For more than 200 years the origin of Earth's magnetic field was attributed to permanent magnetization. Even today no single argument (e.g., that Earth's deep interior is too hot to sustain permanent magnetization) conclusively rules out the permanent magnetization hypothesis. Nevertheless, when all the evidence is considered, this hypothesis can be safely discarded and replaced with an electric current (dynamo) hypothesis. Surprisingly, this can be done even though there is no adequate dynamo model for Earth. The development of geodynamo models began with the disk dynamo of Larmor in 1919 and expanded to include many classes of models, such as αω, α2, α2ω, Taylor state, and Model Z dynamos. Because of mathematical difficulties associated with solving the many coupled partial differential equations of dynamo theroy, numerous simplifying assumptions are made.

The majority of numerical dynamo models assume a three-dimensional velocity field in an inviscid fluid and use mean field theory to solve for axisymmetric magnetic fields. There is also an increasing number of intermediate and strong field models emerging, in which feedback from the magnetic field to the velocity field is permitted. Nevertheless, these models still require several simplifying assumptions and there are many additional problems. For instance, many core parameters are difficult to estimate; there is debate on whether the top of the core is stably stratified and on the effects such stratification might have; what effects the presence of an inner core have; and whether the coupling across the core-mantle boundary significantly affects the geodynamo. Perhaps it is not surprising that dynamo theoreticians, faced with large difficulties in mathematics and many uncertainties in physics, essentially choose to ignore input from fields such as paleomagnetism. However, it is precisely because of such difficulties that paleomagnetism can provide valuable constraints to narrow the range of viable dynamo models. For example, paleomagnetism ultimately should provide constraints on the velocity and magnetic field symmetries of dynamos; determine whether the geodynamo is in the weak, intermediate, or strong field regime; determine if there is a fundamental difference in dynamo processes during superchrons when reversals of the magnetic field essentially cease; and provide valuable information on the growth of the inner core and its possible stabilizing effects on geodynamo processes. ¿ American Geophysical Union 1995