Where Mathematics Comes From

Brilliant wiki entry of the book Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being by George Lakoff and Rafael Nunez. A brief summary :

Mathematics arises from our bodies and brains, our everyday experiences, and the concerns of human societies and cultures. It is:

• The result of normal adult cognitive capacities, in particular the capacity for conceptual metaphor, and as such is a human universal. The ability to construct conceptual metaphors is neurologically based, and enables humans to reason about one domain using the language and concepts of another domain. Conceptual metaphor is both what enabled mathematics to grow out of everyday activities, and what enables mathematics to grow by a continual process of analogy and abstraction;
• Symbolic, thereby enormously facilitating precise calculation;
• Not transcendent, but the result of human evolution and culture, to which it owes its effectiveness. During experience of the world a connection to mathematical ideas is going on within the human mind;
• A system of human concepts making extraordinary use of the ordinary tools of human cognition;
• An open-ended creation of human beings, who remain responsible for maintaining and extending it;
• One of the greatest products of the collective human imagination, and a magnificent example of the beauty, richness, complexity, diversity, and importance of human ideas.