The Art of the Infinite by Robert Kaplan and Ellen Kaplan (ISBN 0-141-00886-5, published by Penguin Books) is one of the most accessible books on maths that I have had the pleasure of reading. The authors demonstrate a profound understanding of the art of explanation without glossing over, dumbing down, or abridging any of the material present within the pages of this excellent book. Moreover, they present a cohesive ‘Big Picture’ explanation of what, to them, maths is (c.f. the title) and make a very good case for it. Of note is the excellent treatment of Fields which would be accessible by merit of the authors’ explanation to a grade 8/9 GCSE Mathematics student, and would be of particular interest for A level Mathematics students in terms of widening their perspective.
A review can’t really do justice to this book – just read it and enjoy, and then take what you’ve learnt from it back into the classroom either as a student or as a teacher. The introductory theme of polygonal numbers which is then taken up more fully in Chapter 4 will be of particular interest to teachers of maths at KS3.