Abstract
Early in the twentieth century Einstein described the problem of the origin of the earth's magnetic field as being one of the five most important unsolved problems in physics. Since then, major advances have been made and it is now generally accepted that the main field originates from some form of dynamo process taking place in the earth's outer core. However, the 'dynamo problem' has not yet been solved and remains one of the most challenging mathematical problems ever formulated. Significant progress was made during the 1950s and 1960s with the nearly axisymmetric model developed by Braginsky and the mean-field concept instituted by Krause and Radler. Since then dynamo theorists have continued to search for ways to simplify the mathematics.
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