The Murder of Evariste Galois
On May 30, a farmer in France had been passing down a road and found a young man who had been shot in the stomach. He was still alive, so the farmer got the authorities involved, who took him to a hospital. Sadly, on May 31, at ten in the morning, he died at the Hôpital Cochin at the age of twenty.[1] His death is such a sad story of a brilliant, passionate young mathematician. Throughout his young life, he had a series of ups and downs, including three rejections from the university where he applied to attend, three convictions that landed him in prison, and the death of his father. Through these difficulties, he developed a drinking problem, which did not bode well with his temper. Shortly after his third stint in prison, he moved into a hostel.
While he was there, he fell in love with a woman who was close to his age. However, she had a fiancée. Regardless, he was in love with her and realized this love was dangerous. And so, he wrote a friend the night before he left the hostel, explaining that he was afraid that someone might kill him because of his connection with her. And he was not wrong. In the early morning of May 30, someone shot him in the stomach. It was a sad outcome for such a brilliant young man with much to contribute to mathematics. Additionally, the murderers remain unknown. His untimely death is a tragic loss to the world of mathematics and a stark reminder of the fragility of life. This is the story of Évariste Galois.
Évariste Galois was born in 1811 in Bourg-la-Reine, France, to Nicolas-Gabriel Galois and Adélaïde-Marie Demante. His father was a Republican, head of the Bourg-la-Reine liberal party, and village mayor. [2] His mother educated him at home until he was twelve years old. She was highly educated in Latin and classical literature and specifically taught him those subjects.[3] Mathematics was not considered necessary at this time in education, so he was not pressed to study it. At twelve, he entered the Lycée Louis-le-Grand, which today would be the equivalent of a high school. While at the Lycée, at the age of fourteen, he developed a fascination with mathematics and politics. By the time he was fifteen, he had read the original papers of Joseph-Louis Lagrange, including Reflections on the Algebraic Solutions of Equations and Lessons on the Calculus of Functions. Reflections inspired his later work on equation theory, and lessons on the calculus of functions were a work reserved primarily for professional mathematicians.
Galois was ready to attend the university by the time he was seventeen. He had his heart set on École Polytechnique, which is considered one of the most prestigious universities for mathematicians. In 1828, he attempted the entrance examination. Still, he failed because he was not prepared enough with the capacity to explain his work during the oral examinations.[4] As a result, instead of attending the Polytechnique, he entered the École Normale, considered a substandard institution. He applied at École Polytechnique again in 1829 and was rejected yet again. Within the same year, on July 2, his father committed suicide after his political opponents had framed him. These events devastated Evariste and filled him up with a sense of injustice, as he had been a firsthand victim of devastating political baseness.
At eighteen, he published his first paper on continued fractions. Additionally, he was developing theories on polynomial equations and submitted two papers to the Academy of Sciences for the Academy’s Grand Prize in Mathematics. Augustin-Louis Cauchy reviewed his work. The Academy did not accept Galois’s work for publication. There are two theories as to why his work was not accepted. Some historians consider that Cauchy had asked him to combine his two papers for submission, which Galois did not. Others believe Cauchy rejected his work based on Galois’s political views, which Cauchy opposed.
This time frame was when King Charles X had succeeded King Louis XIII in 1824. Six years later, the opposition Liberal Party became the majority. Struggling with this political opposition, King Charles staged a coup d’etat, instigating the French Revolution of 1830. Galois was a staunch Republican and wanted to participate in the revolution. However, the director at École Normale locked in the students, preventing them from leaving the grounds. Galois, considerably angry at this outcome, wrote a letter to The Gazette École with which he signed his entire name. Even though the gazette omitted his name from publication, the school gave him a notice of expulsion that would take place on January 4, 1831. Galois, instead, quit school and joined the republican artillery unit of the National Guard on December 31, 1830. While in the guard, he divided his time between mathematics and politics. However, the guard had to disband shortly after he joined as they were worried that they might destabilize the government.
