It is a little regrettable to say that undergraduate life is that due to time schedule arrangements, Qin Ke and Ning Qingyun did not participate in this UPC (International University Physics Competition), so when they were flipping through the news in the newspaper at the international airport, they saw Xia Xia

When China participated in the UPC and achieved fairly good results, the two of them still had some feelings for each other.

Speaking of which, the only competition the two of them had participated in as undergraduates was Qiu Sai. The School of Computer Science of the school had invited the two of them to participate in the ICPC (International Collegiate Programming Contest), but it coincided with the selection time of the Mathematics Breakthrough Award and the academic competition.

The report meeting time conflicted, so the two declined.

The two undergraduates spent their undergraduate years as much as possible consistent with ordinary college students, but after all, there are too many differences. With their strength beyond the undergraduate level, participating in these undergraduate-level events is no longer challenging.

Participating in the Qiu competition was just like fun, and I easily won the gold medal in the all-around award.

The only thing that is a bit challenging is probably the ICPC competition in the computer category, but if you miss it, you miss it.

They have not participated in international physics competitions, which means that the two of them did not have any worthy achievements in physics subjects during their undergraduate studies. At most, they published three papers on fluid dynamics in core domestic journals, which did not reach the international level.

.

As for the projects they collaborated with Professors Hu Qingfeng and He Liangfu, although their performance was outstanding, they were the two professors' own projects. At most, the two of them could write a joint work that could be included in their resumes. Compared with the world-beating mathematics, after all,

It's too inferior.

So much so that now, when scholars at home and abroad mention them, their first impression is that they are "Xia Guo's most outstanding young mathematicians." It is often only when someone reminds them that they remember that they actually studied physics.

Qin Ke closed the newspaper and said with a smile: "It seems that when we are in graduate school, we need to spend more energy on physics, otherwise we will waste our main business. It just so happens that the Navier-Stokes equation we want to study is physics and mathematics.

The combination is quite suitable.”

"Yeah." Ning Qingyun nodded lightly: "But this 'Navier-Stokes equation' is truly the most complex formula in the history of mathematics. It is too difficult. If you look at it from the perspective of interdisciplinary understanding,

, the difficulty is even higher than the Riemann Hypothesis.”

Ning Qingyun has been studying the Navier-Stokes equations with Qin Ke for a period of time. The one he has been looking over recently is an article titled "The Memoirs of the Berlin Academy" by Euler in 1757

Article "General Principles of Fluid Movement".

This is the first time in the history of mathematics that partial differential equations are used to simulate fluid flow, and is known as "the most important basic equation in the field of inviscid fluid mechanics."

Although Euler at that time assumed that the fluid was incompressible and had no viscosity in order to obtain some false assumptions. This also made Euler's version of the partial differential equation of fluid flow no longer of much practical value today, but from an academic point of view

Generally speaking, this is still a reference worth reading repeatedly, and it plays a non-negligible role in using mathematics to simulate and solve fluid mechanics problems.

The Chinese engineer and physicist Claude Louis Navier was inspired by Euler's theory, and added the consideration of intermolecular interaction forces to Euler's basic equations, that is, adding

A viscosity constant was obtained, and a set of partial differential equations for viscous fluid flow was derived.

Twenty years later, the Irish mathematician and physicist Sir George Gabriel Stokes, starting from the continuum hypothesis model and based on Navier's system of partial differential equations, derived another equation with two

The fluid mechanics equation of viscosity constant finally formed the Navier-Stokes equation, also known as the N-S equation for short.

Now Ning Qingyun is delving into Euler's document, which is called "the pioneering work of fluid mechanics", and he is studying the Navier-Stokes equation from the source, which is the most authentic path.

It was precisely because of this article that Ning Qingyun once again realized that the relationship between mathematics and physics is so inseparable that almost all physical phenomena and even physical theorems can be expressed in mathematics.

Hearing Qin Ke talk about the Navier-Stokes equation, Ning Qingyun couldn't help but sigh with admiration: "It's even more unbelievable to think that this is a formula derived nearly two hundred years ago.

