An essential objective of mathematics is to create settings and concepts to better understand our world. Mathematics is present in everyday life. Even more, almost all sciences undergo a process of “mathematization” due to increasing technological progress.

What is exactly that enables the mathematicians to provide the transfer from concrete measurements and observables to abstract mathematical formalisms and models? Some programmatic answers should be given at this early stage essentially inspired by the contributions in Freeden (2009, 2015), Freeden et al. (2019):

Part I: T hermal Strucure of Deep Earth 1

1 Melting of Fe Alloys and the Thermal Structure of the Core

2 Temperature of the Lower Mantle and Core Based on Ab Initio Mineral Physics Data

3 Heat Transfer in the Core and Mantle

4 Thermal State and Evolution of the Earth Core and Deep Mantle

Part II: S tructures, Anisotropy, and Plasticity of Deep Earth Materials 

5 Crystal Structures of Core Materials

It is now 25 years since, along with Francis Hein as a co-author, we published Deep Marine Environments: Clastic Sedimentation and Tectonics with Unwin-Hyman (Pickering et al. 1989). During this time, there have been enormous advances in our understanding of modern and ancient deep-water environments, the physical processes that operate and the resulting deposits. Technology has allowed a much greater interrogation of deep-water environments, for example through improvements in the use of side-scan sonar, the acquisition and processing of seismic-reflection data, together with considerable advances in both industrial and academic deep-water drilling. Experimental, theoretical and observational studies have led to a significantly improved understanding of the fluid dynamics and depositional processes in deep-water settings.

Torsten Bickert Zentrum fu¨r Marine Umweltwissenschaften, Universita¨t Bremen, Germany
Steven N. Carey Graduate School of Oceanography, University of Rhode Island, Narragansett,
Rhode Island, USA Jean-Claude Fauge`res Universite´ de Bordeaux, UMR CNRS 5805 EPOC, Talence Cedex, France
Rudiger Henrich Department of Sedimentology and Paleoceanography, Faculty of Geosciences, University of Bremen, klagenfurter Straße, Bremen, and Fachbereich Geowissenschaften, Universita¨t Bremen, Germany
Reinhard Hesse Earth and Planetary Sciences, McGill University, Montreal, Quebec, Canada