The boy sat in a room filled with Rococo-style gold decorations and large oil paintings, shaking his head and smiling bitterly at the exam paper in front of him.
The candlelight flickered in the luxurious crystal chandelier, which was two meters in diameter, illuminating his fair skin and youthful, delicate features, making him appear as handsome as Paris in an oil painting.
Beside him, an elderly man with a white curly wig and a lace scarf sighed, a hint of disappointment flashing in his brown eyes. He bowed slightly and said, "Your Highness, if you find it difficult, perhaps you could first study the basic courses..."
The boy, addressed as the Crown Prince, was startled and snapped out of his reverie, politely nodding to the old man.
"Mr. Lagrange, I think you may have made a mistake. I meant to conduct the graduation assessment for your course, not the entrance exam."
Indeed, this unassuming old man is none other than Lagrange, the founder of analytical mechanics, a pioneer of group theory, and a famous French mathematician and physicist known as the "Prince of Mathematics."
"Graduation exam?" Lagrange frowned, looking at the thirteen-year-old boy before him. "Your Highness, I'm teaching university-level courses, I'm afraid..."
The elegantly dressed noble youths around them, who were taking the exam, immediately turned to look at them, their eyes filled with curiosity.
At this moment, a boy of about sixteen, wearing a silk jacket with a lace collar and slightly slanted eyes, revealed a disdainful expression and loudly proclaimed:
"Your Highness, I remember you still have two years before you finish the basic courses." He nodded to the old man. "Mr. Lagrange often said that the ladder of mathematics must be climbed step by step; aiming too high will only lead to a painful fall. I think Your Highness should also remember this proverb."
The boy ignored him and said earnestly to Lagrange:
"Sir, I have studied university-level mathematics courses on my own, and I really need to take the graduation exam."
The old mathematician sighed helplessly and turned to his assistant, saying, "Andre, please bring me the exam paper at the very bottom of my folder."
"Yes, Professor."
Soon, several test papers were placed in front of the boy.
He quickly skimmed through it and found that it was several times more difficult than the previous one, but most of it was still at the high school level of later generations, involving a small amount of calculus content, so it was really not difficult for him.
Yes, just over two weeks ago, he was a second-year graduate student in the 21st century. That day, he went to France with his advisor to work on a wind turbine project. He accidentally fell from the top of a tower and woke up to find himself transmigrated into the body of Louis Joseph, the eldest son of King Louis XVI of France. Perhaps due to the influence of time travel, Joseph was born a few years earlier than in history and was now thirteen years old.
Under Lagrange's scrutinizing gaze, Joseph quickly wrote down the answer to the first question, but his mind was already thinking about the course of French history: the French Revolution was about to erupt next year, the entire royal family would be overthrown, and he, as the crown prince, would certainly not escape... King Louis XVI knew nothing but locksmithing, France owed more than 2 billion euros in foreign debt, while its annual income was only 500 million euros.
The collapse of the treasury led to unpaid salaries for civil servants, making daily government operations extremely difficult, halting foreign trade, and causing the colonies to deteriorate. In order to replenish the treasury, the cabinet had no choice but to raise taxes drastically, which almost drained the lives of the lower classes, while the nobles with tax exemptions indulged in extravagant lifestyles of debauchery and debauchery.
Furthermore, France will experience severe hailstorms next summer, and combined with the drought of previous years, a nationwide famine will ensue. This will be followed by famine riots, frantic raids on the Bastille, the unlocking of the Grand Theft Auto expansion, national turmoil, and hundreds of thousands ending up on the guillotine…
So, to save his own life, he counted on his fingers: first, he had to solve France's financial deficit; second, he had to obtain enough food to prevent people from starving; third, he had to deal with the disloyal nobles; and finally, he had to deal with the covetous British and Prussians.
The famine would begin in July, leaving him with only a little over six months. He rubbed his forehead in frustration, feeling powerless to engage in politics due to his young age.
It's a completely hellish start, with little chance of survival...
Not far away, the boy with slanted eyes saw his actions and assumed he was worried because he couldn't do the problems. He immediately scoffed disdainfully: "This idiot, actually comes here claiming he knows university courses, what a disgrace! Why is this good-for-nothing a prince, but I'm not?!"
While thinking about how to save his life, Joseph quickly wrote down the answers and soon finished the first page of the test.
He turned the page impatiently, thinking that once he passed this Lagrange exam, he would have completed his studies at the University of Paris!
More than half a month ago, he proposed to Queen Mary, who was also his adoptive mother, that he wanted to enter politics in order to reverse his inevitable death, but she flatly refused and told him to focus on his studies and wait until he had completed his studies before making a decision.
So he had no choice but to agree with the Queen that he would formally enter politics after completing his studies at the University of Paris.
Of course, given his level, he's a top student in this era. He had already finished most of his exams in the previous two weeks, only because he was delayed by memorizing incorrect information—much of what's considered truth in this era is actually false.
Lagrange watched as the Crown Prince wrote with lightning speed, completely ignoring the other students, his eyes widening in disbelief.
This is a question that would take five years of study at the University of Paris to answer, yet the Crown Prince answered it effortlessly, with clear thinking and not a single mistake!
He was only 13 years old, and he was self-taught! Lagrange was shocked. Could another Leibniz have been born?
Lagrange suddenly glanced at his assistant, his eyes narrowing slightly, wondering if Andrei had leaked the exam questions to the Crown Prince. After all, the Crown Prince's behavior was too extraordinary; even a prodigy like Leibniz didn't start university until he was 14.
He immediately took out paper and pen, quickly wrote a few lines, and handed them to Joseph, saying:
"Your Highness, you don't need to do the rest. As long as you complete these few questions, I will consider you to have passed."
The boy with slanted eyes sneered inwardly: "Ha, is Lagrange letting him off the hook because he can't do it? What a fool trying to curry favor with the royal family! I'll have to find a way to let everyone see the Crown Prince's exam paper later and make him look bad."
Joseph looked at the paper in surprise. There were only 5 questions; the difficulty remained the same, but the number of questions had decreased. Good thing.
He quickly finished the first two questions, and the third question was "Please write out the proof of Rolle's theorem." He was very familiar with this, and without thinking, he wrote it down in the blank space:
Rolle's theorem states that if f is continuous on the closed interval [a, b] and continuous in the open interval (a, b), and f(a) = f(b), then there is at least one point in the open interval (a, b) where the derivative of f(a) is zero.
Proof: Since the function f(x) is continuous on [a, b], the maximum value (M) and minimum value (m) obtained on the closed interval are...
Joseph finished writing in a few strokes, but suddenly noticed that Lagrange next to him was breathing rapidly. He quickly looked up and saw that the old mathematician was excited, staring at the exam paper as if he had seen his first love.
Joseph immediately glanced down at the question and hesitated, "I don't think I made a mistake, right?"
Lagrange grabbed the exam paper, carefully reviewed the proof several times, and muttered to himself, "So it also holds true for differentiable functions! How come I didn't think of that?"
He then looked at Joseph, his gaze burning with fervor: "Your Highness, how did you come up with this idea?"
"Ah? Isn't that…" Joseph suddenly remembered that Rolle had simply proven that between two adjacent real roots of a polynomial equation, the equation has at least one root, and it wasn't until the nineteenth century that someone extended it to the category of differentiable functions.
I was careless, I didn't flash...
"Ahem!" He quickly took back the test paper and changed the subject, "Mr. Lagrange, I'm going to do the last two questions."
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