Labyrinthine insights

Posthumous men

"First the day after tomorrow must come for me. Some men are born posthumously." -Friedrich Nietzsche, The Antichrist (Preface) (tr. by H. L. Mencken)

"My time has not yet come either; some are born posthumously" - Friedrich Nietzsche, Ecce Homo, Why I Write Such Excellent Books (tr. by Anthony Ludovici)

Nietzsche establishes and places himself in this separate category of humanity - that of "posthumous men". Something worth noting is that this cannot be defined as "men who are understood posthumously", this idea is not limited to being understood only after death but implies a broader sense of enduring influence. Such individuals, according to Nietzsche, were always destined to have an impact that would only manifest fully after their physical life had ended. They are "born posthumously" in the sense that their true birth or emergence as influential figures occurs only after their death.

Nietzsche, of course, identified himself with this concept - he understood his ideas, as radical and provocative as they are, might not be grasped and accepted by his contemporaries (and his literary experiences thus far could serve as proof -during his lifetime he faced rejection, ridicule, and his greatest works only selling a few copies- ). When it comes to his confidence upon actually "being born posthumously", this is more thoroughly explained in his autobiographical "Ecce Homo" - "Why I am so wise" (tr. by Anthony Ludovici):

"I am gifted with a sense of cleanliness the keenness of which is phenomenal; so much so, that I can ascertain physiologically—that is to say, smell—the proximity, nay, the inmost core, the "entrails" of every human soul.... This sensitiveness of mine is furnished with psychological antennæ, wherewith I feel and grasp every secret: the quality of concealed filth lying at the base of many a human character which may be the inevitable outcome of base blood, and which education may have veneered, is revealed to me at the first glance." -Why I Am So Wise, Section 7

Nietzsche was acutely aware that his ideas were radical, challenging the prevailing moral, religious, and philosophical norms of his era. He saw himself as a philosopher who was pushing beyond the intellectual boundaries of his time, and he recognized that such pioneering thought often meets with resistance or misunderstanding initially. This paired with a precise awareness regarding history and historical patterns - Nietzsche had a keen sense of what his trajectory would be.

J’ai besoin de tout mon courage pour mourir à vingt ans!

And these were the last words spoken by Evariste Galois, to his brother, before succumbing to his injuries sustained in a duel.

Galois needs no introduction and his few years of life encompass what could very well be described as a revolution. His life was a manifest in regards to mathematics and politics, a true work of a genius who would only get to be born posthumously.

He was, first and foremost, a passionate mathematician, who happened to be rejected twice from the prestigious École Polytechnique (story goes that on the second admission exam, after having received the news of his rejection, Galois stormed out and insulted the examiners, calling them stupid).

After being rejected by the Polytechnique, Galois enrolled at the École Normale, which was more focused on training teachers than on advanced scientific research. Galois became increasingly involved in the political unrest of the time, supporting the republican cause during a period of significant political turmoil in France. His outspoken political views and participation in demonstrations led to conflicts with the school's administration. Eventually, Galois was expelled from the École Normale in 1830 after publishing a politically charged letter criticizing the school's director (even though the letter was never signed).

Meanwhile, in 1829, Galois' father, Nicolas-Gabriel Galois (who was the mayor of his home town Bourg-la-Reine), committed suicide following a public scandal(a priest forging his name on malicious letters addressed to his relatives and then made public). His father's death had a profound impact on Galois, plunging him into a deep depression. This personal tragedy further fueled his already growing disillusionment with the establishment, (and would the same not have happened to any of us?)

Despite these setbacks and personal struggles, Galois had one constant in his life: mathematics. He tried his luck and he submitted articles to the Académie des Sciences. Cauchy was appointed as referee of Galois' paper. Galois sent additional work to Cauchy but later discovered through the Bulletin de Férussac that a posthumous article by Abel covered some of the same material. Following Cauchy's recommendation, Galois then submitted a new paper titled "On the Condition for an Equation to be Soluble by Radicals" in February 1830. This paper was forwarded to Fourier, the secretary of the Paris Academy, for consideration for the Grand Prize in mathematics. Unfortunately, Fourier passed away in April 1830, and Galois' paper was never found afterward, so it was not reviewed for the prize. But, unfortunately, that was not the end of Galois' chain of rejections.

One of the most significant setbacks in Galois' life came in 1830 when he submitted a manuscript to the French Academy of Sciences. The work was reviewed by the esteemed mathematician Siméon Denis Poisson, who ultimately rejected it with the following criticism:

"We have found Galois' argument neither sufficiently clear nor sufficiently developed to allow us to judge its correctness. The author should try to set out his ideas in greater detail so that we can understand them."

And why was Galois speaking a language so foreign to even the elite of the field of pure mathematics at the time? His approach was not only conceptually advanced but also expressed in highly unconventional notation. He used symbols and methods that were unfamiliar to his contemporaries, making his work difficult to understand,for example his concept of permutations and substitutions was different (in the way he used the words at least).

Frustrated by the lack of recognition for his mathematical work and motivated by his personal struggles, Galois became increasingly involved in the political turmoil of his era. He was an outspoken republican, and his political activities led to several arrests. Galois' life came to a tragic end on May 31, 1832, when he was killed in a duel under mysterious circumstances at the age of 20. The exact reasons for the duel remain unclear, and this discussion will take place another day.

Regardless of the reasons for his fatal duel, Galois was so certain that he would die soon that he spent the entire night writing letters to his Republican allies and drafting what would become his mathematical legacy. He composed his well-known letter to Auguste Chevalier, which detailed his ideas, along with three accompanying papers.

But I don't have the time, and my ideas are not yet well developed in this area, which is immense. [...] I have often dared in my life to advance propositions about which I was not sure, but all that I have written down has been in my mind for over an year, and it would not be too much in my interest to make mistakes so that one suspects me of having announced theorems of which I would not have a complete proof. You make a public request to Jacobi and Gauss to give their opinion, not as to the truth but as to the importance of these theorems. After this, I hope there will be people who will profit by deciphering all this mess. I embrace you effusively."

It was only after Galois' death that the true significance of his work began to emerge. In 1846, Joseph Liouville, edited and published the manuscripts in the Journal de Mathématiques Pures et Appliquées, bringing Galois' groundbreaking ideas to the attention of the mathematical community, giving birth to what is known today as the field of "Galois theory".

Évariste Galois is the epitome of Nietzsche's concept of a "posthumous man." His genius was largely unrecognized during his lifetime, and his groundbreaking ideas were misunderstood or dismissed by his contemporaries. His unusual notation and advanced concepts made his work inaccessible to the mathematicians of his time. It was only after his premature death that the mathematical community began to appreciate the profound impact of his work. Galois' legacy, which continues to shape modern mathematics, truly came to life posthumously, making him a quintessential example of someone whose importance was only realized after their death.

Now, dear reader, what have You achieved by the age of 20?