"

Qin Ke’s understanding of the N-S equation has surpassed that of most people. He encouraged:

"The difficulty of the N-S equation is to use the change rate relationship between differentials to express variables such as fluid speed, pressure, density, viscosity, etc., so that it is difficult to determine under what circumstances it has solutions and the smoothness of these solutions. However, it is difficult to determine.

Although it is difficult, once it is completely cracked, its significance should be greater than the Riemann Hypothesis. Especially in fluid mechanics, the development of computational fluid dynamics will make a qualitative leap. For example, the aerodynamic design of aircraft will not need

Expensive wind tunnels are often used. Just like our usual mathematical modeling, historical data combined with N-S equations can be used to deduce more accurate results. In the end, only one or two actual wind tunnel measurements are needed, which can save money.

Tons of money and time.”

Speaking of this, Qin Ke said with a smile: "Anyway, let's work hard. I heard that our teacher Jiang has been studying N-S equations. If we study with him, we are with the right person."

"Yeah!" Ning Qingyun's eyes were filled with fighting spirit. Mathematics and physics are her favorite fields, especially since the N-S equation has such great application value.

But she added: "We will work hard together, but I still hope you can solve the Riemann Hypothesis first."

"Riemann Hypothesis..." Qin Ke suddenly stretched, a confident light flashing in his eyes: "It's almost here."

"Almost?" Ning Qingyun stood up suddenly, her eyes full of surprise: "You... are you sure you can deduce the fifth set of expressions?"

"I have some idea." Qin Ke nodded.

Since his mathematics level was upgraded to the "Grand Master Level", he has developed mathematical thinking ability and intuition comparable to those of the Philippine Prize winners. His whole person seems to have been promoted to a whole new level, especially his mathematical intuition is even more astonishing. He can often "intentionally or unintentionally"

"You will find the right direction in a short time.

Of course, he was a bit tricky. He held the "Complete Explanation of the Riemann Hypothesis" in his hand. Although he restrained himself from looking at the detailed derivation process of the fifth set of expressions, he had read it several times before, even if he could not understand it all at the time.

, finally I have an impression and know how to deduce it, which is probably the right direction.

This impression coupled with mathematical intuition made it much easier for Qin Ke to derive the fifth set of expressions of the Riemann Hypothesis.

When he and Ning Qingyun were on vacation at the beach a few days ago, his relaxed spirit and continuous research further promoted the explosion of inspiration. Now Qin Ke has vaguely touched on the core idea of ​​​​the derivation, and what is missing is just continuous attempts.

, to find the only correct key to the final destination.

"You...can you complete the derivation process before October?" Ning Qingyun now has almost blind trust in Qin Ke. Qin Ke said that if he is sure, he must be sure, but he doesn't know when it will be done.

That's all.

"If it's fast, it might only take a few days; if it's slow, it might take several months." Qin Ke said confidently: "This is a question of probability. Let's see if I can get lucky and find the correct answer first based on intuition."

At this time, Chen Ming and Chen Lan, who were accompanying them, had come over to remind them to board the plane. Qin Ke and Ning Qingyun could not go into details, so they followed them through the special passage and boarded the plane.

One day later, the two flew to Boston. This year's Steele Prize award ceremony of the American Mathematical Society (AMS) was held in the auditorium of the famous university here, the Massachusetts Institute of Technology (MIT).

As the most important mathematics award held by AMS every year, the awarding process of the Steele Award is comparable to that of the Kohl Award. It consists of an award ceremony plus an academic lecture.

The difference is that the reports of the three winners of the Steele Prize of each session will be arranged on the fifth day, which is the last day of the academic report meeting, as the finale.

The scale of the Steele Award Ceremony and Academic Lecture is naturally not as large as the International Congress of Mathematicians at IMU, but it is still very lively. Members of the American Mathematical Society are eligible to attend, and there are also famous mathematicians from all over the world.

As well as the faculty and students of the host school, even if there are certain restrictions on the number of places, the total number of attendees still exceeds 2,000.

It was the first time for Qin Ke and Ning Qingyun to come to Boston, so they arrived two days early because they naturally wanted to take the time to visit this historic city in the United States.

The city of Boston has a vital influence on the modern history of the United States. It was the "Boston Tea Party" that took place here, which ultimately triggered the famous War of Independence.

