There's a single instance in Einstein's notebooks where he attempts to use numerical methods to come up with a result. He manually graphs some result of the cosmological constant and then integrates it by counting the squares under the curve.

An esteemed emeritus professor of engineering I know used to cut out the graph and weigh it on a sensitive scale to integrate. It was not an uncommon technique.

I find that hard to imagine, considering we're talking about coupled partial differential equations in four dimensions. Well, if that's true, it really goes to show his desperation, I guess.