It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

There is much to be learned and pondered by reading "Proofs and Refutations," by Imre Lakatos. It highlights the importance of mathematical definitions, and how definitions evolve to capture the essence of the object they are defining. It also provides an exhilarating encounter with the ups and downs of the mathematical reasoning process, where…

Presents theorems about lines and lattice points, and relates these to combinatorial analysis. (RS)