I am the Dauphin of France

Chapter 1: Prologue

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

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

The luxurious crystal chandelier, two meters in diameter, cast flickering candlelight on his fair skin and delicate, youthful features, making him look like the handsome Paris from the paintings.

Beside him, an elderly man with a white curly wig and a lace cravat sighed, disappointment flickering in his brown eyes, and bowed slightly to him, saying, "Your Highness, if you find it difficult, perhaps you should start with the basic courses..."

Joseph, startled, snapped out of his reverie and nodded politely to the old man: "Mr. Lagrange, I think you might be mistaken. I said I wanted to take your graduation exam, not the entrance exam."

Yes, this unassuming old man was none other than the founder of analytical mechanics, a pioneer in group theory, and the renowned French mathematician and physicist known as the "Prince of Mathematics"—Joseph-Louis Lagrange.

"Graduation exam?" Lagrange frowned at the thirteen-year-old boy in front of him. "Your Highness, what I teach are university courses, you might..."

The surrounding noble youths, dressed in splendid attire and taking their exams, immediately turned their heads, eyes full of curiosity.

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

"Your Highness, I remember you should have two more years to complete the basic courses." He nodded to the old man, "Mr. Lagrange often says that the ladder of mathematics must be climbed step by step, aiming too high will only result in a hard fall. I think Your Highness should remember this maxim."

Joseph ignored him and seriously said to Lagrange:

"Sir, I have self-studied university mathematics courses, I really need the graduation exam."

The old mathematician sighed helplessly and turned to his assistant, "Andre, please bring me the exam papers from the bottom of my file."

"Yes, Professor."

Soon, several exam papers were placed in front of Joseph.

He quickly glanced through them and found that they were several times more difficult than the previous ones, but most were still at the high school level of the future, with a few involving calculus, which was not difficult for him at all.

Yes, until more than half a month ago, he was still a second-year graduate student at Tsinghua University in the 21st century. That day, he had gone to France with his tutor for a wind turbine project and accidentally fell from the top of a tower. When he woke up, he found himself transmigrated as the eldest son of King Louis XVI of France—Louis Joseph. Perhaps due to the transmigration, Joseph was born a few years earlier than in history, now being thirteen years old.

Under Lagrange's scrutinizing gaze, Joseph quickly wrote the answer to the first question, his mind pondering the course of French history: The French Revolution would break out next year, and the entire royal family would be executed. As the crown prince, he would surely not escape... King Louis XVI was good for nothing but locksmithing, and France owed more than 2 billion in debt with an annual income of only 500 million.

Due to financial collapse, civil servants' salaries were delayed, government operations were barely functioning, foreign trade was stagnant, and the colonies were deteriorating. To replenish the treasury, the cabinet had to heavily tax the people, leaving the commoners drained while the tax-exempt nobility indulged in extravagance and luxury.

Moreover, France would suffer severe hail next summer, coupled with the droughts of previous years, leading to a nationwide famine. This would trigger peasant revolts, the storming of the Bastille, the start of the Revolution, national turmoil, and tens of thousands sent to the guillotine...

So, to save his own head, he counted on his fingers: First, solve France's financial deficit; second, secure enough food to avoid famine; third, deal with the rebellious nobles; and finally, fend off the covetous British and Prussians.

With the famine starting in July, he had just over half a year left, and he rubbed his forehead in frustration. Because of his young age, he couldn't access state affairs, leaving him with nowhere to exert his efforts.

A hellish beginning, with little hope...

Not far away, the slanted-eyed boy saw his actions and assumed he was distressed by the difficult questions, sneering: This fool claimed to know university courses, what a disgrace! Why is such a dunce the crown prince and not me?! 

While thinking about how to save his life, Joseph quickly wrote down the answers, soon completing the first page of the exam. 

He eagerly turned the page, thinking that passing Lagrange's subject would mean completing his studies at the University of Paris!

More than half a month ago, he had proposed to Queen Marie, his mother, to participate in politics to avert his impending doom, but she had promptly refused, telling him to focus on his studies and wait until he was well-educated.

So he had made a deal with the queen that after completing the courses at the University of Paris, he would officially enter politics.

Of course, with his level, he was a top student in this era. In the past half month, he had already completed most subjects, only delayed by having to memorize incorrect knowledge—many things considered truths in this era were actually fallacies.

Lagrange, watching the crown prince's swift writing, had long since stopped paying attention to the other students, his eyes widening.

This was material that took five years of study at the University of Paris to complete, yet the crown prince was solving it effortlessly, with clear logic and not a single mistake! 

He was only thirteen, and self-taught! Lagrange was stunned, wondering if another Leibniz had been born.

Lagrange suddenly glanced at his assistant, squinting, thinking that Andre might have leaked the questions to the crown prince. 

After all, the prince's performance was too extraordinary; even the prodigy Leibniz had started university at fourteen.

He immediately took out paper and pen, wrote a few lines, and handed it to Joseph, saying:

"Your Highness, you don't need to finish the rest, just complete these few questions, and I'll consider you passed."

The slanted-eyed boy sneered inwardly: Ha, Lagrange is letting him off easy, huh? Sucking up to the royal family, idiot! I'll make sure everyone sees the prince's test paper and watch him make a fool of himself.

Joseph was surprised to see only five questions, with the difficulty unchanged but the quantity reduced. 

Good news.

He quickly finished the first two questions and saw that the third was "Please write the proof process of Rolle's theorem," which he was very familiar with. Without thinking, he wrote:

Rolle's theorem states that if fff is continuous on the closed interval [a,b][a, b][a,b] and differentiable on the open interval (a,b)(a, b)(a,b), and if f(a)=f(b)f(a) = f(b)f(a)=f(b), then there is at least one point in (a,b)(a, b)(a,b) where the derivative is zero.

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

Joseph quickly finished writing, but suddenly noticed Lagrange beside him breathing rapidly. He looked up to see the old mathematician staring at the paper with the look of someone seeing their first love.

Joseph immediately scanned the question, hesitantly asking, "I shouldn't have written it wrong, right?"

Lagrange snatched the paper, carefully examined the proof several times, and muttered, "So it also holds for differentiable functions! How did I not think of that?"

He then looked at Joseph, his eyes burning with intensity, "Your Highness, how did you come up with this?"

"Ah? Isn't it just..." Joseph suddenly remembered that Rolle had only simply proven it for polynomials with adjacent real roots, and it wasn't extended to differentiable functions until the nineteenth century.

Shit, he’s careless, he has written down future information…

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