MacCauley mentioned NC tools a while back. Tools that can be controlled automatically, making making many things (like gun barrels) much easier. Apparently, a Frenchman came up with the idea in the early 1800s or possibly the late 1700s, but died before he could do anything with it, then it had to wait on the post-war era.
I'd nominate elementary algebra (the idea, basically, of letting numbers be represented by *other things* for calculational purposes). The Greeks did a lot of mathematical work, so did the Indians, and it seems really weird no one came up with the seemingly simple idea of saying, "Oh, what if I called the perimeter of this square p to simplify my calculation and help formulate a general rule"? Instead, they had to suffer through long-winded passages trying to explain things that could be dealt with in a line or two of middle-school math. I mean, which is easier to understand:
"The perimeter of a square is four times the length of any one side" or
p = 4s
Algebra is probably the greatest mathematical invention of all time, rivaled only by numbers themselves. It would be absolutely impossible to do vast amounts of modern mathematics without them and the tendency towards abstraction they represent.