Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

May 30, 2023

Galois’ Fatal Duel

Posted by John Baez

On this day in 1832, Evariste Galois died in a duel. The night before, he summarized his ideas in a letter to his friend Auguste Chevalier. Hermann Weyl later wrote “This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind.”

That seems exaggerated, but within mathematics it might be true. On top of that, the backstory is really dramatic! I’d never really looked into it, until today. Let me summarize a bit from Wikipedia.

Galois lived during a time of political turmoil in France. In 1830, Charles X staged a coup d’état, touching off the July Revolution. While students at the Polytechnique were making history in the streets, Galois, at the École Normale, was locked in by the school’s director. Galois was incensed and wrote a blistering letter criticizing the director, which he submitted to the Gazette des Écoles, signing the letter with his full name. Although the Gazette’s editor omitted the signature for publication, Galois was expelled.

Galois joined the staunchly Republican artillery unit of the National Guard. He divided his time between math and politics. On 31 December 1830, his artillery unit was disbanded for fear that they might destabilize the government. 19 officers of this unit were arrested and charged with conspiracy to overthrow the government.

In April 1831 these officers were acquitted of all charges. On 9 May 1831, a banquet was held in their honor, with many famous people present, including Alexandre Dumas. The proceedings grew riotous. At some point, Galois stood and proposed a toast in which he said, “To Louis Philippe,” with a dagger above his cup. The Republicans at the banquet interpreted Galois’s toast as a threat against the king’s life and cheered.

The day after that wild banquet, Galois was arrested. He was imprisoned until 15 June 1831, when he had his trial. The jury acquitted him that same day.

All this time, Galois had also been doing math! Earlier, the famous mathematician Poisson had asked Galois to submit a paper to the Academy, which he did on 17 January 1831. Unfortunately, around 4 July 1831, Poisson wrote a reply declaring Galois’s work “incomprehensible” and saying his “argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor”. But Poisson ended on a positive note: “We would then suggest that the author should publish the whole of his work in order to form a definitive opinion.”

Galois did not immediately receive this letter. He joined a protest on Bastille Day, 14 July 1831, wearing the uniform of the disbanded artillery and heavily armed with several pistols, a loaded rifle, and a dagger. He was again arrested. During his stay in prison, Galois at one point drank alcohol for the first time at the goading of his fellow inmates. One of these inmates recorded in a letter what Galois said while drunk:

“And I tell you, I will die in a duel on the occasion of some coquette de bas étage. Why? Because she will invite me to avenge her honor which another has compromised. Do you know what I lack, my friend? I can confide it only to you: it is someone whom I can love and love only in spirit. I’ve lost my father and no one has ever replaced him, do you hear me…?”

In his drunken delirium Galois attempted suicide, and would have succeeded if his fellow inmates hadn’t forcibly stopped him.

Remember Poisson’s letter? While Poisson wrote it before Galois’s arrest, it took until October for this letter to reach Galois in prison. When he read it, Galois reacted violently. He decided to give up trying to publish papers through the Academy and instead publish them privately through his friend Auguste Chevalier.

Later he was released from prison. But then he was sentenced to six more months in prison for illegally wearing a uniform. This time he continued to develop his mathematical ideas and organize his papers. He was released on 29 April 1832.

Galois’s fatal duel took place on 30 May. The true motives behind the duel are obscure. There has been much speculation about them. What is known is that, five days before his death, he wrote a letter to Chevalier which clearly alludes to a broken love affair.

Some archival investigation on the original letters suggests that the woman of romantic interest was Stéphanie-Félicie Poterin du Motel, the daughter of the physician at the hostel where Galois stayed during the last months of his life.

Whom did Galois fight in his fatal duel? Alexandre Dumas named Pescheux d’Herbinville, who was actually one of the 19 artillery officers whose acquittal was celebrated at the banquet that led to Galois’s first arrest. On the other hand, newspaper clippings from only a few days after the duel may suggest that Galois’ opponent was Ernest Duchatelet, who was imprisoned with Galois on the same charges. The truth seems to be lost to history.

Whatever the reasons behind his fatal duel, Galois was so convinced of his impending death that he stayed up all night writing letters to his Republican friends and composing what would become his mathematical testament: his famous letter to Auguste Chevalier outlining his ideas, and three attached papers. But the legend of Galois pouring his mathematical thoughts onto paper the night before he died seems to have been exaggerated. The papers were already mostly written.

Early in the morning of 30 May 1832, Galois was shot in the abdomen. He was abandoned by his opponents and his own seconds, and found by a passing farmer. He died the following morning at ten o’clock in the Hôpital Cochin after refusing the offices of a priest. Evariste Galois’s younger brother Alfred was present at his death. His last words to Alfred were:

“Ne pleure pas, Alfred! J’ai besoin de tout mon courage pour mourir à vingt ans!”

(Don’t weep, Alfred! I need all my courage to die at twenty!)

On 2 June, Galois was buried in a common grave in the Montparnasse Cemetery. Its exact location is apparently unknown.

Eleven years later, in 1843, the famous mathematician Liouville reviewed one of Galois’ papers and declared it sound. Talk about slow referee’s reports! It was finally published in 1846.

