QO provides a radically new perspective on mathematics. In QO, mathematics develops like anything else, as a set of interrelated quantum systems. This leads to profound insights, none of which are new, but few of which are generally accepted.

- Mathematical truths are contingent, rather than eternal. Some mathematical statements are neither true or false, but have the truth value 'undefined', at least for now.
- Only finite mathematics is sound.
- Only mathematics which can be constructed is sound. Concepts that refer to themselves cannot be constructed and are therefore unsound. 'Reductio ad absurdum' arguments prove nothing.
- Mathematics which manifests itself in the universe can be trusted, because the universe cannot contradict itself.

Start your examination of QO mathematics by looking at:

- The mathematical phenomena which a theory of everything should be expected to account for
- The QO view on mathematics
- The influence of mathematics on our understanding of the nature of natural order