they would have found it was the absolute worst possible design. (Basic max-min problem, the first derivative tells you where to look but doesn't tell you if you got a max, min, or inflection point.) But by then billions were invested, careers on the line...and they still build them.

And another high-tech, low-tech issue.

One reason to prefer high-tech is fewer casualties. However given current events, it is likely that the US will want a much larger military force about as quickly as it can ramp up, and has just become much more tolerant of potential casualties. Which means that anyone in the military with brains is probably reviewing their possible designs and selecting ones which they can ramp up production on fairly rapidly. And that means a lot more low-tech...

Cheers,
Ben