Mathematics under the microscope

Alexandre Borovik

"This book will be interesting--perhaps for different reasons--to school teachers of mathematics, to math majors at universities, to graduate students in mathematics and computer science, to research mathematicians and computer scientists, to philosophers and historians of mathematics, and to psychologists and neurophysiologists. The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the "small scale" structure of mathematical concepts and algorithms reflect the workings of the human brain? What are the "elementary particles" of mathematics that build up the mathematical universe? One of the principal points of the book is the essential vertical unity of mathematics,...