[Jtarii]

>People used to memorize log and trig tables, and no one would say that's part of being a competent mathematician at this point.

That would be closer to engineering or accounting than mathematics. I don't think mathematicians do much arithmetic at all.

[xhkkffbf]

Go read the story that Richard Feynman tells of betting an abacus user. He used his knowledge of some strange numbers. It's in _Surely You Must Be Joking_.

I suspect his facility with numbers and his knowledge of tables like this really helped him do physics research.

See also his stories on approximation.