The Correct Way to Handle y(x)+δy(x)
August 15th is Shen Qi's planned departure date. He will fly from China to New York, and from New York to Princeton New Jersey, to begin his overseas studies.
Shen Qi is now in the countdown phase of his departure abroad, and he is inseparable from Ou Ye.
With 154 days left until their departure abroad, Shen Qi and Ou Ye had an in-depth discussion about when equations of the form x^2 - Ay^2 = B have integer solutions.
This is a classic problem, and Fermat was the person who studied Diophantine equation most deeply and made the greatest achievements in this area.
The assumptions of Fermat's Last Theorem were written in a book by Diophantus, but because there was too little space in the book, Fermat mischievously left it unfinished.
Propose a hypothesis, prove the hypothesis, propose another hypothesis, and wait for future generations to prove it.
For centuries, mathematicians have been fascinated by this numerical game.
While teaching at Princeton, Wiles spent ten years writing a paper in which he proved Fermat's Last Theorem, thus completing Fermat's unfinished thesis perfectly.
The numbers game is far from over; Goldbach Conjecture and the Riemann Hypothesis have puzzled number theorists for many years.
These two monumental problems spanning centuries deal with a very simple subject: prime numbers, which are natural numbers that are divisible only by 1 and themselves.
The ultimate proof of the ξ-function model may have to start with the simplest Diophantine equation.
Once the ξ-function model is fully proven, Goldbach Conjecture and the Riemann Hypothesis may be solved simultaneously.
"This is absolutely a monumental achievement, one that will be remembered for generations to come," Shen Qi said to Ou Ye. "This work is entrusted to you; it is the historical mission of number theorists."
"This is so difficult." Ou Ye took the Rubber Band off her wrist and skillfully tied her hair into a ponytail.
"Knowing the difficulty, we must rise to the challenge." Shen Qi patted his left shoulder with his right hand.
Ou Ye obediently turned her head and leaned on Shen Qi's shoulder. "I want to accomplish this great task with you."
Then the movie started.
Oh, by the way, this is a movie theater, one of the three most popular places for couples to visit.
The female protagonist on the big screen was incredibly brave. Wielding a submachine gun, she fired wildly, eliminating an astonishing horde of zombies without taking any damage herself.
The only problem is the zombie boss; conventional weapons can't destroy it.
The zombie boss displayed its might, ripping out a heart with a single claw and biting off a head with a single bite.
All of the female protagonist's teammates were killed, their bodies torn to pieces.
"Hahaha." Shen Qi laughed loudly. He put his arm around Ou Ye and casually untied the Rubber Band of Ou Ye's ponytail.
Ou Ye's ponytail came undone, and her long, straight, black hair cascaded down.
Ou Ye's hair brushed against Shen Qi's cheek, making him feel a little itchy, but her hair smelled wonderful.
The fragrance of hair, body scent, and a faint herbal aroma blend together, creating Ou Ye unique scent that can only be appreciated up close.
Lovers embrace, and even a horror film reveals the tone of a romance.
"Aren't you afraid of my long hair covering my face?" Ou Ye asked softly, her lips close to Shen Qi's earlobe.
"What's there to be afraid of with your own woman? You're not a ghost," Shen Qi said, then added, "Even if you were a ghost, I wouldn't be afraid. I just like female ghosts."
"You're so annoying!" Ou Ye opened her mouth and bit Shen Qi's earlobe, not too hard, not too soft. If she bit too lightly, he wouldn't feel it. If she bit too hard, she was afraid of hurting him.
With 152 days left until their departure abroad, Shen Qi and Ou Ye spent the entire day in the library, each studying their own material, and feeding each other when they got tired.
The same thing happened for the next few days.
Ou Ye's renewed enthusiasm for learning put immense pressure on Zhou Yu'an.
I'm already in the second semester of my sophomore year, and I'm almost halfway through my undergraduate studies. If I don't work hard to catch up now, I'll fall behind.
Zhou Yu'an studied diligently, sleeping only 5 hours a day, and frantically researched integrable systems and Differential Geometry, setting himself a main focus to compete with Ou Ye, who specialized in number theory.
145 days until I leave the country. Today is the weekend.
Shen Qi kept his promise and took Ou Ye to Beidaihe for a vacation. Traveling together is an essential lesson for lovers; as long as their hearts are connected and love prevails, it doesn't matter where they travel.
Ou Ye never mentioned her Switzerland trip again. Instead, she punched Shen Qi in the chest with her little fist. "Beidaihe, Beidaihe, Beidaihe! My parents and I have been here more than five times."
"This is my first time traveling to Beidaihe, it's beautiful." Shen Qi sat on the beach, gazing intently at the night sky.
There were only a few tourists on the beach at night, among them Shen Qi and Ou Ye, a couple.
"He used to call me 'Sweetie,' now he calls me 'Sister-in-law,' haha, men." Ou Ye muttered to herself, drawing circles on the sand with her finger.
"That analogy is inappropriate. You will always be my Zixia, one of a kind." Shen Qi continued to observe the night sky. Tonight was cloudy and windy, with the moon appearing and disappearing intermittently.
Suddenly, Shen Qi grabbed a handful of fine sand and threw it into the air, staring intently at the air.
The sand danced in the wind, scattered by its current.
Shen Qi was focused on the trajectory and dispersion speed of the sand in the air.
During the first atomic bomb test, Fermi threw a handful of shredded paper into the air. By observing with the naked eye and calculating in his mind, he accurately calculated the yield of the atomic bomb based on the trajectory of the shredded paper in the shock wave.
On the beach in Beidaihe tonight, the weather is cloudy and windy. Shen Qi is doing something similar to Fermi: he is calculating the wind speed and direction.
Ou Ye was still drawing circles, so Shen Qi smoothed out the circles Ou Ye had drawn on the beach and wrote down a simple formula in the same spot: y(x) + δy(x).
"Repeating circles has no mathematical meaning, Ou Ye. Can you draw the mathematical curve of y(x) + δy(x)?" Shen Qi asked.
"Super easy." Ou Ye immediately drew a crescent moon on the beach, which is Lagrange variation curve.
Just then, the wind blew away the clouds, and the moon appeared—a crescent moon, exactly like the crescent moon curve drawn by Ou Ye.
Shen Qi's calculations were remarkably accurate, with the time of the moon's appearance having an error of less than one second.
A beautiful day, a lovely scene, and perfect weather—a perfect moment to cherish.
Shen Qi, with his arm around Ou Ye, pointed to the night sky. "Look, how amazing! You just finished drawing the Lagrange crescent curve on the beach, and a real crescent moon appeared in the night sky. I believe this is the power of love."
The waves lapped against the beach, and the bright moonlight shone down, illuminating the y(x)+δy(x) and the crescent curve corresponding to y(x)+δy(x) on the sand.
The scene instantly evoked romance; a woman in love tends to have a lower IQ, and Ou Ye blushed.
"The moon is my witness, Ou Ye, I will always love you and take care of you." Shen Qi pressed his forehead against Ou Ye's, their noses touching. "If I break my promise, I will never be able to draw the correct mathematical curve."
"Don't lie to me." Ou Ye's face turned red to the roots of her neck, her eyes glazed over.
Under the moonlight, Shen Qi kissed Ou Ye.
The kiss was long and lasted for several minutes.
As the lovers' kiss ended, the moon hid behind the clouds in the night sky.
"You... did it on purpose, you timed it perfectly." Ou Ye gasped, her body burning like fire from her first kiss.
Ou Ye liked this feeling; her heart felt like it was about to jump out of her chest. Whether it was intentional or unintentional, it didn't matter.