The biggest highlight of the entire opening ceremony was the speeches of several mathematics experts who had won the Fields Medal, the Wolf Prize in Mathematics, and the Abel Prize.

Compared with domestic scholars who often give long speeches of half an hour, each of their speeches lasted only three to five minutes, which was very concise. In contrast, there was not much content. They simply summarized the history of IMO in two sentences. Best wishes.

There is not much new idea about the candidates getting good grades and contributing to the future of IMO, etc.

Only Professor Martin, an Austrian Philippine Prize winner, mentioned a few words that touched Qin Ke:

"I appreciate the reform of this IMO, which has made great efforts in the direction of innovation. Mathematics is an interesting thinking game, because it can always constantly introduce new things, and you can always find the joy of 'creation',

Even if it is a very simple theory, when you look at it from a high level, you can still find different mathematical aesthetics and different gains."

“My research focus is mainly on the theory of stochastic partial differential equations. However, in the past two years, I have been invited to assist the motherland in revising the textbooks for middle school students. I have tried to find a new way of thinking that can help middle school students better understand mathematics and learn mathematics.

Mathematics, solving mathematical problems..."

Professor Martin's words were also only about three minutes long, but they greatly touched Qin Ke, because they coincided with what he had been thinking recently, and also gave him some inspiration.

In the past two days, he has been studying S-level knowledge "Exploration and Detailed Solution of Nonlinear Partial Differential Equations 'Navier-Stokes Equations' (Part 1), (Part 2)" in his spare time. Every time he reads it, he feels like

Have new experiences and insights.

The biggest insight is the change in the way of thinking. The reason why "Part 1" and "Part 2" are complicated and difficult to understand is not only because many of the theories are very profound and require extremely high levels of mathematics and physics, but also because their levels are very high.

High. Its thinking mode is not limited to a certain discipline or direction, but directly integrates the knowledge of these disciplines from a higher level that combines theoretical science and practical science to transform theory into practice.

Qin Ke once again looked at his "theoretical results", whether it was the several papers he had written or the "The Wonderful Mathematical Journey of Kitten Lemon and Puppy Keke (First Part)" written by him and Ning Qingjun.

, as well as the "New Mathematical Olympiad Knowledge System" explained to Ning Qingyun during the special training and class for the Mathematical Olympiad training team. The biggest highlight is actually that the way of thinking is at a higher level than the knowledge points, which makes his theoretical achievements more apparent.

Efficient, turning difficult problems into easy tasks.

Then, can my nascent Mathematical Olympiad theoretical system be optimized and improved?

The answer is yes, that is to innovate in the way of thinking, to integrate Olympiad knowledge with a higher vision, and to form a new, more scientific and concise theory.

However, Qin Ke's current Mathematical Olympiad level has reached the peak that all high school students in the world can achieve. In other words, it has also reached a bottleneck period. How easy is it to make progress?

Until the end of the opening ceremony, Qin Ke was still immersed in such thinking, but had no inspiration or breakthrough for a while, so he had to give up temporarily and planned to study it after the game.

After passing the security check and document inspection, and applauding Ning Qingjun, Wang Changai and other four team members one by one at the entrance of the examination room, Qin Ke entered his examination room. In the same examination room with him was Liang Shaoping.

The layout of the examination room for each IMO is determined by the venue, and this time it was naturally arranged by the University of Oslo. Qin Ke was lucky enough to be arranged to take the exam in a simple and elegant auditorium.

The auditorium was huge and could seat nearly two hundred candidates. Qin Ke quickly found his seat. There was already a small pack of biscuits, a piece of chocolate and a small bottle of mineral water on it. The amounts were not large. They were organized for the candidates.

They prepared it to temporarily replenish nutrients during the five-hour exam without having to run to the bathroom frequently.

Some of the candidates around were looking at these biscuits and chocolates very freshly, and they looked like they were newbies taking part in the competition for the first time; some were indifferent, looking calmly at the reference materials they brought, and they should be veterans who had participated in the competition last year.

According to Deng Hongguo, the Asian named Hill on the American team won the gold medal the year before last and the championship last year because he used two different and very creative new methods to solve the last big question last year.

, was unanimously recognized by the judging panel, and he was specifically designated as the champion.

Deng Hongguo regarded him as a strong enemy of Qin Ke and Ning Qingyun.

Coincidentally, Qin Ke recognized Hill at a glance and sat three rows in front of him.

At this time, Hill was turning the pen in his hand with extremely delicate movements, and his expression was very relaxed, even smiling.

His flexible pen-turning movements made people unconsciously marvel at him. His finger movements were as precise as a machine, turning back and forth hundreds of times at an alarming speed, but he never missed it. Judging from his state, as long as he didn't want to stop,

If you come down, it will be like you can go on forever.

Not to mention anything else, just by looking at the precise control of his fingers, you can know how superb his brain is in controlling fine movements. Such a person must also have a super-class IQ.

Another thing that caught Qin Ke's attention was a tall man from the Xiong Kingdom, with blue eyes and very white skin. Different from Hill's movement, he was the other extreme of quietness.

