"Andrew Wiles. Actually, I've heard of him. He's a giant in contemporary mathematics," Shen Qi said. His eyes never left Wiles on the stage.
Zhou Yu'an looked at him as if it were obvious. "Of course you have. He won the Fields Medal and proved the fiendishly difficult Fermat's Last Theorem. Who in mathematics hasn't heard of Wiles?"
"But we had no idea that old man was Wiles!" they exclaimed in unison.
"Why would someone that important go to the supermarket himself to buy salad dressing?" Shen Qi wondered. Even his dad, a small-time business owner, never went to the supermarket. If he needed anything, he just told his staff to get it.
"Hey, Shen Qi, Zhou Yu'an, what are you two whispering about? Are you friends with Professor Wiles?" the deputy team leader asked.
Shen Qi shook his head. "Not really, but I know Professor Wiles is a mathematical expert with an incredible depth of knowledge. He might be the best around here."
"As if you need to tell me that. Quiet down and listen to Professor Wiles read the contest rules. It's a rare honor for the organizers to have him as head of the jury." The deputy team leader put his earpiece back in. It was connected to a simultaneous translation device.
"Who would've thought that in the same city, there'd be a weakling who couldn't subtract numbers under ten and a master of the Mathematics Community? The gap between them is enormous. It's like the difference between a total scrub and a god of war." Shen Qi put on his earpiece and listened to Wiles read the contest rules.
"...That concludes the reading of the contest rules. Children, the last thing I'd like to say is this: where there is number, there is beauty. The work we do is beautiful, and it is worthy of our lifelong devotion." Wiles's closing words came from the Greek mathematician Proclus. He had quoted the same passage at the 1998 Fields Medal ceremony, and now he quoted it again.
Applause thundered through the auditorium. The British, the foreigners, the Europeans, the Americans, the Asians, the contestants from every country, the coaching teams, and even the security guards keeping order—all paid Wiles their highest respect.
People seemed to forget that Wiles wasn't the star of this year's IMO. He was only a juror, simply reading out the contest rules as part of his duties.
But did that matter?
Shen Qi was deeply moved. So this was what it meant to reach the very top of one's field: boundless glory and the respect of the world, regardless of nationality, skin color, or race.
"I hope that one day I can achieve something as great as Professor Wiles. Now that's what it means to bring honor to your family and rule the world!"
Shen Qi felt that he'd gained a lot from this trip abroad. Some things had to be experienced firsthand; otherwise, you could never feel the kind of shock that reached down to your soul.
Professor Wiles had served up a hearty bowl of inspiration to more than six hundred young contestants from 102 countries. The rising stars of Europe, Asia, the Americas, Africa, and Oceania were raring to go. The contest was about to begin.
On the morning of July 26, the first day of this year's IMO got underway at the University of South Bank, London.
Professor Wiles, the head of the jury, had clearly explained the contest rules and schedule. There were six problems in total, three today and three tomorrow. Each problem was worth seven points, for a maximum score of 42.
Each contest day lasted four and a half hours. Contestants could bring any stationery or drawing instruments they wanted, but no electronic devices were allowed in the venue.
Since the contest lasted so long, contestants could bring their own food and drinks, as well as up to three reference books.
Right, it was an open-book exam. You could eat and drink and even look things up.
The IMO seemed so easy. Almost like summer camp.
But was that really the case?
Obviously not.
Shen Qi had brought muffins and teddy-bear biscuits, bottled water, and a can of Red Bull from a local supermarket. His three reference books were An Introduction to Analysis, The Art of Conjecture, and Studies in Analytic and Differential Geometry.
When Shen Qi got the first day's test paper, he realized that the three reference books were pretty much useless. The teddy-bear biscuits and Red Bull were what he really needed.
The three problems on the first day's paper had already been translated into Chinese. Shen Qi had to crack the first one first, because it was the threshold problem.
A line of cold Chinese characters was printed on the paper: "Problem 1, threshold problem. A correct answer earns 7 points. An incorrect answer or no answer earns -7 points."
This threshold problem was downright vicious. If you got it right, you could earn a maximum of seven points. If you got it wrong or left it blank, did you think you'd get zero? Not a chance.
Read it carefully: an incorrect answer or no answer to the threshold problem earned -7 points.
That meant the floor for this IMO paper wasn't zero. It was -7.
One careless mistake, and you were done for.
You'd come all the way to Great Britain and go home with a negative score. Wouldn't that be humiliating?
Zero scores had finally had their day. After all this waiting, the moment had finally arrived.
Shen Qi didn't dare be careless. He read the threshold problem for the third time:
"An Oxford University mathematics professor has three clever students. Their names are Tom, Jerry, and Thomas."
"One day, the professor wanted to find out which of the three students was the cleverest."
"He stuck a slip of paper with a number on it to each student's forehead."
"Tom, Jerry, and Thomas could each see the numbers on the other two students' foreheads, but not the number on their own."
"The professor said, 'The number on each of your slips is a positive integer, and two of the numbers add up to the third. So, Tom, what number is on your forehead?'"
"Tom said, 'Sorry, Professor, I don't know.'"
"The professor then asked Jerry, 'Hey, Jerry, what about you? Do you know what your number is?'"
"Jerry said, 'Sorry, Professor, I don't know.'"
"The professor continued, 'Thomas, my dear, you're the only one left. What's your answer?'"
"Thomas said, 'Sorry, Professor, I don't know.'"
"'That's all right, Tom, Jerry, and Thomas. Let's try again,' the professor said."
"The second time, Tom and Jerry still couldn't say what their numbers were, but Thomas gave his number: 144."
"The professor nodded. 'Congratulations, Thomas. Your answer is correct.'"
"If you understood the little story above, what are the numbers on Tom's and Jerry's foreheads, respectively? ( ), ( )."
That was the entire first threshold problem. A correct answer earned 7 points; an incorrect answer or no answer earned -7.
Shen Qi knew that in the face of this deadly threshold problem, Real Analysis and Stieltjes integral, the Cayley transformation matrix and Weierstrass quadratic form, hyperelliptic integrals and Abel's theorem... all those advanced mathematical formulas, theorems, and corollaries were useless.
It was a pure logic problem, chosen as the threshold problem by a vote of the team leaders from 102 countries.
No matter what reference books you brought, they wouldn't help. What you really needed was a middle-school math textbook.
The only mathematical knowledge required was addition, subtraction, multiplication, and division with numbers under 500, along with the ability to solve simple linear equations.
What remained could be summed up in two words: brainpower.
The international rules seemed different from China's. Shen Qi didn't even have to think to know that the Chinese team leader had voted against making this a threshold logic problem. But the minority had to defer to the majority, so that vote had made no difference.
Chinese students were good at solving problems by applying set methods, while the international scene placed greater emphasis on young people's logical thinking.
Shen Qi fell into deep thought. It was only after arriving at the international competition that he realized what could take on the whole world wasn't some profound theory, but the times table and the simplest linear equations.
He got a bit of an idea and followed the clues to derive three necessary conditions, then wrote down a system of linear equations.
Now, whether he got seven points or minus seven came down to pure brainpower.
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