I haven't memorized Taylor series for all known functions, so I occasionally have to reach for a calculator. I guess I am mentally weak and the sine of a broken education system.

Oh wait? We've arbitrarily choosen multiplication tables and fractions as "the thing" to memorize because that's what was done before calculators were ubiquitous. Thank God. Now I can go back to being smug and imposing my value system on people I've never met about when calculator use is appropriate. :-)