Because structural geology combines field observations of deformed rock with the physics of rock deformation, structural geologists must understand concepts developed by the great natural philosophers and physicists of the last few centuries, including Descartes, Hooke, Newton, Euler, Lagrange, Fourier, Gauss, Navier, Cauchy, Stokes, and Kelvin.
These mathematicians and scientists helped to develop the disciplines of calculus, differential geometry, and continuum mechanics into thoroughly tested and immediately useful tools for the description and analysis of deformed materials. We put these tools to work to solve important problems in structural geology.
The word "discipline" used above in describing calculus, differential geometry, and continuum mechanics has other meanings for students of structural geology. One kind of discipline is required to bring precise measurements back from a rigorous field campaign and another kind of discipline is required to apply the fundamental mathematical and mechanical concepts to models of geologic structures that are essential to understand Earth's tectonic history.
The motivation for this course of study is partly aesthetic (we behold the beauty of the nature as expressed in earth structures) and partly intellectual (we comprehend the constructs of the human mind as manifest in mathematics and continuum mechanics).