In this paper, Galois showed that there is no general formula for solving a polynomial equation of degree 5 or more using only familiar functions like roots. But the really important thing is the method he used to show this: group theory, and the application of group theory now called Galois theory.

And for something amazing in his actual letter, read this:

• Bertram Kostant, The graph of the truncated icosahedron and the last letter of Galois, Notices of the AMS 42 (September 1995), 959–968.

Posted at May 30, 2023 5:16 AM UTC

TrackBack URL for this Entry:

10 Comments & 0 Trackbacks

Re: Galois’ Fatal Duel

Beautiful and inspiring life story.

There’s a biography by Paul Dupuy.

I wish there were some big budget films on his life. IMDB suggests that there are two titles on his life: The 1965 version and the 2010 version, though I haven’t been able to find them online, the first one seems to be there on YouTube. There’s also this short documentary by Diego Cenetiempo.

Posted by: Parth Patel on May 30, 2023 1:54 PM | Permalink | Reply to this

Re: Galois’ Fatal Duel

Beautiful and inspiring? Suicidal, expecting all along that he’d die in a duel, and then getting shot and left to die in a field?

To me it’s a miserable story. Just think of how math might be different if Galois hadn’t died at 20.

But it’s certainly fascinating, and it would make an exciting movie if done right.

Posted by: John Baez on May 30, 2023 4:13 PM | Permalink | Reply to this

Re: Galois’ Fatal Duel

While the history of 19th century mathematics might have been quite different if Galois had lived, I think it’s unlikely that mathematics itself in the 21st century would be significantly different.

I can’t find it now but I once read a quote by Richard Feynman (perhaps ironically, given how much cult-of-genius attaches itself to him) saying that he always found it strange when people would say things like “Imagine all the things we wouldn’t know about physics if Einstein had never lived.” Feynman said that actually, the really important ideas tend to be discovered when they are needed and once the necessary background is in place, which is why near-simultaneous independent discoveries happen as often as they do. If Einstein had never been born, special and general relativity would have come along not much later than they actually did, just associated with someone else’s name, and people would be wondering about all the things we supposedly wouldn’t know if that person hadn’t been born. The delay in discovering Galois theory might have been longer if Galois hadn’t done it, but I imagine that well before the 20th century all its central ideas would have been in place, just with a different name.

Posted by: Mark Meckes on May 30, 2023 6:05 PM | Permalink | Reply to this

Re: Galois’ Fatal Duel

Here it is:

Scientists still ask the what if questions. What if Edison had not invented the electric light — how much longer would it have taken? What if Heisenberg had not invented the S matrix? What if Fleming had not discovered penicillin? Or (the king of such questions) what if Einstein had not invented general relativity? “I always find questions like that … odd,” Feynman wrote to a correspondent who posed one. Science tends to be created as it is needed. “We are not that much smarter than each other,” he said.

From James Gleick, Genius: The Life and Science of Richard Feynman (1992)

Posted by: Mark Meckes on May 30, 2023 7:27 PM | Permalink | Reply to this

Re: Galois’ Fatal Duel

Mark wrote:

While the history of 19th century mathematics might have been quite different if Galois had lived, I think it’s unlikely that mathematics itself in the 21st century would be significantly different.

If “time heals all wounds” in this way, then you could argue that it doesn’t really matter what any one of us does in the long term, at least as far as math goes. But personally I tend to think that if Galois had lived longer, or even gotten his work understood sooner, 21st century math would be a bit “ahead” of where it is now.

Similarly, without Einstein someone would have come up with photons, but he sped it up.

(The photon was the elementary particle that took the longest time for people to accept. Einstein came up with “quanta of light” in 1905, but only by 1926 did people believe in them enough for Lewis to invent the term “photon”. Pais argues that special and general relativity were motivated by trying to make classical physics consistent with Maxwell’s equations, while light quanta were Einstein’s truly revolutionary idea — an idea that helped pull down the whole house of classical mechanics, determinism, etc.)

By the way, I mainly think Galois’ story is a miserable one because of what happened to him, not what happened to mathematics. I just digressed into wondering how math might be different if he weren’t a miserable kid whose father committed suicide, in the midst of a torn nation.

Posted by: John Baez on May 30, 2023 9:14 PM | Permalink | Reply to this

Re: Galois’ Fatal Duel

If “time heals all wounds” in this way, then you could argue that it doesn’t really matter what any one of us does in the long term, at least as far as math goes.

Well, sure. As John Maynard Keynes pointed out, “In the long run we are all dead.” But Keynes was not being as fatalistic that quote sounds when taken out of context; he was actually arguing for paying attention to what happens in the short- and medium-term. I agree that individuals like Galois and Einstein introduced some revolutionary ideas that probably would have taken longer to be discovered and accepted without their contributions (and also that the rest of us can make meaningful, if more modest, contributions). But I would say that we’re still in the medium-term for Galois’s and Einstein’s impacts, relative to the history of science.

What I find more compelling here is that, if you think that math and science would look appreciably different without the contributions of a few exceptional individuals more than a hundred years ago, it is absurd to think that every individual who could have made such contributions actually had the opportunity to do so. Given what a tiny fraction of humanity has access to higher education, how many other potential Galoises and Einsteins have lived and died in obscurity?

