Chapter 1: Prologue
Early winter of 1787, East Wing of the Palace of Versailles.
The young man sat in a room adorned with Rococo golden patterns and large oil paintings, shaking his head with a wry smile as he stared at the examination paper before him.
Candlelight from a luxurious two-meter-diameter crystal chandelier flickered, casting its glow upon his pale skin and delicate, refined features, making him appear as handsome as Paris in an oil painting.
Beside him, an elderly man in a white curly wig and a lace cravat sighed, disappointment flickering in his brown eyes. He bowed slightly and said, "Your Royal Highness, Crown Prince, if you find it challenging, perhaps you could begin with the foundational courses..."
The young man, addressed as Crown Prince, paused, instantly snapping out of his reverie. He politely nodded to the elder. "Monsieur Lagrange, I believe you might be mistaken. I said I wish to take the graduation examination for your course, not the entrance exam."
Indeed, this unassuming old man was none other than Lagrange, the founder of analytical mechanics, a pioneer of group theory, and a renowned French mathematician and physicist, celebrated as the "Prince of Mathematics."
"Graduation examination?" Lagrange frowned, looking at the thirteen-year-old before him. "Your Royal Highness, I teach university-level courses. I'm afraid you might..."
The elegantly dressed noble youths around them, who were also taking their exams, immediately turned to look, their eyes filled with curiosity.
At that moment, a youth of about sixteen, wearing a silk jacket with a lace collar and possessing slightly slanting eyes, scoffed aloud. "Your Royal Highness, Crown Prince, I recall you still have two years left to complete your foundational courses." He nodded towards the elder. "Monsieur Lagrange often says that the ladder of mathematics must be climbed one step at a time; to aim too high will surely lead to a painful fall. I believe Your Royal Highness should also remember this proverb."
The old mathematician sighed helplessly and turned to his assistant. "Andrei, please fetch the examination paper from the very bottom of my folder."
"Yes, Professor."
Soon, several examination papers were laid before the young man.
He quickly scanned them, finding that the difficulty had increased severalfold compared to the previous paper. Still, most of it was at a high school level from his original time, with a small amount of calculus. For him, it presented no real challenge.
Indeed, less than a month and a half ago, he had been a second-year graduate student in the 21st century. That day, while working on a wind turbine project in France with his advisor, he had accidentally fallen from the top of a tower. When he awoke, he found himself transmigrated into the body of Louis Joseph, the eldest son of King Louis XVI of France. Perhaps due to the transmigration, Joseph had been born a few years earlier than in actual history, and was now thirteen.
Under Lagrange's scrutinizing gaze, Joseph rapidly wrote down the answer to the first question, his mind preoccupied with the course of French history: The French Revolution was set to erupt next year, the entire royal family would be guillotined, and as the Crown Prince, he certainly wouldn't escape... King Louis XVI knew nothing but repairing locks, France was burdened with over two billion in foreign debt, while its annual revenue was only five hundred million.
Due to the financial collapse, civil servants were owed their salaries, government operations were struggling, foreign trade had stagnated, and the colonies were steadily decaying. To replenish the treasury, the cabinet had no choice but to impose heavy taxes, practically draining the common people dry, while privileged nobles with tax exemptions spent their days squandering fortunes in ponds of wine and forests of meat.
Furthermore, next summer, France would suffer severe hailstorms. Coupled with the droughts of previous years, a nationwide famine was imminent. This would be followed by peasant revolts, the storming of the Bastille, ushering in the era of the Great Revolution, national turmoil, and hundreds of thousands of people sent to the guillotine...
Therefore, to save his own head, he tallied the necessities on his fingers: First, he needed to resolve France's financial deficit; second, secure enough food to prevent starvation; third, deal with the ill-intentioned nobles; and finally, contend with the covetous British and Prussians.
But the famine would begin in July, leaving him only a little over half a year. He rubbed his forehead in frustration, his young age preventing him from engaging in state affairs, leaving him with power but no means to wield it.
It was truly a hellish start, with slim chances of survival...
Not far away, the slanting-eyed youth saw his gesture and merely assumed he was fretting over his inability to solve the problems. He sneered disdainfully, 'This idiot! To claim he knows university-level courses? How utterly disgraceful! Why is such a blockhead the Crown Prince, and not me?!'
Joseph continued writing his answers rapidly, his mind still preoccupied with how to save his life. He soon completed the first page of the examination.
He eagerly turned the page. Once he passed this course with Lagrange, he would officially have completed his studies at the University of Paris!
Less than a month and a half ago, he had proposed to Queen Marie—his adoptive mother—that he participate in state affairs, hoping to avert his destined demise. However, she had promptly refused, instructing him to focus on his studies and discuss it again once he had achieved something.
Thus, he had made an agreement with the Queen: he would formally enter politics only after completing his courses at the University of Paris.
Of course, with his abilities, he was an academic ace in this era. Over the past month and a half, he had already passed most of his subjects. This was partly delayed because he had to memorize outdated and erroneous information, as much of what was considered truth in this age was actually fallacious.
Lagrange watched the Crown Prince write with astonishing speed, no longer paying attention to the other students, his eyes widening with each passing moment.
These were questions that took five years to complete at the University of Paris, yet the Crown Prince answered them effortlessly, with clear logic, and not a single mistake!
He was only thirteen, and self-taught at that! Lagrange's heart pounded. Could another Leibniz have been born?
Lagrange suddenly glanced at his assistant, his eyes narrowing slightly. 'Could Andrei have leaked the questions to the Crown Prince?' he wondered. After all, the Crown Prince's performance was too extraordinary. Even a super prodigy like Leibniz didn't start university until he was fourteen.
He immediately took out paper and pen, swiftly scribbling a few lines, then handed it to Joseph. "Your Royal Highness, you don't need to do the rest. Just complete these few questions, and I will consider you passed."
The slanting-eyed youth saw this and secretly sneered. 'Hah, is Lagrange going easy on him because he can't do it? What a fool, pandering to the royals! I'll have to find a way for everyone to see the Crown Prince's paper later, and properly humiliate him.'
Joseph glanced at the paper in surprise. There were only five questions; the difficulty hadn't changed, but the quantity had decreased. A good thing, indeed.
He quickly finished the first two questions. The third question read: "Please write down the proof for 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 exists at least one point c in the open interval (a, b) such that its derivative f'(c) is zero. Proof: Since the function f(x) is continuous on [a, b], it attains its maximum (M) and minimum (m) values within the closed interval...
Joseph finished writing in a few quick strokes, but suddenly felt Lagrange's breathing quicken beside him. He looked up to see the old mathematician's face alight with emotion, staring at the examination paper as if he had just reunited with his first love.
Joseph immediately glanced back down at the questions, then hesitated. "I didn't write anything wrong, did I?"
Lagrange snatched up the examination paper, carefully reviewing the proof several times. He mumbled, "So it holds true for differentiable functions too! How did I not realize this?"
He then looked at Joseph, his gaze burning like fire. "Your Royal Highness, how did you come up with this?"
"Ah? Isn't it just..." Joseph suddenly remembered that Rolle had merely proven that between two adjacent real roots of a polynomial equation, there was at least one root. It wasn't until the nineteenth century that someone extended it to the realm of differentiable functions.
'I wasn't careful enough,' he thought.
"Cough!" He quickly retrieved the examination paper, changing the subject. "Monsieur Lagrange, I shall proceed with the remaining two questions."
Comments