In May 2014, soon after the MA Conference in Nottingham, and soon after the passing of Roger Wheeler, a staunch member of the MA, who had been my teacher at school, I had the idea that my presidential address in April 2016 might be entitled ‘Inspiring Teachers’. The concept was a talk that might trace my mathematical experiences from grammar school sixth form, through my development in retirement as a contributor to masterclasses for the UK Mathematics Trust and the Royal Institution, learning from the students and from the inspiring teachers at whose masterclasses I assist, to the small understanding of Key Stage 2 Mathematics that I am gradually acquiring through an hour a week with some Year 6 students and their remarkable teachers in a local primary school.

A month or so later, when the organising committee was giving shape to Conference 2016, my words were taken as the title of the conference itself. It is deliberately ambiguous and it was gratifying to me to find this last April that its ambiguity had struck melodious chords with other speakers. My presidential address, however, was conceived as a lecture. Like all my lectures it was designed to be an oral presentation. It was not designed to be written down and published as an article. Please bear that in mind gentle reader, and judge accordingly. If you find something of value here I shall be delighted; if not, I shall not be surprised.