While involved in the revolution, he continued with his mathematics. He tried to start teaching a private class in advanced algebra. Still, his efforts were minimal as he was more involved with political activism. Regardless, on January 17, 1831, Galois submitted his work on the theory of equations to Siméon Denis Poisson.
While Poisson reviewed his work, Galois continued his efforts in the revolution even though his guard had disbanded. During this time, nineteen officers of his unit were arrested and charged with conspiracy to overthrow the government. However, the officers were acquitted by April. As such, the military unit held a banquet in their honor. At the banquet, Galois stood and proposed a toast to Louis Philippe with a dagger over his cup. His fellow guardsmen cheered. As a result, he was arrested the next day and put in detention at Sainte-Pelagie prison for a month. Luckily, his attorney’s convincing argument influenced the jury to acquit him. However, a month later, on Bastille Day, Galois marched at the protest in his National Guard uniform, heavily armed with pistols, a loaded rifle, and a dagger. He was arrested and put in prison again. While in prison, he tried alcohol for the first time, which led to an attempted suicide. However, his inmates stopped him.
Concurrently, while this was going on in Galois’s life, Poisson, on July 4, 1831, declared Galois’s work “incomprehensible” and suggested that “the author published the whole of his work to form a definitive opinion.”[5] However, with all that Galois was doing for the revolution, he was unaware of this. Galois’s trial was set for October 23, 1831, when he was sentenced to six months in prison for illegally wearing a uniform. While in prison, he developed his mathematical theories and finally received Poisson’s letter. Galois was livid. As a result, he decided to stop publishing his papers through the Academy and instead publish them privately through his friend Auguste Chevalier. Regardless, he followed through on Poisson’s advice and developed his work until he was released from prison on April 29, 1832.[6]
Within the month of getting out, he stayed in a hostel, where he might have met the love interest, Stephanie-Felicie Poterin du Motel. She was the daughter of the physician at the hostel. At this point, things get extraordinarily chaotic for him. According to letters between Galois and his friends, she had confided in him about some troubles that she was in. His letters about this confidential information to his friends have confirmed this disclosure. The night before Galois died in a duel, he wrote to his cousin that he found himself “in the presence of a supposed uncle and a supposed fiancé, each of whom provoked the duel.” He continued, “I am the victim of an infamous coquette and her two dupes.”[7]
By Évariste Galois — Iyanaga, Shokichi, “ガロアの時代 ガロアの数学 第一部 時代篇” , Springer-Verlag Tokyo, 1999, Public Domain, https://commons.wikimedia.org/w/index.php?curid=7374476
This letter, among others, was written the night before his murder. He had stayed up all night writing these letters, including his mathematical testament in a letter to Auguste Chevalier outlining his mathematical theories. It was attached to three manuscripts, which likely included the work that he had been doing while in prison and the annotated copy of the manuscript that he submitted to the Academy.
After he died in the hospital, there were mild riots in the street. You see, Galois was a noted Republican and considered a dangerous political opponent by many. So, some theorists and historians believe that a female agent provocateur might have set up Galois. Novelist Alexandre Dumas named Pescheux d’Herbinville as his opponent in the duel, based on newspaper descriptions. But Dumas is the only one who named him as the opponent. However, this doesn’t make sense because d’Herbinville was one of the nineteen officers who was acquitted and celebrated at the banquet Galois attended. Additionally, a description of his opponent alludes to Galois’s cellmate, Earnest Duchatelet. But these are all speculations, and to this date, his killer has not been identified.
And so, on June 2, 1832, Evariste Galois was buried in a common grave at Montparnasse Cemetery.[8] In his hometown, Bourg-la-Reine, a cenotaph in Galois’s honor, sits next to the graves of his relatives. Galois’s friend, Chevalier, accused the academics at École Polytechnique of having killed Galois, believing that had they not rejected his work, he would have become a mathematician instead of devoting his life to the republican political activism for which he was killed.[9]
GALOIS’S WORK
His work had not been published for over ten years, possibly due to the timing of his death and the French Revolution. Galois’s manuscripts were finally published in France’s Journal of Pure and Applied Mathematics in the October-November 1846 issue. In this work, Galois’s profound analyses led to what is now called Galois Theory. This work shows that there is no quintic formula, meaning that fifth and higher-degree equations are not solvable by radicals. And although mathematicians like Niels Henrik Abel and Paolo Ruffini had published previous work on this theory, Galois had extensive deep research to show this proof.
