The Planning Committee for the Intercommission Committee on Theory (hereafter simply The Planning Committee) fully recognizes the importance of the IAG restructuring and the realization of the new structures. The need for such a new structure has become even more apparent for Section IV on Geodetic Theory and Methodology, since: (i) geodetic observing systems have advanced to such an extent that geodetic measurements are now of unprecedented high accuracy and quality, can readily cover a region of any scale up to tens of thousands of kilometres, consist of non-conventional data types, and can be provided continuously; and (ii) as a consequence, the status of Section IV within the IAG and its current missons and research areas has to be re-examined. In order to meet the challenges of the technologically advanced geodetic observing systems, and by recognizing that theory exists everywhere in all Sections of IAG, it is appropriate to restructure Section IV in such a way that it could interact more actively and/or directly with other IAG commissions to be established and would demonstrate theoretical challenges of geodesy to non-geodesists. Although the Planning Committee feels that it would have been more appropriate to turn Section IV into an Intercommission on Theory, this issue, unfortunately, would have become too late to be discussed any longer, since the name „Intercommission Committee on Theory" has been approved by the IAG EC and no change can be possible, at least, within the period of next four years.

The Planning Committee is fully aware that geodesy, as it stands now firmly as a subject of science, has been built up on the theoretical breakthroughs made over the past 350 years, from Newton, Gauss, Clairaut, Stokes,  Einstein, Bruns, Helmert, Vening Meinesz, Kaula, and others. It is also fully aware of the fact that theoretical breakthroughs in geodesy come only when geodesy can demonstrate itself as a great challenge and thus can attract the great intellects of the time. We should also note, however, that great theoretical breakthroughs in geodesy have almost always been achieved only by those who were themselves among the greatest scientists of the time in mathematics and physics, but seldomly by those who worked in geodesy as a profession. This partly explains why we believe that an Intercommission on Theory is more appropriate than an Intercommission Committee on Theory, which shall be further explained in possible structures of the Intercommission on Theory. (Should the Intercommission Committee on Theory and the Intercommission on Theory make no differences?) In particular, bear in mind that at present, with the technological revolution in space geodesy, geodesy has again exposed new theoretical problems that have never been encountered before, and is therefore full of challenges. The Planning Committee has thus good reasons to believe that significant theoretical advance can be expected in the near future. However, effort must be made to first demonstrate such challenges and secondly to attract young talent to geodesy. From these points of view, the Planning Committee would also like to suggest that in the process of IAG restructuring, IAG has to think more about the consequences of the new structures, in particular, for instance, geodesy as a profession of service; geodesy as a subject of science (not just the science of applications of mathematics and physics); and geodesy as a proper balance between professional service and science.

The mission of the proposed Intercommission on Theory is

• In recognization of the fact that geodesy has exposed new mathematical problems that have not been encountered or not properly or thoroughly solved in mathematics, the Intercommission Committee on Theory thus particularly encourages frontier research in the fields of mathematics as encountered in geodesy;
• Being aware that "rich soil" and "bright minds" are two of the prerequiresites for theoretical breakthroughs in geodesy, the Intercommission Committee on Theory should help the IAG in articulating the challenges of geodesy, in terms of mathematics and physics, with the aim to attract young talent to geodesy. It should also actively interact with scientists in other areas of science and engineering;
• Being aware of the fact that theory is contained within all the Commissions/Sections, the Intercommission Committee on Theory should be a channel of cooperation amongst the different commissions, on the ground of methodology; and finally,
• In recognization of the fact that geodesy has an important role to play in understanding the physics of the Earth, the Intercommission Committee on Theory thus particularly encourages closer research ties with the relevant areas of the Earth Sciences.

In order to make the Intercommission Committee on Theory functional, and to achieve its goals, the Planning Committee feels that the following structures are necessary:

• A Committee Panel;
• Some Working Groups and/or Joint Working Groups with commissions for Common but Unsolved Problems that urgently need attention from both practical and theoretical points of view; and
• Some Internal Entities for physical foundations in geodesy and for mathematical foundations in geodesy, mainly serve the interactions by bringing the awareness of geodesists to new physical and mathematical advancement that might be of importance in geodesy.

• To demonstrate in a most complete possible picture the theoretical challenges facing in geodesy;
• To establish a channel of comminications among different commissions, which would then be used to promote cooperation among the geodesists with major interests in the subjects of different commissions.

Some working groups and/or joint working groups with commissions should be established to meet theoretical challenges in geodesy, depending on whether frontier research can be expected and/or whether the solution to such challenges can contribute to science in general. Thus working groups and/or joint working groups with commissions are mainly designed to solve problems of interest of the IAG. At this moment, the Planning Committee would, for instance, identify the following problems for the establishment of working groups and/or joint working groups with commissions:

• Inverse Problem Theory, including Gravitational Modelling from Space Gravity Missions;
• Mathematical and Statistical Theory for Mixed-Integer Observational Models and for Models of (In)SAR-type Observations;
• Mathematical and Statistical Theory for Continuous Measurements;
• Statistical Models for Spatial Informatic Data;
• Global Optimization; and
• Integration of Geodetic and Geophysical Data to Extract and/or Confirm, Test Geophysical Phenomena/Processes.

The Internal Entities are designed to bring recent mathematical and physical developments to the attention of geodesists. The subjects of these Internal Entities should thus cover, for example,

• Newtonian mechanics, theory of relativity, quantum physics, satellite orbits, boundary value problems, fundamental aspects of reference frames in geometry and gravity space;
• Statistics, probability, optimization, numerical and approximation methods (e.g. wavelets);
• Standards and fundamental parameters for use in Geodesy, Geophysics, Astronomy, and reference Earth models,

but are not necessarily limited to these topics.

As a conclusion, the Planning Committee feels that the Intercommission Committee on Theory should be fully independent, and should be well represented in the EC, as any other commissions or services. Also it must be emphasized that the structures of the Intercommission Committee on Theory are rather preliminary and need to be further discussed substantially in the near future.

Veronique Dehant: veroniq@oma.be;

Peiliang Xu: pxu@rcep.dpri.kyoto-u.ac.jp