## Leonhard Euler

## Évariste Galois

Ahmet Eren Doğan

Évariste Galois (1811-1832) was a French mathematician born in Bourg-la-Reine, a suburb of Paris. His parents were well-educated in religion, philosophy, and literature. His father, Nicholas Gabriel Galois, was an important citizen of Bourg-la-Reine. He was the head of the liberal party and became the mayor of the village in 1815.

Galois was educated at home by his mother until he turned 12. He was taught religion, greek and latin. In 1823, he enrolled at Louis-le-Grand, a prestigious high school in Paris, where his interest in mathematics started.

At the beginning of his high school experience, he was able to receive good school reports and several awards. After he took his first mathematics class in 1827, his serious interest in mathematics started. He started putting less effort into his schoolwork and spent most of his time doing maths. He read the works of Adrien-Marie Legendre and Joseph-Louis Lagrange. Although these works were written for mathematicians, Galois was able to read them very easily.

Galois published his first paper on continued fractions in 1829. After this moment, a sequence of tragic events was waiting for him. In the same year, he sent two papers to the French Academy of Sciences which were going to be read by Augistin-Louis Cauchy. Unfortunately, Cauchy lost Galois’s papers. Galois attempted twice to enter École Polytechnique, but he failed in both examinations. His examiners mentioned that he had a great mathematical ability but he was unable to express his ideas properly. After these failed attempts, he enrolled in École Normale Superieure. Again in the same year, Galois’s father committed suicide due to a political dispute with a priest.

In 1830, Galois published three short articles and he rewrote the paper that was lost by Cauchy. He sent his paper to the academy again. This time, Jean-Baptiste-Joseph Fourier took his paper to read and he died a few weeks later. The paper was lost again and it was never found.

After the July Revolution, Charles X was sent into exile. However, another king, Louis-Philippe, ascended the throne which strongly disturbed the republicans. Galois wrote an article where he expressed his republican views. This courageous act of Galois caused him to get expelled from École Normale Superieure. Nevertheless, he didn’t stop getting involved in political activities. In a dinner with around 200 republicans, he raised his glass, with a dagger in his other hand, and exclaimed “To Louis-Philippe!”. He was arrested right after the dinner but he was acquitted soon. On the 14th of July, Galois was wearing the uniform of the Artillery of National Guard and carrying loaded guns and dagger. He was arrested again and sent into prison where he stayed for 6 months. During his time in prison, he kept developing his mathematical ideas. One day in the prison, he said that he was going to die in a duel and he mentioned that nobody has replaced his father and he had no one to love in heart.

While in prison, Galois fell in love with Stephanie-Felice du Motel and they started writing letters to each other. After getting released from the prison, he fought a duel on 30 May 1832. The reason behind the duel is unclear but many sources agree that the duel was about Stephanie. In his last night, Galois wrote a scientific last testament and sent it to one of his friends. Galois got wounded in the duel and died in hospital on 31 May. His last words to his brother were “Do not cry Alfred, I need all my courage to die at twenty.” His work was not understood by others during his lifetime but after decades, his papers were published by Liouville. The theory Galois developed in his papers is today known as Galois Theory.

Galois found the necessary conditions for algebraic equations to be solvable by radicals by using the concept of a group. He said that the solvability by radicals was possible when the group of automorphisms was solvable, meaning that solvability by radicals is possible when the group can be broken down into smaller parts that are easily comprehensible. Hence he understood that solving equations with 5 or higher degrees required a different approach than quadratic, cubic and quartic equations.

References

Évariste Galois. Maths History. (n.d.). Retrieved April 20, 2023, from https://mathshistory.st-andrews.ac.uk/Biographies/Galois/

Kaplansky, Irving and Barrow-Green, June. "Évariste Galois". Encyclopedia Britannica, 21 Oct. 2022, https://www.britannica.com/biography/Evariste-Galois. Accessed 22 April 2023.

Wikipedia contributors. "Évariste Galois." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 2 Apr. 2023. Web. 20 Apr. 2023.