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Youth

Thomson attended the Royal Belfast Academical Institution, where his father was a professor in the university department. In 1834, aged 10, he began studying at the University of Glasgow, not out of any precociousness; the university provided many of the facilities of an elementary school for able pupils, and this was a typical starting age. In school, he showed a keen interest in the classics along with his natural interest in the sciences. At age 12 he won a prize for translating Lucian of Samosata's Dialogues of the Gods from Ancient Greek to English.

In the academic year 1839/1840, Thomson won the class prize in astronomy for his "Essay on the figure of the Earth" which showed an early facility for mathematical analysis and creativity. His physics tutor at this time was his namesake, David Thomson. Throughout his life, he would work on the problems raised in the essay as a coping strategy during times of personal stress. On the title page of this essay Thomson wrote the following lines from Alexander Pope 's " An Essay on Man ". These lines inspired Thomson to understand the natural world using the power and method of science:

Go, wondrous creature! mount where Science guides; Go measure earth, weigh air, and state the tides; Instruct the planets in what orbs to run, Correct old Time, and regulate the sun;

Thomson became intrigued with Joseph Fourier's Théorie analytique de la chaleur (The Analytical Theory of Heat) and committed himself to study the "continental" mathematics resisted by a British establishment still working in the shadow of Sir Isaac Newton. Unsurprisingly, Fourier's work had been attacked by domestic mathematicians, Philip Kelland authoring a critical book. The book motivated Thomson to write his first published scientific paper under the pseudonym P.Q.R., defending Fourier, which was submitted to The Cambridge Mathematical Journal by his father. A second P.Q.R. paper followed almost immediately.

While on holiday with his family in Lamlash in 1841, he wrote a third, more substantial P.Q.R. paper On the uniform motion of heat in homogeneous solid bodies, and its connection with the mathematical theory of electricity. In the paper he made remarkable connections between the mathematical theories of thermal conduction and electrostatics, an analogy that James Clerk Maxwell was ultimately to describe as one of the most valuable science-forming ideas.