Character of mathematics
Since at least the early 1900s several major schools of thought have existed:
• Formalism (e.g. David Hilbert): Mathematics studies formal rules that have no intrinsic meaning, but are relevant because of their applications or history.
• Platonism (e.g. Kurt Gödel): Mathematics involves trying to discover the properties of a world of ideal mathematical forms, of which we in effect perceive only shadows.
• Intuitionism (e.g. Luitzen Brouwer): Mathematics is a precise way of handling ideas that are intuitive to the human mind.
The results in this book establish a new point of view somewhere between all of these.