"The answer to the last problem I wrote down was √3/2, too," Shen Qi said.
"That's amazing!" Qi Jianhong said excitedly.
"It's all right, little brother Jianhong. Not that amazing." Shen Qi smiled. Ever since the National Preliminary, this little brother had blindly worshipped him. What a pain. The burden of being a big shot was so heavy.
Qi Jianhong explained, "Oh, no, no. I mean I'm amazing."
Shen Qi was embarrassed. "What the hell are you amazing for?"
"I actually got one problem right on the National Final paper! Bro, tell me, am I amazing or not? My answer's the same as yours, √3/2, which means I got it right." Qi Jianhong was pretty pleased with himself.
"You're so annoying. Shoo, go cool off somewhere else." Shen Qi picked up the Mathematical Herald again and continued reading.
Qi Jianhong asked, "You got all three problems right in the first half of the National Final, didn't you?"
"I just did them for fun. Depends on my mood."
"Bro, you're rock solid!"
The other team members returned to the dorm one after another. They discussed the exam, and most of them agreed that the National Final paper was ridiculously hard. Getting even one problem right deserved a prayer of thanks.
Teacher Tian hadn't set any strict targets for the team. He'd heard that one contestant from the powerhouse Zhedong Province had fainted during the exam and been unable to continue answering the questions. With no choice, the contestant had withdrawn, crying uncontrollably. After waking up, he fainted from crying again, and the Chinese Mathematical Society had brought in a counselor to provide psychological support.
At least the psychological resilience of the team members from their province was up to par. They weren't the so-called fragile types, and Teacher Tian was very pleased. He told them, "Our trip to the capital is almost over. Tomorrow, there are just three problems left. I hope you see it through to the end and come away with something, so you won't have any regrets about your youth. Being good at math may not make you rich, but you must remember: mathematics is the only language with which to speak to God."
Shen Qi raised his bottle of mineral water and spoke with passion. "Teacher Tian put that beautifully. Come on, let's down this cup of chicken soup!"
"Cheers!"
"Cheers! This chicken soup is all-natural and organic, and it's non-toxic!"
The team members raised their colas and Sprite, then downed them in one go, their spirits soaring.
"You bunch of little brats..." Teacher Tian laughed helplessly. He liked the atmosphere on the team. They were like a completely different group from a few days ago.
The stars shifted, the heavens changed, the moon sank beneath the Milky Way, and the sun rose in the east.
Time really flew. Before they knew it, the next day had arrived.
As mentioned earlier, the National Final was divided into two halves. Yesterday's four and a half hours spent solving three problems had been the first half. Today, the second half would also last four and a half hours, with the remaining three problems.
It was a war of endurance, testing not only the contestants' mathematical ability but also their perseverance and mental fortitude. Most of them weren't even legally adults yet.
It was almost over. The results were about to be revealed.
The second-half paper for the National Final had been handed out, and Shen Qi settled down to take the exam.
The first-half papers had all been sealed the previous day. They would be unsealed after four and a half hours, and all six problems from both halves would be graded together.
Shen Qi was confident he could score highly on yesterday's three problems, but the battle wasn't over yet. He had to fight to the end and couldn't afford to be careless.
Outside the exam hall, Shen Qi was lively by nature. But once he had a pen in hand and the paper spread out before him, he immediately entered battle mode. Come on, let's fight!
The first problem of the second half of the National Final asked: What are the complex roots of P(x+iy)?
Shen Qi thought for a moment, then began writing.
Integers, fractions, irrational numbers, negative numbers, and complex numbers—the world of number systems was simple, yet complex.
Apart from complex numbers, which existed in a hazy way on paper and in academic research, the other number systems were used every day by ordinary people. Mathematics might seem abstract and profound, but in truth, it was the basic discipline most widely used in everyday life.
Mathematics could be used to buy groceries, settle accounts, trade stocks, and manage finances. It could also serve as the only language for speaking to God and glimpsing the vast universe. It stood high above us, yet was everywhere in the streets and markets.
Proofs and calculations based on pure number systems were algebra in its purest form. Although most mathematicians favored geometry, algebra still held an important place.
What were the complex roots of P(x+iy)?
Where had it come from, and where was it going?
The first university textbook Shen Qi had studied on his own was Advanced Algebra. He liked Cauchy, though Cauchy also gave him a headache.
In any ranking of the greatest mathematicians in history, no matter the country, Cauchy would certainly have a place. He was absolutely a level-15 reference template—though the system had sampled Gauss instead.
The reason Shen Qi liked Cauchy was that Cauchy had advanced algebra single-handedly. His contributions to algebra were unparalleled.
The first problem in the second half of the National Final would inevitably require Cauchy's Theorem.
Shen Qi quickly found the product of the differences between the two roots, known in algebra as the discriminant. It was a sharp blade; in its presence, linear combinations of polynomials and derivatives were utterly helpless, crumbling in defeat.
P(x+iy) was a cowardly wimp, hiding behind a polynomial in x and cowering out of sight. It relied on the defensive tower of "the discriminant is not zero" to wear down Shen Qi's minions.
"Heh. You think I'm afraid to dive under the tower and kill you? Heh. You're too naive, P(x+iy)."
Shen Qi unleashed his ultimate move with sweeping force. Protected by the shield of d'Alembert's Rule and backed by Cauchy's Theorem, he charged straight under the defensive tower of "the discriminant is not zero." With brutal efficiency, he tore P(x+iy) apart into u(x,y)+iv(x,y), then emerged unscathed.
Under Shen Qi's powerful, fierce assault, P(x+iy) instantly lost the will to resist and obediently handed over its most precious secret: a+bi.
The first problem of the second half of the National Final had been defeated.
When you had the advantage, you had to press it. There was no room for mercy in a math competition.
After algebra came geometry.
The second problem was an Analytic Geometry problem, much like the order of yesterday's problems.
Plane Analytic Geometry at the high school level was the foundation of Coordinate Geometry. The figures in a coordinate system looked like ripples or butterflies. Symmetry had its own harmony, while asymmetry had a rhythmic beauty of its own.
The simpler a girl seemed, the harder it often was to win her over and conquer her, because the conditions she set were strict.
Shen Qi spent a full hour thinking about this problem. He could draw a lemniscate, a quadratrix, or a folium; every curve in the coordinate system represented a meaning and corresponded to an answer.
Shen Qi had to get through the fog of coordinates as quickly as possible and find the most beautiful, most correct curve.
"Yes, that's it. A logarithmic spiral."
Shen Qi finally began writing. He had encountered logρ=aθ, a curve that looked like a seashell or a snail. Round and round she went, until at last she passed through the point o where the x-axis and y-axis intersected.
There were countless beautiful faces, but only one final destination. The beautiful girls of the coordinate system—the curves—no matter how demanding they were, would eventually pass through the origin and return to their simple, unadorned beginnings.
"Done!"
Two and a half hours had passed. Shen Qi had completed the first two problems of the second half of the National Final. Counting yesterday's three, he had finished five problems in total.
"Phew..." Shen Qi took a deep breath and rested for a moment. A few months ago, he wouldn't have dared imagine that he might get to compete in China's top high school math contest and become one of the TOP 60. Oh, no, no—one contestant had fainted and withdrawn, so it was TOP 59.
Now, he was only one small step away. Shen Qi might soon touch the first gold medal of his life: a national-level mathematics gold medal.
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