Some academic mathematicians are terrible at arithmetic.<p>There&#x27;s no correlation at all between being able to add up a grocery bill in your head and being good at abstraction.<p>My accountant is very good at mental arithmetic. I don&#x27;t expect him to win the Fields Medal any time soon.<p>This is more relevant than it should be. Too many people leave school thinking math <i>is</i> mental arithmetic, and have no idea what symbolic manipulation is, or why it&#x27;s useful.