Wednesday, February 01, 2006

Èvariste Galois

Èvariste Galois was born on October 25, 1811 in La Reine, France. Galois was educated by his mother up until he was 12. There was some discussion about sending him to college when he was 10 but in the end, it was decided that he should stay at home. In 1815, his father was elected mayor of La Reine.

In 1823, enrolled in school. In 1824-1825, he received good grades, but in 1826, he was forced to repeat a grade because he failed rhetoric. In 1827, Galois enrolled in his first math class.

In 1828, just one year after his first math class, Galois took the entrance examination for the Ecole Polytechnique, the top university. He failed.

Despite the setback, Galois continued his studies of mathematics including work by Lagrange and Legendre. In April 0f 1829, he published a paper on continued fractions which included the proof that reduced quadratic equations are represented by purely periodic continued fractions.

Later that year, a scandal erupted when a vulgar poems were distributed and attributed to Galois's father. The result was more than Galois's father could stand and he committed suicide on July 2, 1829. Just a few weeks later, Galois made his second attempt at entrance to the Ecole Polytechnique. Again, he failed. In December of 1829, Galois entered Ecole Normale.

Galois submitted a paper on the theory of equations to be published. He learned that the same topic had just been covered in a posthumous article written by Niels Henrik Abel. Galois rewrote the article on the conditions whereby an equation is soluble by radicals and resubmitted it. The paper was ver well received and was submitted to Fourier who was secretary of the Paris Academy for the Grand Prize. Unfortunately, Fourier died in April of 1830 and Galois's paper got lost. In June, the Grand Prize of the Paris Academy was awarded to Niels Henrik Abel and Carl Jacobi.

In July of 1830, there was revolution in France. Charles X quickly departed and riots broke out. The head of the Ecole Normale locked the students in a the school to prevent them from joining in the unrest. In 1830, the director of the Ecole Normale wrote an editorial criticizing the students for their behavior. Galois wrote a response defending the students and criticizing the decision to do a student lock up. After writing this reply, Galois was expelled.

Galois next entered the Artillery of the National Guard. In December of 1830, King Louis Philippe disassembled the Artillery of the National Guard because he saw them as a threat to his power. 19 of the guards had been accused of conspiracy but were later released. On May 9, 1831, a great celebration was put together. Galois was there. At one point, Galois raised his glass to make a toast and held up a dagger at the same time. This was taken as a threat against the king. That same evening, Galois was arrested. He was held in prison until June 15 when he was acquitted.

On July 14, Galois was arrested for wearing the uniform of the Artillery of the National Guard which had been outlawed. While in prison, he found out that one of his math papers had been rejected and he attempted suicide. He was stopped by the other prisoners. Finally, on April 29, he was released.

By this time, he was in love with a young woman he had met. On May 30, he entered into a duel. It is believed that it was over the young woman. During the fight, he was severely wounded and died on May 31, 1832 at the age of 20.

Galois's papers were collected and sent out. Eventually, they made their way to Joseph Liouville who was deeply impressed. Liouville presented them to the French Academy in September 1843. These papers were published in 1846 and form the basis of what is today known as Galois Theory.

Today, Galois is considered to be one of the most original and talented mathematicians of all time and Galois Theory is one of the great gems of modern mathematics.


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