Completing the Answer Sheet

Shen Qi knew that the people who created the Math League national exam papers were renowned mathematicians in China, while those who created the IMO international exam papers were world-renowned mathematicians.

Last year, the national exam papers were jointly created by the Deputy Director of the Institute of Mathematics of the Chinese Academy of Sciences, and mathematics professors from Tsinghua University and Fudan University. The IMO finals papers last year were jointly created by mathematics professors from Princeton University, Trinity College Cambridge, and the University of Tokyo.

The creators of this provincial semi-final exam paper must certainly be experts with standing in the provincial mathematics community.

The Vice President of the Provincial Mathematics Society was about 1.6 meters tall, with a few sparse strands of gray hair on his forehead. His lips were thin, and when he spoke, he revealed a mouth full of yellow, smoke-stained teeth, clearly indicating he was a heavy smoker.

Shen Qi would believe it if someone said he was an uncle haggling at the market. But to call him a provincial mathematics expert made Shen Qi feel sad. Could it be that mathematicians, as they reach the later stages of their careers, all turn out like this? The more advanced the academics, the lower the appearance?

"Expert, since you're the one who made the exam, take a look then." Shen Qi compromised. Go ahead and look, it's your turf, what else can I do?

The Vice President smiled without speaking, took two steps back, maintaining a safe distance.

Shen Qi calmed his emotions and continued working on the final Geometry problem.

This problem was difficult, and also very interesting.

The problem required the solver to draw a schematic diagram of the motion of planets in the Solar System, using only ellipses, straight lines, and points.

At first glance, it seemed like a physics or astronomy problem.

But without understanding mathematics, it would be difficult for the solver to draw the correct diagram.

And if one only understood mathematics, and knew nothing about basic physics or astronomy, they also couldn't provide the correct diagram.

"Interesting, quite interesting." After drawing the first ellipse, Shen Qi pondered his next move.

To provide the correct answer, one needed at least three basic pieces of physics or astronomy knowledge: that the Solar System has eight planets, that they revolve around the Sun while also rotating, and Kepler's First Law.

The fact that the Solar System has eight planets is common knowledge. In 2006, the International Astronomical Union redefined Pluto as a dwarf planet, removing it from the list of the nine major planets in the Solar System, hence there are eight planets.

Venus, Mars, Mercury, Jupiter, Saturn, Earth, Neptune, and Uranus all revolve around the Sun; this is also common knowledge, something even elementary school students know.

Kepler's First Law states: "The orbit of every planet is an ellipse with the Sun at one of the two foci." This law is recorded in high school physics textbooks.

In reality, many high school students possess a vast amount of knowledge across various subjects. This information is scattered in their brains, stored in fragmented pieces. If they cannot connect it logically and effectively, they will frustratingly realize, I've read so many books, but I still can't solve problems! I can't even start on those comprehensive, difficult questions.

This is where the importance of mathematics becomes evident. Mathematics is a powerful, universal tool that serves all natural sciences. It provides concise and effective mathematical descriptions and a focused, logical way of thinking.

Even Newton couldn't perfectly explain astronomical, mechanical, and optical phenomena using purely physical language, so he invented Integral Calculus. He used mathematical language to explain physical phenomena and celestial motion. Einstein did the same, as did Kepler.

Kepler's First Law is only one sentence long. It took Kepler a vast amount of mathematical theory to derive this sentence. He was an all-around scholar, highly accomplished in astronomy, mathematics, and optics.

Aside from mathematics, Shen Qi's other subject stats were all level 1, including physics.

A level 1 physics stat was just barely enough. What Shen Qi needed to do was to explain Kepler's First Law using geometric drawing methods. He designated point S to represent the Sun, and points A, B, C, D, E, F, G, and H to represent the eight planets of the Solar System.

Explaining planetary motion in the Solar System using geometric drawing also involved some algebraic calculations. For example, taking Earth's orbital period and its semi-major axis as units of time and distance, this essentially forms a system of equations. Kepler spent seven years using complex algebraic methods to solve this system of equations. Newton and Leibniz were not yet born when Kepler died, so Kepler did not know about the existence of Integral Calculus, which was like a cheat code.

Shen Qi was not yet born when Newton and Leibniz died, so Shen Qi knew how to technically use Integral Calculus.

By combining geometric drawing methods with Integral Calculus, Shen Qi had grasped the laws of planetary motion in the Solar System and described them using his mathematical approach.

Of course, two-dimensional drawing is only a simple quantitative and qualitative representation. A two-dimensional diagram can only illustrate a schematic. A precise explanation in higher dimensions was beyond Shen Qi's current mathematical level.

Watching Shen Qi about to solve the final problem, the Vice President's emotions were complex: "This young man, Shen Qi, from Nangang Second High School is a talent! I remember eight years ago, his school produced a math prodigy. The tides have turned, and after many years of dormancy, Second High School has finally erupted."

In a total of 2 hours and 35 minutes, Shen Qi completed all three major problems on the semi-final exam paper. After reviewing it, he submitted his paper and left the examination hall.

Five minutes later, the Vice President announced, "The 3-hour exam time is up. Please submit your papers."

"Difficult!"

"Too difficult!"

"I only managed to do one 5-point question in 3 hours, the rest of the time I was just spacing out!"

"Despair!"

The remaining 11 contestants complained about the difficulty of the semi-final exam paper, with none confident of achieving a perfect score.

All 12 contestants, including Shen Qi, remained at the Provincial Mathematics Society headquarters for lunch.

Meanwhile, the grading work was proceeding at full speed.

Including the Vice President, 12 judges simultaneously graded the 12 semi-final exam papers, one paper per judge.

The grading progressed quickly, with preliminary results available after 10 minutes.

"He Tao, Zhudao First High School, 5 points."

"Luo Ming, Nangang City Foreign Language School, 35 points."

"Qian Shengyi, Qingjiao Experimental Middle School, 20 points."

"Tang Zhengwei, Zhanyang Middle School, 20 points."

"Shen Qi, Nangang Second High School, 60 points." The Vice President personally graded Shen Qi's semi-final paper.

"Shen Qi, him again?"

"He actually got a perfect score again?"

"Is this student Shen Qi really that amazing?"

"The difficulty of the semi-final paper is several times that of the first test."

The other judges expressed surprise. Among the 12 contestants, only Shen Qi received a perfect score of 60. The second-highest score was 35, achieved by three contestants who tied for second place.

The Vice President nodded. "The initial review results are indeed as stated. Only Shen Qi received a perfect score, leading the second-place contestants by a full 25 points. Now, we will begin the second review. Please exchange the test papers you have."

"Give me Shen Qi's paper, I'll review him."

"Me, me! Give me Shen Qi's paper!"

"Old Qin, I remember you graded Shen Qi's First Test paper. It's someone else's turn to grade the second review paper, right?"

"Old Qu, take this pack of cigarettes. They're 'He Tian Xia', over a hundred yuan a pack at the store. Give me Shen Qi's second review paper to grade."

"'He Tian Xia' is so impressive? Old Qin, you think I'm so poor I can't afford good cigarettes?"

"Old Qu, why do you always have to pick a fight with me? I think you should change your name to 'Old Pick-a-Fight'."

"What's wrong with picking a fight with you? I'll pick a fight with you to death!"

The judges began to argue amongst themselves, vying for the right to review Shen Qi's second test paper.

The Vice President flew into a rage. "What kind of conduct is this! What kind of conduct! You're all highly educated intellectuals, what are you arguing about! A'Ping, make 11 copies of Shen Qi's paper. Each judge gets one, and we'll review it simultaneously."