Nature is not only stable and static but also unstable and dynamical‑ this has been shown by physics during the last 40 years. Today, instabilities are regarded as productive and creative sources of change, pattern formation, and growth. They constitute the nomological nucleus of self-organization, chaos and complexity, time's arrow and chance.

This change in understanding nature has also modified sciences. Physics has traditionally limited its scope to stability. Currently, it is expanding and renewing itself: alate-modern physicsis emerging, and discloses rich interdisciplinary perspectives for the future of mathematical sciences.