Boston is also a famous academic city, home to two world-famous universities - Harvard University and MIT.

It also has a very famous aquarium called the New England Aquarium, which is one of the few super-large aquariums in the world.

Of course, there are also Chinatown and the unique Boston Library, which are all worth visiting.

However, considering safety factors and Chen Ming's recommendation, Qin Ke and Ning Qingyun finally chose only Harvard University, the Aquarium, the Library and Copley Square as their travel route.

There is no need to visit MIT specifically. When you attend the conference, you have a few days to explore slowly.

Qin Ke and Ning Qingyun's short but happy two-day trip passed in the blink of an eye. On their third day in Boston, they ushered in the Steele Award Ceremony.

This year's Steele Award for Lifetime Achievement was awarded to 71-year-old Professor Yevhen Marcus, an emeritus professor at the School of Mathematics at MIT who has made impressive achievements in algebra and geometric topology.

Amazing research results, "Geometric Topology" he published thirty years ago is still regarded as a classic textbook by countless universities. He won the Oswald Veblen Geometry Award and the Mathematics Teaching Influence Award in his lifetime.

The Elie Cartan Award, the National Medal of Science of the United States, the Balzan Prize in Mathematics, the Crafford Prize, and it is said that there is a great chance of winning the Abel Prize, the top award in mathematics, this year.

Such a mathematics master deserved to win the Steele Prize for Lifetime Achievement, and no one had any objections. Therefore, when the old man came on stage to receive the award, the audience applauded like thunder.

Qin Ke received the "Steele Award for Pioneering Research Contributions", and Ning Qingyun received the "Steele Mathematical Review Award". Although the weight is slightly lighter than the Lifetime Achievement Award, it is still the top award of AMS.

One of the great prizes in mathematics.

For these two young mathematicians from Xia Guo, who have rocketed up in recent years and become famous all over the world, the audience in the audience looked a little subtle, especially the proud students of MIT, who looked younger than themselves on the stage.

Qin Ke and Ning Qingyun both expressed surprise and admiration, but some of them always wore colored glasses and felt uncomfortable.

No matter what, when Qin Ke and Ning Qingyun received the medals and certificates, the audience still applauded.

The Steele Award medal is exquisitely carved, and the certificate is also beautifully printed.

This is the first mathematics award of the same level that the two have received after the Breakthrough Prize in Mathematics, the Cole Prize in Number Theory, the Craford Prize, and the Ramanu Gold Medal (unique to Qin Ke). Qin Ke handed the medal and certificate to Ning Qingyun

Keep them together.

Ning Qingyun liked this job very much, and even specially prepared a corner in the study room at home to display Qin Ke and his award certificates.

Whenever she sees two certificates and two medals closely together, the girl feels a sense of joy and fulfillment in working together.

After the award ceremony, the usual dinner party, and interviews with the media, Qin Ke and Ning Qingyun returned to the hotel, both feeling a little tired.

Especially Ning Qingyun, who was physically weak, drank some red wine in the evening and her face was flushed with alcohol, so Qin Ke asked her to go to bed early.

Ning Qingyun took a quick shower and then went to sleep obediently. Of course, before going to bed, she blushed shyly, but her little mouth pouted slightly and asked for a kiss. It was very cute. Qin Ke kissed her hard, okay?

It was easy to control it and let her rest peacefully.

The long journey and two days of intensive sightseeing really made Ning Qingyun exhausted. The girl only lay down for less than three minutes before falling into a sweet dreamland.

Qin Ke's spirit was still good. After practicing the Eastern Secret Code and Wing Chun alone, he felt that his energy was restored and he felt refreshed.

When I opened the window, I saw stars dotted outside. The night in a foreign country was not much different from the night in a domestic metropolitan city. It was just as lively.

Qin Ke was used to this. He picked up his mobile phone and looked at it. Foreign media had already posted the news about the two winning the award online, and the Internet was a hot topic. Many relatives and friends who stayed up late learned about it from the Internet.

After hearing the news, another congratulatory text message was sent.

Qin Ke asked Shiguang to reply on his behalf, while he continued to study the Riemann Hypothesis.
To be continued...