Dr John Mackie initiated a discussion on the teaching of advanced mathematics in schools, dealing with the question of whether the subject should be taught primarily 'as a science' (meaning: with full attention to logical development and rigour) or 'as an art' (meaning: with the ability to perform mathematical manipulations and solve problems). While presenting examples and arguments on both sides, and bearing in mind the needs of different types of child, Dr Mackie urged that mathematics should be presented to the child as a science. In the discussion which followed, Dr Rutherford urged that mathematical specialists at school should be given some idea of modern concepts in mathematics (e.g. the concept of a 'group'); Professor E T Whittaker was against a too early insistence on mathematical rigour, and would allow 'geometrical intuition' where purists would refuse it; Professor Copson wished that students could be taught to look on mathematics as a 'language', which must be used precisely and grammatically.