The Crown Prince of France - Chapter 1

Chapter 1: The Prologue

Early winter, 1787, the eastern wing of the Palace of Versailles.

Joseph sat in a room adorned with Rococo-style golden patterns and grand oil paintings, shaking his head with a wry smile as he stared at the test paper in front of him.

The flickering candlelight of an opulent crystal chandelier, nearly two meters in diameter, cast its glow on his fair skin and delicate features, making him resemble the handsome Paris depicted in the oil paintings.

Beside him stood an elderly man wearing a white curly wig and a lace cravat. Sighing, the elder’s brown eyes betrayed disappointment as he bowed slightly and said, “Your Royal Highness, the Crown Prince, if you find this difficult, perhaps you should start with the basics...”

Joseph was momentarily stunned, returning from his wandering thoughts. He nodded politely at the elder.
“Mr. Lagrange, I think you’ve misunderstood. I am here for the graduation exam of your course, not the entrance exam.”

Indeed, this unassuming old man was none other than Joseph-Louis Lagrange, the founder of analytical mechanics, a pioneer of group theory, and a mathematician and physicist hailed as the Prince of Mathematics.

“Graduation exam?” Lagrange frowned, scrutinizing the thirteen-year-old boy before him. “Your Highness, the courses I teach are at the university level. I’m afraid that—”

Around them, a group of aristocratic boys, dressed in lavish attire, immediately turned their heads, their eyes filled with curiosity.

At that moment, a boy of about sixteen wearing a silk coat with a ruffled collar and slightly upturned eyes sneered disdainfully. He said loudly,
“Your Royal Highness, the Crown Prince, I believe you still have two years before completing the foundational courses. As Mr. Lagrange often says, the ladder of mathematics must be climbed step by step. Ambition without substance will only lead to disaster. Your Highness should remember this wisdom.”

Joseph ignored him and addressed Lagrange earnestly.
“Sir, I’ve self-studied university-level mathematics. I really need the graduation exam.”

The old mathematician sighed helplessly and turned to his assistant. “André, fetch the test papers from the bottom of my bookstand.”

“Yes, Professor,” the assistant replied.

Shortly, a set of test papers was placed in front of Joseph.

He quickly glanced through them and noticed that the difficulty was several times higher than before. However, most of the problems were equivalent to modern high school-level mathematics with a bit of calculus—a breeze for him.

Yes, just over a month ago, he had been a second-year graduate student at Tsinghua University in the 21st century. That day, while accompanying his mentor to France for a wind turbine project, he had fallen from the top of a tower. When he woke up, he discovered that he had transmigrated into the body of Louis Joseph, the eldest son of King Louis XVI of France. Due to the effects of the transmigration, Joseph had been born several years earlier than his historical counterpart, making him thirteen years old at this time.

Under Lagrange’s scrutinizing gaze, Joseph quickly wrote down the answer to the first question. His mind, however, was preoccupied with thoughts of France’s historical trajectory: the French Revolution would erupt next year, leading to the execution of the entire royal family. As the Crown Prince, he was unlikely to escape...

King Louis XVI knew little beyond locksmithing, while France’s external debt exceeded 2 billion livres, with an annual revenue of only 500 million.

The financial collapse resulted in unpaid salaries for civil servants, government operations grinding to a halt, stagnated trade, and deteriorating colonies. To patch the financial deficit, the cabinet had resorted to heavy taxation, squeezing the peasantry dry while the tax-exempt nobles indulged in extravagant lifestyles.

Next summer, a catastrophic hailstorm, coupled with the effects of previous droughts, would lead to a nationwide famine. Then would come the peasants’ uprisings, the storming of the Bastille, and the French Revolution’s reign of terror, culminating in tens of thousands sent to the guillotine.

To save his head, Joseph calculated: first, he must resolve France’s financial deficit; second, he had to secure enough grain to prevent mass starvation; third, he needed to suppress rebellious nobles; and finally, he had to contend with the ever-watchful British and Prussians.