So when I hear someone say something like “Just think of how math might be different if Galois hadn’t died at 20,” I can’t help wondering instead how math might be different if so many children whose names we’ll never know had the nutrition, education, and encouragement to make as big a mark as they were capable of.

Posted by: Mark Meckes on June 1, 2023 2:10 PM | Permalink | Reply to this

Re: Galois’ Fatal Duel

Just think of how math might be different if Galois hadn’t died at 20.

I’ve always wondered the same about William Clifford, who died relatively young at age 33. I suspect that if he lived longer, physicists would be primarily using Clifford algebras for physics and differential geometry instead of Gibbs’s vector algebra or tensors.

Posted by: Madeleine Birchfield on June 6, 2023 12:56 AM | Permalink | Reply to this

Re: Galois’ Fatal Duel

My line “Beautiful and Inspiring” didn’t come out right. It’s this fascinating internal story (and not the external social/academic one) that I tried to allude to, I apologize for not doing it explicitly.

(ofc, I agree that this is a miserable social story of a young mathematician who could have gone ahead of time if lived long enough, and therefore miserable mathematics history. but, if we see from the perspective of Galois himself, internally, this is a an Inspiring story. because, he could have just gone missing or whatever and do all the mathematics he wanted to. compare, for example, Grothendieck (I consider his story to be miserable too, but only socially/academically, and as a history of mathematics. Imagine how much more could he have developed mathematics had he lived more within the academic environment. but, internally his story is “Beautiful and Inspiring” too). and, this is a beautiful story, because, assuming the romantic legend is true, the phrase “I can love and love only in spirit” could only be of a beautiful/true lover.)

Posted by: Parth Patel on May 31, 2023 10:00 AM | Permalink | Reply to this

Thanks for posting this🙏

It’s heartbreaking stuff, but we at least honour his memory by these retellings.

Posted by: Bertie on May 31, 2023 7:49 PM | Permalink | Reply to this

Re: Galois’ Fatal Duel

William Clifford, 50 years before Einstein, and after reading Riemanns lectures on curvature, declared in a note titled, The Space Theory of Matter, to the Proceedongs of the Cambridge Philosophical Society that all motion of matter is due to curvature. This anticipates Einstein’s theory of gravity. In fact, one can argue that he out-Einsteined Einstein since he argues all motion is due to curvature. Then, the only two forces known were the electromagnetic, recently unified by Maxwell, and gravity. Thus Clifford was arguing that both gravity and electromagnetism was due to curvature. This is prescient since in Einstein’s gravitational theory, gravity is due to curvature of spacetime and also classical electromagnetism can be interpreted as the curvature of a vector bundle. And if one keeps to his view, then one should argue that the weak and strong force - both unknown to him - should also be due to curvature. This also proves to be true in the classical picture as they are also due to curvature of vector bundles.

I’d also argue that Clifford had a misleading title. He wasn’t theorising about the nature of matter. But about its motion. A more accurate title would be, The Space Theory of Motion.

I want to add that although Faraday is usually credited with the insight that electromagnetism should be thought of as a field theory which then prompted Einstein to rewrite gravity as a field theory, he was anticipated in this by Aristotle.

Aristotle gets short shrift today, especially by modern physicists, but he was an astute thinker and I think the modern caricature of Aristotles philosophy is assinine. There are very good reasons why Aristotle was admired for a very long time in the Christendom as well as the Islamic civilisation - he represented the pinnacle of Greek scientific thought. Physics did not begin with Galileo, as Einstein and many others argue. He just moved it on.

Aristotle stated that motion occurs only when a force is applied and then only by contact. Thus he did not believe in force at a distance. This is how Newton concieved his gravity theory. And although he concieved it this way, he did not believe that this was correct. And in this, he was correct as later developments showed. He stated that force should occur by contact. And this is what Faraday also dreamed up with his lines of forces and which Maxwell put into mathematics. But the original insight was due to Aristotle.

Today, the only force that doesn’t appear to admit that conception, is the force that collapses a quantum wave. It appears to occur instantaneously. In an experiment by Garisi et al, reported in Nature, they set a lower bound of 1550c. However, if New Scientist is to be believed, in an article written by Padavic-Callaghan in 2022, it isn’t instantaneous with it taking between 0.1 billionth to 0.1 sextillonth of a second. So perhaps Aristotle is correct here too.

One other point. Richard Laming, around 1850 conjectured that electrons occupied shells around a central nucleus. He even suggested that chemical reactions were due to sharing of electrons. This is well before Rutherford’s experiments prompted a similar model, and in which he had also been anticipated by Nagaoka in 1904, the same year that Thompson had suggested the plum pudding model and which he rejected.

One last thought. Modern geometry is in the process of unchaining itself from Descartes coordinates. Since geometry was originally concieved by Euclid without coordinates, one can argue that we are returning to Euclid. So again, new wine in old bottles.

Posted by: Mozibur Rahman Ullah on June 30, 2023 4:45 AM | Permalink | Reply to this

Post a New Comment