The Mathematical Brain is a 1999 book by lucid writer and psychologist Brian Butterworth. The key question to which the whole 400 pages ultimately relates is whether homo sapiens are inherently mathematical - Butterworth firmly believes that there is a module, or modules, of the brain that are dedicated to the concept of numeracy. For this, he presents some compelling evidence: the universality of counting systems, for example. There is certainly scope for debate on the existance of this "number module", but Butterworth never becomes over-confident in the truth of his own hypothesis.
There are regular and extensive digressions throughout, mostly of a mathematical nature: the history of zero, extracts from Le Guin's The Masters, and even a complete proof of Godel's incompleteness theorem. All these are eventually related back to the way human counting systems have evolved over the ages, but this book is not just a history of mathematics. Butterworth's real enquiry is why does this number module, if indeed we have one, find some numbers so much more difficult to work with.
He also explores why the human's inate ability to estimate probabilities is so inaccurate. Surely the existence of a number module would make handling such tasks straight-forward? Apparently not. Butterworth even looks at patients who, due to unfortunate brain injuries, lost the ability to count altogether. Nevertheless, these people still retained the ability to recall tables they had memorised, and even the techniques involved in multiplying numbers anew. The problem simply seemed to be a crushing inability to calculate. Is this evidence for a number module? Butterworth argues that it is. I would think of this like a computer: the hard-coded tables and the instructions for multiplying were still stored in the "hard disk", but the processor itself - the number module - was not able to follow the instructions correctly. Butterworth himself likens this "number blindless" to colour blindness - an inescapable biological restriction.
This book is certainly able to be followed by any layman. The technical appendices are not essential for appreciating the book, and all mathematical and psychology-related vocabulary is introduced gently and explained carefully. Butterworth is a wonderful writer, turning his complex and high-level insight into carefully reasoned arguments. The book is not for those who dislike distractions, because often the links to the main topic are tenuous to say the least and passages feel more like mathematical trivia demonstrations then exploration of the number module concept, but for those with an interest in mathematics and human perception thereof, I can only recommended it.