Évariste Galois (1811–1832) is a romantic hero who, like all romantic heroes, died in a duel. Those were different times, and people, especially young people, were subjected to customs that, often to mask arrogance and bullying, were called “rules of chivalry”. He was completely enthralled by mathematics, to which he devoted himself with passion, together with a love for the ideas of justice and equality among people, in a thrilling mix of abstract thinking and concreteness of the world, almost as if everything were part of a single way of thinking and living. And for him it was exactly so.
Galois’s story was a sad one: his life even before the fatal duel was not rich in happy moments. His mathematical work was neglected by the scientific community and his intemperance and rebelliousness led him to prison for almost all of the last year of his short life: between mathematics and politics, he had no luck at all. But his is a story that teaches that, even though deep insights struggle to make their way, when they emerge they live on far longer than those who proposed them. Today, Galois is one of the great, genuine, immortal scientists, since the essence of his work, once it was understood, created and continues to guide many modern research methods. And his ideas have spread in science like grain germinating in a field.
Then too, the story of Galois reminds us that often people of genius do not seem able to adapt to their world, as if they were too different. Their interests, the ability to sense general ideas... all this makes them unable to be satisfied with what is enough for ordinary people. However, we should not trust appearances: even though his short life was full of internal tension and instability, of behaviours that seem irrational and even contradictions, Galois was a dreamer who wished for clarity and order.
About the search for the solution of algebraic equations, he knew the attempts made by Lagrange, the results by Gauss and Abel; he also knew that his ideas went beyond that and were crucial to recognising the equations that are solvable by radicals. But his work at first literally disappeared, then was ignored and, in the end, the reviewers were not able to assess whether the result was correct since the proof was neither clear enough, nor sufficiently developed.
Certainly, Galois did not care much about clarity in his presentation. Then, his methods were too new for them to be immediately appreciated. We cannot blame the reviewers, especially when we consider that it would take the relentless effort of two or three more generations of mathematicians to arrive at an understanding of his work.
But is it a flaw to be too far ahead of one’s time? Can we really find fault with one who sees so clearly in his head the solution of the problem as to assume that it is clear for everyone? The young man lived the events of his time and the inability to even communicate his findings with an always present sense of injustice. His view of society was of one in which genius was systematically discouraged, not only in mathematics, and mediocrity and tradition was encouraged. He did not even have a chance to get noticed.
Was for this reason too that Galois radicalised his political tendency, already begun in previous years and originated in his family? History does not answer. It allows us to reconstruct the events, but not the convictions. It is a fact that he made friends with a fellow—Auguste Chevalier—with whom he shared ideas inspired by an egalitarian and spiritual philosophy. So many young people still rely today on these ideals. In Galois’s case, his education, his passionate temperament, his sense of injustices suffered, and the credit he felt he had with destiny did the rest. The growing closeness and the ties of political solidarity to the ideals of the movement to which the two friends belonged took him to a turbulent political activity. It was just a natural consequence.
The night before the duel, with an impending omen of death, Galois wrote his political comrades three letters that today are his spiritual and scientific testament. He took his leave from friends, science and life. He did not blame anyone but himself, claiming the correctness of his behaviour. The sense of injustice had disappeared and, in the inevitability of fate, just the sadness and almost a request for forgiveness for dying for something other than the common good remained.
But in his letters there is also mathematics, pure, without doubt, hesitation or regret. To his dear friend Auguste he summarised his ideas about algebraic equations and from this letter we are now able to fully grasp his ideas.
Young, brilliant, impatient, disrespectful Évariste. It seems that his destiny weighed on him more because of the lack of recognition for his work than for the loss of his own life. He wrote frantically to his friends: Le sort ne m’a pas donné assez de vie pour que la patrie sache mon nom (Fate did not give me enough life for my fatherland to know my name).1 Of life he had truly too little.