As a lecturer my toughest initial task in turning enthusiastic students into able mathematicians is to force them (yes, force them) to write mathematics correctly. Their first submitted assessments tend to be incomprehensible collections of symbols, with no sentences or punctuation. ‘What's the point of writing sentences?’, they ask, ‘I've got the correct answer. There it is – see, underlined – at the bottom of the page.’ I can sympathize but in mathematics we have to get to the right answer in a rigorous way and we have to be able to show to others that our method is rigorous.

A common response when I indicate a nonsensical statement in a student's work is ‘But you are a lecturer, you know what I meant.’ I have sympathy with this view too, but there are two problems with it.