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George Green had four terms (about 18 months) of formal schooling between the ages of eight and nine, according to MacTutor. For over 20 years, he worked in a dusty brick windmill in Sneinton, Nottingham. Yet in 1828, this self-taught miller printed a 72-page essay that would become foundational in mathematical physics, introducing concepts we now call Green's theorem and the potential function, as detailed in his Wikipedia biography).
Who was George Green the mathematician?
Born in 1793, Green spent his early life managing the corn mill built by his father. The work was demanding and nearly constant, requiring him to adjust heavy sails to the wind speed, manage the grain supply to prevent fires, and repair ton-weight millstones.
Despite his lack of formal education, he found his way to the University of Cambridge much later in life. Green enrolled at Gonville and Caius College in 1833 at the age of 40. He graduated in 1837 as the fourth Wrangler—the fourth highest-scoring student in his class—and died a few years later in 1841 at the age of 47, as noted in his MacTutor biography.
How did a miller learn advanced mathematics?
Green was entirely self-taught in higher mathematics. At age 30, he joined the Nottingham Subscription Library (Wikipedia)), which gave him access to the *Philosophical Transactions of the Royal Society* and the latest mathematical knowledge from French analysts. He studied these texts at the top of his windmill between his shifts.
Today, you do not have to tackle advanced university mathematics completely alone. If you are learning new material and need to see how the ideas fit together, the Fermi Concept Library maps out every concept in mathematics and physics, each with its own lesson and its place in the wider subject.
What did George Green introduce in his 1828 essay?
In 1828, Green published his 72-page essay, *An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism*. He paid for the printing himself and sold it to just 51 subscribers, mostly local doctors and clergymen who likely did not understand the mathematics inside (Wikipedia)).
The essay bridged physical phenomena and mathematical analysis by introducing several vital concepts:
The potential function: A mathematical tool that assigns a single number to every point in space to describe a force field, such as gravity or electricity. Instead of tracking complex directional forces, physicists can look at how this single number changes from one spot to another.
Green's theorem: A method to translate information about what is happening along the boundary of a flat shape into information about what is happening inside it.
Green's functions: A technique for solving complex equations by breaking a large problem down into a system's response to a single, tiny point of input.
How was the 1828 essay rediscovered?
Green's essay was nearly lost to history. It was only in 1845, four years after Green's death, that a 21-year-old mathematician named William Thomson (who would later become Lord Kelvin) rediscovered the work, according to MacTutor.
Thomson had seen a footnote referencing Green's essay and managed to obtain three copies from his former tutor. He took the essay to Paris and shared it with prominent French mathematicians, establishing Green's legacy as a founder of the Cambridge school of mathematical physics.
How can you learn difficult subjects on your own?
Green's life offers a blueprint for independent study. If you are tackling a complex subject outside of a formal classroom, try this framework:
Find primary sources: Green joined a subscription library to read actual academic papers, rather than relying on popular summaries. Go directly to the best textbooks and journals available.
Look for unifying ideas: Green simplified the mathematics of fields by introducing the single "potential" function. When facing a dense topic, try to isolate the core principle that connects the details.
Persist in isolation: It can be frustrating to learn without peers. Accept that the process will take time and require deep focus.
Write it down: Green published his essay even though his local subscribers could not understand it. Writing out your findings forces you to clarify your reasoning.