With the famine starting in July, he had only a little over six months. Frustrated, he rubbed his temples. At his current age, he couldn’t yet intervene in state affairs, leaving him powerless.

It was a hellish start, with barely a glimmer of hope...

Not far away, the upturned-eyed boy, noticing Joseph’s gestures, assumed he was struggling with the test and scoffed disdainfully. What a fool! Coming here claiming to know university-level mathematics? An embarrassment! Why is someone like him the Crown Prince, and not me?

As Joseph mulled over survival strategies, he continued writing answers at a brisk pace. He soon completed the first page of the test paper.

Impatiently flipping to the next page, he thought: once he passed Lagrange’s course, he would have completed his studies at the University of Paris!

A month earlier, he had approached Queen Marie Antoinette—his mother in this timeline—proposing to participate in state governance to avert the looming catastrophe. She had decisively refused, insisting he focus on his studies and wait until he was academically accomplished.

Thus, he had struck a deal with the Queen: once he completed the University of Paris’ curriculum, he would be allowed to participate in state affairs.

Given his level of proficiency, he was a veritable academic prodigy in this era. Over the past month, he had completed most of the subjects, delayed only by the need to unlearn erroneous knowledge—much of what was considered “truth” in this era was actually fallacy.

Lagrange, observing the Crown Prince’s rapid progress, had long ceased paying attention to the other students. His eyes widened with every passing moment.

These were problems meant to be tackled after five years at the University of Paris, yet the Crown Prince solved them effortlessly, with impeccable clarity and not a single mistake!

He was only thirteen—and self-taught! Lagrange’s heart trembled. Was another Leibniz being born before his eyes?

His gaze drifted to his assistant, André, narrowing slightly. Could André have leaked the questions to the Crown Prince? The boy’s performance was too extraordinary. Even Leibniz had only begun university studies at fourteen!

Grabbing a pen and paper, Lagrange hastily jotted down a few lines and handed them to Joseph.
“Your Highness, no need to complete the rest. Just solve these few problems, and I will consider you passed.”

The upturned-eyed boy smirked secretly. Ha! Lagrange must think the Crown Prince incapable and is lowering the bar. Foolish flatterer! I must find a way to expose the Crown Prince’s incompetence later.

Joseph looked at the paper in surprise. There were only five questions, with no increase in difficulty but a reduced workload. What luck!

He swiftly solved the first two questions. Then, encountering the third, he saw it was: “Please write out the proof process for Rolle’s theorem.” This was something he knew by heart. Without hesitation, he wrote:

Rolle’s theorem: Let fff be a function that is continuous on the closed interval [a,b][a, b][a,b], differentiable on the open interval (a,b)(a, b)(a,b), and satisfies f(a)=f(b)f(a) = f(b)f(a)=f(b). Then, there exists at least one point c∈(a,b)c \in (a, b)c∈(a,b) such that f′(c)=0f'(c) = 0f′(c)=0.

Proof: Since f(x)f(x)f(x) is continuous on [a,b][a, b][a,b], it attains maximum and minimum values on the interval...

Joseph completed the proof in a few quick strokes but suddenly noticed Lagrange’s breathing had become erratic. Alarmed, he looked up to find the old mathematician staring at the paper with an expression akin to discovering his first love.

Joseph hastily reviewed the question, muttering, “I don’t think I made any mistakes, did I?”

Lagrange grabbed the test paper, scrutinized it repeatedly, and muttered to himself, “So it’s also valid for differentiable functions! Why didn’t I think of that?”

His gaze turned to Joseph, fiery with admiration.
“Your Highness, how did you think of this?”

“Ah? Isn’t it just...” Joseph suddenly remembered. In his original timeline, Rolle had only dEymondstrated the theorem for polynomial equations, and its extension to differentiable functions had not occurred until the 19th century.

Careless, too careless...

“Ahem!” He quickly reclaimed the paper and changed the subject.
“Mr. Lagrange, I need to finish the last two questions.”

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