One of the great joys of mathematics is the incontrovertible feeling that you’ve understood something the right way, all the way down to the bottom.
Articles about mathematics
The whole idea of mathematics is to make things easier. It allows us to understand the world is ways that would be impossible without it. So it’s a great shame that many people see it as shrouded in mystery. Eugenia Cheng tries to overcome this problem in this book about mathematics and cooking (and in some cases, the mathematics of cooking).
The intricate details of mathematics can be tricky to get straight, but the concepts should be intelligible if presented properly. In this book, Cheng works towards an understanding of Category Theory, her own specialist area of mathematics. (I think this is the “mathematics of mathematics” mentioned in the subtitle.) Each chapter starts with a simple recipe, which Cheng uses to illustrate a mathematical concept. This strategy works well: you really get a good idea of what the concept is and why it’s useful, without getting hung up on complexities.
This amazing book sets out a mathematical framework for describing and constructing numbers, and then generalises this to a way of analysing certain games. You probably need a postgraduate degree in mathematics to really understand all of it. I am not quite that qualified, but I know enough to be awed by what can be done by simply starting with nothing. Literally nothing: Conway starts with just an empty set, and proceeds to show how to spin this out into integers, rational numbers, real numbers, infinite numbers, infinitesimal numbers, and (believe it or not) more.
The whole class of numbers he constructs is called the Surreal numbers, and that’s a fair evocation of the way this book stretches my mind. I can generally understand the steps in the various derivations, but it takes some time and effort to develop the intuition to really understand the later constructions and to see where they are heading. Conway obviously had this intuition: after working on the ideas for some years, he wrote this book in just a week.