In January 1827, after a few weeks in the eleventh grade, then known as the rhetoric class, Galois was sent back to the tenth grade. That year, a new Preparatory Mathematics option had just been introduced.
Even then, the place of mathematics in education was a matter of debate. After being promoted under Napoleon and during the French Revolution, the subject was now taught only as an option. It was in this setting that Évariste Galois, despite returning to the tenth grade, attended Hyppolite Vernier’s classes. The young man became so engrossed in the subject that he neglected everything else. In 1827–1828, during his year in the rhetoric class, the pattern continued: "He is consumed by a passion for mathematics." Galois sat the entrance examination for the École polytechnique and failed on his first attempt. He then continued his studies at the lycée Louis-Le-Grand in Louis-Paul-Émile Richard’s advanced mathematics class.
The young mathematician was already interested in solving polynomial equations. But he was also still a student, and several of his papers have survived.
Some thoughts on logarithms
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As they are today, logarithms were part of the required syllabus and appear several times in Galois’s papers. The story goes that during his second attempt at the École polytechnique entrance examination, Galois was questioned on this topic (common logarithms) and considered the question too easy; his temperament did the rest to antagonize the examiners. Logarithms also appear in a notebook found with his papers, containing some of his earliest mathematical work. Let's look at what Galois wrote on the subject and how today’s final-year high-school students can make sense of it.
