ABSTRACT
Mathematics is uniquely, beautifully, incredibly precise. The human brains that we use for math, on the other hand, are anything but perfect. How could this be true? Is mathematics really eternal, universal truths we discover? Or could it simply be a human invention? Introducing a neuroscience-inspired approach to this puzzle, this chapter addresses formal logical thinking, the phenomenon to which, people like to believe, math owes its special status. Formal logic is not perfect, and it cannot be the only tool of math or any other genuine intellectual creativity. Philosophy, psychology, linguistics, epistemology, and the history of science all seem to support that idea; most importantly, strict mathematical logic itself agrees, as Gödel’s incompleteness theorem tells us. Real breakthroughs in science demand both conscious logical thinking and subconscious, emotional, intuitive processes (for example, the “Eureka moment”). What’s more, emotion precedes cognition and paves the way for formal logical thought.
This chapter also refers to George Lakoff’s theory about the nature of human thought. According to Lakoff, people divide things into categories, and think about them not in a logical, but rather an analogical way, in accordance with superficial similarities. This categorization is the foundation of all our thinking, from the perception of concrete objects up to the very highest mathematical concepts; clearly, however, it does not have much to do with pure reason.
