I am the Crown Prince of France

Chapter 1: Prologue

Early Winter of 1787, Eastern Wing of the Palace of Versailles.

Joseph sat in a room adorned with Rococo-style golden decorations and large oil paintings, shaking his head with a bitter smile at the exam paper in front of him.

The flickering candlelight from the luxurious crystal chandelier, which was about two meters in diameter, reflected off his fair skin and delicate, youthful features, making him appear as handsome as Paris in a painting.

Beside him, an elderly man wearing a white curled wig and a lace cravat sighed, his brown eyes showing a hint of disappointment as he bowed slightly and said, "Your Highness, the Dauphin, if you find this difficult, perhaps it would be better to start with the basic courses…"

Joseph was startled, suddenly snapping out of his daydream, and politely nodded to the old man:

"Mr. Lagrange, I think there's been a misunderstanding. I requested to take your graduation exam, not the entrance exam."

Indeed, the unremarkable old man before him was none other than Joseph-Louis Lagrange, the founder of analytical mechanics and a pioneer in group theory, a renowned French mathematician and physicist hailed as the "Prince of Mathematics."

"Graduation exam?" Lagrange frowned as he looked at the boy, who was only thirteen years old. "Your Highness, I teach university-level courses. I'm afraid…"

The other young noble boys in the room, dressed in luxurious attire and working on their exam papers, immediately turned their heads, eyes full of curiosity.

At this moment, a sixteen-year-old boy with slightly slanted eyes, wearing a silk jacket with a lace collar, sneered and spoke loudly:

"Your Highness, I believe you still have two years left before you complete the basic courses." He nodded to the old man, "Mr. Lagrange often says that mathematics is like a ladder that must be climbed step by step. If you aim too high, you will surely fall and hurt yourself. I think His Highness should keep that advice in mind."

Joseph ignored him and seriously said to Lagrange:

"Sir, I have studied university-level mathematics on my own. I really need to take the graduation exam."

The old mathematician sighed helplessly and turned to his assistant, "André, please bring the exam paper from the bottom of my folder."

"Yes, Professor."

Soon, a few exam papers were placed in front of Joseph. He quickly skimmed through them and found that they were several times more difficult than the previous ones, but most of them were still at a high school level by modern standards, with a few involving calculus, which posed no real challenge to him.

Yes, just over half a month ago, he had been a second-year graduate student at Tsinghua University in the 21st century. On that day, he was working with his advisor on a wind turbine project in France when he accidentally fell from the top of a tower. When he woke up, he found himself transformed into the eldest son of King Louis XVI of France—Louis-Joseph. Perhaps due to the effects of the time travel, Joseph was born a few years earlier than in history and was already thirteen years old at this point.

As Joseph quickly wrote down the answer to the first question under Lagrange's scrutinizing gaze, his mind was occupied with thoughts about the course of French history: next year, the French Revolution would break out, and the entire royal family would be executed. As the Dauphin, he certainly wouldn't be able to escape… King Louis XVI was good for nothing except lock-making, France was over 2 billion livres in debt, yet the annual revenue was only 500 million.

Due to the financial collapse, civil servants' salaries were delayed, the government was struggling to function, foreign trade had stagnated, and the colonies were rotting away. To make up for the fiscal deficit, the government had no choice but to raise taxes massively, nearly draining the lower classes to the bone, while the nobility, who enjoyed tax exemptions, continued their extravagant lifestyles.

Moreover, next summer, France would suffer from severe hailstorms, exacerbating the impact of previous droughts, leading to a nationwide famine. What followed would be riots by starving people, the storming of the Bastille, the onset of the French Revolution, and the resulting chaos, with tens of thousands sent to the guillotine…

So, to save his neck, he counted on his fingers: first, he had to solve France's financial deficit; second, he needed to secure enough food to prevent mass starvation; third, he had to deal with the disloyal nobility; and finally, he had to fend off the British and Prussians who were eyeing France hungrily.

But with the famine starting in July, he only had a little over half a year left. Frustrated, he rubbed his forehead; due to his young age, he couldn't even get involved in government affairs yet, leaving him powerless.

It was a hellish beginning, with almost no hope…

Not far away, the boy with slanted eyes saw Joseph's movements and assumed he was troubled by the difficult questions. He sneered disdainfully: This fool actually came and claimed to know university-level material, what an embarrassment! Why is this idiot the Dauphin, and not me?!

As Joseph continued to think about how to save his life, he rapidly answered the questions and soon finished the first page of the exam. Impatiently, he turned the page. Once he passed Lagrange's exam, he would have officially completed his studies at the University of Paris!

A little over half a month ago, he had asked Queen Marie, his current mother, for permission to participate in government affairs to try and alter his doomed fate, but she had firmly refused, insisting that he focus on his studies and wait until he was fully educated.

So he had no choice but to strike a deal with the Queen: once he completed the University of Paris curriculum, he would officially start participating in governance.

Of course, with his level of knowledge, he was a genius in this era. In the past half-month, he had already finished most of the subjects, though it took some extra time because he had to correct a lot of erroneous information—many things that were considered truths in this era were actually misconceptions.

Lagrange, watching the Dauphin's swift progress, had long since stopped paying attention to the other students. His eyes grew wider and wider.

These were problems that would take five years of study at the University of Paris to solve, yet the Dauphin was answering them effortlessly and with clear logic, not making a single mistake!

He was only thirteen years old and self-taught! Lagrange was shaken to his core. Could another prodigy like Leibniz have been born?

Suddenly, Lagrange glanced at his assistant, his eyes narrowing. Could André have leaked the exam questions to the Dauphin? After all, the Dauphin's performance was too extraordinary. It should be noted that even a genius like Leibniz didn't start university until he was fourteen.

Immediately, he took some paper and quickly wrote down a few lines, then handed it to Joseph, saying:

"Your Highness, you don't need to complete the rest of the exam. Just answer these few questions, and I'll consider you passed."

The boy with slanted eyes secretly sneered: Ha! Lagrange must be giving him an easy way out because he sees that the Dauphin can't answer the questions. What a sycophant! I need to find a way to make everyone see the Dauphin's exam and watch him make a fool of himself.

Joseph looked at the paper in surprise. There were only five questions, the difficulty hadn't changed, but the number of questions had decreased. That was good news.

He quickly completed the first two questions, then saw that the third question was: "Please write out the proof of Rolle's theorem." This was something he was very familiar with, and without hesitation, he wrote in the blank space:

"Rolle's theorem: Let f be continuous on the closed interval [a, b] and differentiable on the open interval (a, b). If f(a) = f(b), then there is at least one point in the open interval (a, b) where the derivative of the function equals zero.

Proof: Since the function f(x) is continuous on [a, b], it attains its maximum (M) and minimum (m) on the closed interval…"

Joseph quickly finished writing, but suddenly noticed that Lagrange's breathing had become rapid. He looked up and saw the old mathematician staring at the exam paper with an expression like he had just seen his first love.

Joseph immediately looked down and skimmed through the question again, hesitating: "I shouldn't have made a mistake, right?"

Lagrange grabbed the exam paper, carefully scrutinized the proof several times, and muttered:

"So it's valid for differentiable functions too! How did I not think of that?"

He then looked at Joseph, his gaze burning:

"Your Highness, how did you come up with this?"

"Huh? Isn't it just…" Joseph suddenly remembered that Rolle had only proven this for polynomial equations with two real roots. It wasn't until the 19th century that someone extended it to differentiable functions.

He had been careless, forgetting to hide his knowledge…

"Ahem!" He quickly took back the exam paper and changed the subject, "Mr. Lagrange, I need to finish the last two questions."

(End of Chapter)