He sat there quietly, as quiet as a stone, with no trace of nervousness or anxiety, and no hint of boredom. He seemed to be relaxing himself and meditating.

As expected of IMO, the most high-end event that gathers Mathematical Olympiad experts from all over the world, Qin Ke was a little more motivated to fight.

Ten minutes later, the DAY1 competition was about to begin. The test papers were distributed five minutes in advance. This was to allow the candidates to review the papers in advance to see if there were any errors or omissions, so they could only read but not write.

Qin Keli finished the paper in three minutes. The questions are indeed difficult. If it is just a conventional solution, Qin Ke is confident that he can complete it within 35 minutes. But if he uses a novel solution, he will need further thinking, which will take about 50 minutes.

.

This chapter is not finished yet, please click on the next page to continue reading the exciting content! How about simply using three solutions to complete the entire paper?

Qin Ke decided to give himself a new challenge.

Firstly, it will make this IMO more interesting, and secondly, it will also ensure that the champion of this year is in the arms.

——IMO has always encouraged the use of multiple solutions, because it has always advocated "creativity". However, the vast majority of candidates have difficulty completing the entire paper within the specified time. Only a few geniuses, like last year

Hill, of the American team, was able to figure out two brand-new solutions to a certain big question with ease.

Before the exam officially started, Qin Ke held up a sign with "HELP" written on it, and immediately a young brown-haired invigilator came over and asked in English: "Excuse me, this student, what do you need?"

Qin Ke said softly: "Can you give me two more answer sheets?"

The invigilator said in shock: "Is there something wrong with the answer sheet in your hand?"

"No, I'm afraid it won't be able to write my answer."

Because there are two more questions in this IMO, the organizing committee specially prepared a larger answer sheet, which can be folded in half to write on four sides. Normally, it is enough. Unexpectedly, some students asked for additional answers early.

paper, and two at a time.

This was the first time the invigilator encountered such a situation. He couldn't make up his mind and ran to ask the invigilator team leader in the examination room. The invigilator team leader unexpectedly looked at the national flag on Qin Ke's desk. This student was from Xia Guo.

Players? Xia Guo used to be considered a first-rate strong team. Unfortunately, it has been on a decline in the past ten years and is now reduced to a third-rate weak team.

He shook his head and said: "The ancient country likes to make mysteries like this, give it to him."

The invigilator received the instructions and quickly brought Qin Ke two answer sheets.

Basically, not many people care about the little things that happen here. Everyone is seizing the time to review the problem. Even if they can't write, they must first look for ideas to solve it.

At this time, the melodious bell for the start of the exam rang, and only nearly one-fifth of the candidates in the examination room began to pick up their pens and move towards the first threshold question.

Naturally, Hill from the American team and the meditation candidates from Xiong Country were among them. They both picked up their pens and answered the questions calmly.

The remaining candidates had bitter expressions on their faces, and some were so anxious that they kept scratching their heads. They were obviously stumped by the first threshold question at the beginning.

In fact, according to convention, the questions on DAY1 will be easier than those on DAY2, and the first question is the easiest among all the questions on DAY1. However, the difficulty of this IMO has increased a lot, and it puts forward higher requirements for flexibility of thinking.

The difficulty of the questions is also randomly distributed. Unfortunately, this threshold question is one of the more difficult in the entire paper, so it stumps four-fifths of the people.

“1,n is a given positive integer, S={(x,y,z)|x,y,z ∈{0,1,2,…,n},x y z is greater than 0} is (n 1

)^3-1 points. Try to find the minimum number of planes whose union contains S but does not include (0,0,0)."

Qin Ke didn't even start writing. This question was not difficult for him. It only took him five seconds to come up with a solution and two slightly innovative solutions.

But just when he picked up the pen and was about to write the answer, inspiration suddenly flashed through his mind.

Inspiration is like a naughty child. When you look for it everywhere, it always hides and hides. But when you don't look for it, it will naughtily appear in front of you.

Qin Ke suddenly thought about the fourth solution to this problem. As long as the difference method is used, the answer can be very simple. However, it requires the use of Lagrange's mean value theorem and partial derivative theory, which are all knowledge levels of college mathematics.

, beyond the scope of high school students.

According to IMO rules, you can only use high school mathematics knowledge and below to solve problems, otherwise you will not get points. If you insist on using college knowledge and theorems to solve problems, it is not completely impossible, provided that you first use high school knowledge.

, you can only quote it after completing the derivation of the theorem.

Let Qin Ke first deduce the relevant knowledge points of Lagrange's mean value theorem and partial derivatives. Of course, it is not difficult to do it, but if you have to write a long derivation process, then this fourth solution is of little significance. After all, Qin Ke

I thought of this solution just because it is "simple".

Can we use the thinking model of college mathematics and the knowledge points from high school to write the most concise solution?

This inspiration passed through Qin Ke's brain like an electric spark. He slowly closed his eyes and tried hard to capture this bit of inspiration.

By the way, why not try it yourself?

Isn't this what I have been thinking about these days, using a higher level of vision and a higher level of thinking to combine and optimize low-level knowledge points to form a new model that is more efficient, simpler, and easier to understand?

Knowledge system?
Chapter completed!