Mathematics is like an oracle. Its revelations are as clear and precise as can be. But what they ultimately mean remains unclear. We might see them as instructions and nothing more: the world is becoming increasingly digitalised, and the practical importance of mathematics in our day-to-day lives is growing rapidly. But this would be to obscure the deeper significance of mathematics. Einstein expressed his astonishment that mathematics was so perfectly adapted to the objects of the world. David Hilbert, probably the most influential mathematician of the late 19^th and early 20^th centuries, is said to have responded to the news that one of his students had decided to give up studying mathematics in order to become a poet, by observing tersely: ‘Good, he did not have enough imagination to become a mathematician’. On closer inspection, mathematics is a great adventure in thought, sitting somewhere between the mind and the physical world.

*A clear and concrete guide to the world of mathematics

*Mathematics and philosophy – the not-too-dissimilar sisters

*What mathematics can do and how we can understand it

*Gordon Gillespie is a little different from most other authors of popular mathematics books in that he is also a philosopher