"Thomson was a mathematical prodigy. At age 16, he mastered ’s ' and wrote and published a defense of it. Fourier’s theory allowed one to determine the distribution of heat in a body on the sole assumption that heat flow is proportional to temperature gradient. The approach was macroscopic, geometrical, and nonhypothetical, and Thomson took to it easily. During his undergraduate years at , he traveled to Paris and met the mathematical savants—in particular, mathematician Joseph Liouville and experimental physicist , who both considered Michael Faraday’s curved lines of force outré. At Liouville’s urging, Thomson produced for the ' a demonstration that the lines of force, whether electric or magnetic, followed from inverse square laws. The relevant mathematics was a near cousin to that for heat flow, but the insight was new and would be seminal in the thinking that led James Clerk Maxwell to electromagnetic field theory."