Shen Qi knew that the papers for the national Math League competition were set by renowned mathematicians from across the country, while the papers for the IMO International Competition were set by internationally renowned mathematicians.
Last year's national competition paper was jointly set by the deputy director of the Chinese Academy of Sciences' Institute of Mathematics, a Tsinghua mathematics professor, and a Fudan mathematics professor. The paper for last year's IMO finals was jointly set by a Princeton mathematics professor, a mathematics professor from Trinity College, Cambridge, and a mathematics professor from the University of Tokyo.
The person who had set this provincial semifinal paper was definitely a respected expert in the province's Mathematics Community.
The Provincial Mathematics Society's Vice President stood a little over five feet tall. A few sparse, withered strands of hair hung over his forehead, and his lips were thin. Whenever he opened his mouth, he revealed a set of yellow, smoke-stained teeth. He was obviously a heavy smoker.
Shen Qi could believe he was some uncle haggling at a market. Calling him a provincial mathematics expert made Shen Qi feel sad. Did everyone who worked in mathematics end up like this late in their careers? The more advanced the scholarship, the more down-at-heel the scholar's appearance?
"Since you're the expert who set the paper, why don't you take a look?" Shen Qi gave in. Go ahead and look, if you want. This is your turf. What can I do?
The Vice President smiled without answering, then stepped back two paces to keep a safe distance.
Shen Qi steadied himself and continued working on the last geometry problem.
It was a difficult problem, and an interesting one.
The problem required contestants to draw a diagram showing the motion of the planets in the Solar System, using only ellipses, straight lines, and points.
At first glance, it looked like a physics or astronomy problem.
But without a grasp of mathematics, it would be difficult to draw the correct diagram.
And someone who understood only mathematics, with no knowledge of even basic physics or astronomy, couldn't draw it correctly either.
"Interesting. Very interesting." After drawing the first ellipse, Shen Qi pondered his next move.
To get the correct answer, he needed at least three basic facts from physics or astronomy: the Solar System had eight planets, they all rotated on their axes while orbiting the Sun, and Kepler's First Law.
It was common knowledge that the Solar System had eight planets. In 2006, the International Astronomical Union had reclassified Pluto as a dwarf planet and removed it from the list of the Solar System's nine planets, leaving eight.
Mercury, Venus, Earth, Mars, Jupiter, Saturn, Neptune, and Uranus all orbited the Sun. That was common knowledge, too. Even elementary school students knew it.
Kepler's First Law stated: "The orbit of every planet is an ellipse with the Sun at one of the two foci." The law was covered in High School Physics textbooks.
In fact, many high school students had accumulated a great deal of knowledge in all sorts of subjects. But it sat scattered throughout their minds, stored as disconnected fragments. Unless they could link it all together through sound reasoning, they would find themselves lamenting, "I've read so many books, but I still can't solve problems! When I face a complex question like this, I don't even know where to start."
That was where the importance of mathematics came in. Mathematics was a powerful universal tool, serving all the natural sciences. It provided concise, effective descriptions and a logical framework for connecting and focusing ideas.
Even Newton couldn't fully explain astronomical, mechanical, and optical phenomena using physics alone, so he developed calculus and used mathematics to explain physical phenomena and the motion of celestial bodies. Einstein had done the same, as had Kepler.
Kepler's First Law could be stated in a single sentence, but deriving it had required a great deal of mathematical theory. Kepler was a polymath with outstanding achievements in astronomy, mathematics, and optics.
Apart from mathematics, all of Shen Qi's other subject ratings were Level 1, including physics.
His Level 1 physics rating was just enough. He planned to explain Kepler's First Law through geometric constructions. He marked the Sun as point S, and the Solar System's eight planets as points A, B, C, D, E, F, G, and H.
Explaining planetary motion through geometric constructions also involved some algebra. For example, using Earth's orbital period and its semimajor axis as units of time and distance formed a system of equations. Kepler had spent seven years solving that system with laborious algebraic methods. When he died, Newton and Leibniz had yet to be born, so he had no idea that calculus existed—a tool that might as well have been a cheat code.
Newton and Leibniz had both died before Shen Qi was born, so Shen Qi knew how to use calculus as a technical tool.
By combining geometric constructions with integral calculus, Shen Qi had figured out the motion of the planets in the Solar System and described it mathematically.
Of course, a two-dimensional drawing could only provide a simple quantitative and qualitative depiction. It could show a diagram, but even at his current level, Shen Qi couldn't provide a precise description in higher dimensions.
As he watched Shen Qi close in on solving the last problem, the Vice President's feelings grew complicated. "That kid Shen Qi from Nangang Second High School is a real talent! I remember they had a math prodigy eight years ago. What goes around comes around. After years of silence, Second High School has finally made a comeback."
It took Shen Qi a total of two hours and thirty-five minutes to complete all three problems on the semifinal paper. After checking his work, he handed it in and left the exam room.
Five minutes later, the Vice President announced, "The three-hour exam is over. Please hand in your papers."
"Hard!"
"Way too hard!"
"I only managed one five-point question in three hours. I spent the rest of the time staring into space!"
"I'm doomed!"
The other eleven contestants all complained that the semifinal paper had been far too difficult. Not one of them was confident of getting a perfect score.
All twelve contestants, including Shen Qi, stayed at the Provincial Mathematics Society headquarters for lunch.
Meanwhile, the grading was already in full swing.
All twelve judges, including the Vice President, graded the twelve semifinal papers, one each.
The grading went quickly. Preliminary results were ready after ten 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 had personally graded Shen Qi's semifinal paper.
"Shen Qi? Him again?"
"He got a perfect score again?"
"Is this Shen Qi really that incredible?"
"The semifinal paper was several times harder than the First Test."
The other judges were astonished. Shen Qi was the only one of the twelve contestants to score a perfect 60. Three contestants tied for second place with 35 points.
The Vice President nodded. "That is indeed the preliminary result. Shen Qi is the only one with a perfect score, leading the second-place contestants by a full 25 points. Now we'll begin the second review. Please exchange the papers you have."
"Give me Shen Qi's paper. I'll review it."
"Give it to me! Let me review Shen Qi's paper!"
"Old Qin, I remember you graded Shen Qi's First Test paper. Surely it's someone else's turn to review his semifinal paper?"
"Old Qu, I'll give you this pack of cigarettes—Heaven and Earth. They cost over a hundred yuan a pack at the store. Let me review Shen Qi's semifinal paper."
"So what if they're Heaven and Earth? Old Qin, do you think I'm so poor I can't afford good cigarettes?"
"Old Qu, why are you always picking fights with me? You should change your name to Old Quarrelsome."
"What's wrong with picking a fight? I'll fight you to the death!"
The judges actually started arguing over who would get to review Shen Qi's semifinal paper.
The Vice President flew into a rage. "What kind of behavior is this? You're all Senior Intellectuals, and you're squabbling like this? A-Ping, take Shen Qi's paper and make eleven photocopies. Give one to each judge so they can all review it at the same time."
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