I will go into some of the details of Galois’s findings, starting with the Galois theory. Galois Theory profoundly connects field theory and group theory, focusing on the solvability of polynomial equations. Galois demonstrated that a polynomial is solvable by radicals if and only if its Galois group is a solvable group, generalizing earlier work that showed the general quintic equation cannot be solved by radicals.
Speaking of groups, Galois introduced the concept of permutation groups to analyze the roots of polynomials. Galois showed that the symmetries of the roots of a polynomial, which is known as a Galois Group, can show if the polynomial can be solved by radicals. Another incredibly brilliant theory that he contributed to was field theory. Many historians and mathematicians believe that Galois had the most pioneering models on field theory. In his work, he developed field extensions by adding the roots of polynomials and analyzing their properties.
Galois also introduced resolvent polynomials. This was done to determine the Galois group of a given polynomial. So not only did he introduce Galois Groups, but he also introduced a way to solve them by providing resolvent polynomials.
Galois, through his work, established the foundations of abstract algebra. For some, abstract algebra is a challenging subject. I know I struggled extensively studying abstract algebra. But still, as somebody who prefers pure mathematics over applied mathematics, I fell in love with the subject. Galois’s work laid the foundation for group theory and the study of polynomial equations, which influenced the development of modern algebra. His ideas about the symmetry of roots of equations and the group structure associated with them became central to pure mathematics.
Lest we never forget his passion for justice. His involvement in the political turmoil of his time, as he fought for the ideals and justice for the people, highlights a remarkable intersection of intellectual brilliance and civic commitment. Despite his life being cut tragically short, it’s clear that his profound insights laid the groundwork for modern abstract algebra and revolutionized our understanding of polynomial equations. His pioneering work on Galois theory, field extensions, group theory, and more to this day inspire and influence physicists, chemists, computer scientists, and, of course, mathematicians. Undoubtedly, his legacy is a testament to how brilliant ideas can transcend time, fundamentally shape the landscape of mathematics, and unlock new realms of possibility.
Thank you for listening to math science history. And until next time, carpe diem!
[1] Bruno, Leonard C., and Lawrence W. Baker. Math and Mathematicians : The History of Math Discoveries around the World. Detroit, Mich.: U X L, 1999.
[2] Bruno, Leonard C., and Lawrence W. Baker. Math and Mathematicians : The History of Math Discoveries around the World. Detroit, Mich.: U X L, 1999.
[3] Rothman, Tony. “The Short Life of Evariste Galois.” Scientific American 246, no. 4 (1982): 136–49.
[4] Sarton, George. “Evariste Galois.” The Scientific Monthly 13, no. 4 (1921): 363–75.
[5] Taton, Rene. “Les relations d’Evariste Galois avec les mathématiciens de son temps.” Revue d’histoire des sciences et de leurs applications 1, no. 2 (1947): 114–30. https://doi.org/10.3406/rhs.1947.2607.
[6] Dupuy, P. “La Vie d’Évariste Galois.” Annales Scientifiques de l’École Normale Supérieure 13 (1896): 197–266. https://doi.org/10.24033/asens.427.
[7] Dupuy, P. “La Vie d’Évariste Galois.” Annales Scientifiques de l’École Normale Supérieure 13 (1896): 197–266. https://doi.org/10.24033/asens.427.
[8] Bruno, Leonard C., and Lawrence W. Baker. Math and Mathematicians : The History of Math Discoveries around the World. Detroit, Mich.: U X L, 1999.
[9] Lützen, J. “Chapter XIV: Galois Theory.” In Joseph Liouville 1809–1882: Master of Pure and Applied Mathematics, 559–80. Studies in the History of Mathematics and Physical Sciences. Springer New York, 2012. https://books.google.com/books?id=px_vBwAAQBAJ.