In 1828 at the age of 35, he published possibly his greatest work, entitled "An Essay on the Application of Mathematical Analysis to the Theories of Electridcity and Magnetism." In this publication, he made his first attempts to apply mathematical theory to electrical phenomena. Many of its subscribers were not able to really understand the contents, importance, or significance of this work. Two years later, one of the exceptions to this, Sir Edward Bromheadm, met with George and encouraged him to publish two other recognized 'memoirs', "Mathematical Investigations Concerning the Laws of Equilibrium of Fluids Analogous to the Electric Fluid" and "On the Determination of Exterior and Interior Attractions of Ellipsoids fo Variable Densities." He also published a paper entitled "Researches on the Vibrations of Pendulum in Fluid Media."

In 1833, at the age of 40, he turned down an invitation from Cambrige University and admitted himself to Caius College. He gained recognition and went on to publish papers on wave theory dealing with the hydrodynamics of wave motion and reflection and refraction of light and sound.