Oh, So That's How It Is

"Algorithm, I understand!" Xiao Junlong was exceptionally intelligent, and he quickly grasped the essence from Witten's hints.

"Xiao, come on," Witten said with a smile, handing a paper cup to Xiao Junlong.

Xiao Junlong used his Fingertip Divine Skill to poke a hole in the bottom of the paper cup.

Some men have a habit of growing their little fingernail long, like Xiao Junlong. This habit is mainly due to scientific research considerations, as it makes it easier to poke things like paper cups.

With his left hand pressing the water dispenser switch, Xiao Junlong used his right hand to hold the paper cup suspended in the air to catch the water.

Under the combined influence of the water dispenser's Fluid Mechanics and Earth's gravity, the water column penetrates the hole at the bottom of the paper cup and flows into the dispenser's trough.

"Through this experiment, we observed that when the water flow speed remains constant, no matter what additional external force I apply to the paper cup to cause its deformation, the final result is always the same: all the water in the paper cup will leak out." Xiao Junlong looked at Witten and said admiringly, "Professor Witten is a true master. He used the simplest experiment to reveal the essence of the most difficult problem to solve."

Witten maintained a mysterious smile and remained silent. Shen Qi asked, "So, Dr. Xiao?"

After finishing the simple experiment, Xiao Junlong went to the whiteboard and wrote a few lines of formulas on it with a water-based pen, "There are many Finite Element Algorithm that satisfy the velocity-pressure conditions. Inspired by this experiment, we can initially determine that the Local Gauss Integral Algorithm is an effective way to solve the general solution of the Navier-Stokes equations with universal significance. Therefore, the next step should focus on the Local Gauss Integral Algorithm."

"Yes, Dr. Xiao's point of view is feasible." Zhou Yu'an also thought so, but he was a step too slow to react, allowing Xiao Junlong to show off his perception first.

Shen Qi remained noncommittal. He asked Witten, "What do you think, Edward?"

Witten walked up to the water dispenser, squatted down, and did something unexpected.

Witten tilted his head, opened his mouth, aimed his mouth at the water outlet, and pressed the water outlet switch with his hand.

The water jet cascaded down and flowed into Witten's mouth.

"What?" Zhou Yu'an was dumbfounded.

"What kind of operation is this?" Xiao Junlong frowned, completely baffled.

"Could this be..." Zhou Yu'an suddenly realized, trembling with excitement. "I remember when I was doing my PhD at Princeton, Professor Faltings got drunk one night and mentioned an incredible algorithm to me, the Infinite Flow Algorithm for Partial Differential Equations!"

Xiao Junlong fell into deep thought, "Infinite Flow? Do you want to know the meaning of life?"

Zhou Yu'an: "Don't get sidetracked, Lao Xiao. You don't understand what infinite flow is at all! In short, it's an exact, unrestricted algorithm for solving the unstable parameters of the Navier-Stokes equations with high Reynolds Number!"

"Is there really such an algorithm? But that statement itself seems contradictory!" Xiao Junlong looked skeptical. His Doctoral Supervisor had never taught him anything about Infinite Flow Algorithm; he had never even heard of them.

At this moment, Witten finished his experimental demonstration, stood up, nodded to Zhou Yu'an, and said, "I discussed the Infinite Flow Algorithm for Partial Differential Equations with Professor Faltings. It only exists in a very small academic circle and has not been publicly reported."

Witten turned to Shen Qi: "Qi, you should know about this algorithm; it's an original creation of Princeton."

Shen Qi said, "Yes, I know, and I've studied it. But the problem is that the Infinite Flow Algorithm for Partial Differential Equations is similar to the Navier-Stokes equations. It has applications, but its propositional correctness has never been thoroughly proven, which is why it hasn't been publicly reported. In other words, using the Infinite Flow Algorithm to solve the Navier-Stokes equations is equivalent to using one hypothesis to verify another. We don't need hypotheses now; what we need is 'Euclid axioms'."

Several people present could recite Euclid's academic contributions fluently.

Euclid derived 23 definitions and 467 propositions from ten axioms, thus constructing the classic and immortal Euclidean geometry system.

Axioms are common-sense knowledge, basic propositions that do not require further proof.

Theories built on assumptions cannot be widely accepted by the academic community. Shen Qi needs impeccable "axioms." Even if he can't come up with ten, he would be happy with just one.

"Therefore, proving the Infinite Flow Algorithm for Partial Differential Equations is a prerequisite for solving the Navier-Stokes equations. Do you agree with my point of view?" Shen Qi asked the group.

Witten: "Agreed."

Zhou Yu'an and Xiao Junlong: "Completely agree."

"Do you have a specific plan?" Zhou Yu'an asked Shen Qi.

"Let me do an experiment too." Shen Qi walked to the water dispenser. At today's academic exchange meeting, the water dispenser was undoubtedly the star of the show.

"Whoa!" Shen Qi let out a shout and pulled the water bottle out with tremendous strength and unparalleled power.

Zhou Yu'an was stunned, Xiao Junlong was dumbfounded, and even Witten looked puzzled.

Shen Qi pressed the water tap, and a trickle of water gushed out of the outlet, before stopping after a while.

"This tactic is called 'drawing the firewood from under the cauldron,'" Shen Qi said in Chinese, then turned to Witten in English: "If the fire under the pot goes out, the food in the pot will never cook properly. The most effective method for proving the Infinite Flow Algorithm of Partial Differential Equations should be the Direct Increment Method or the Decrement Method. This requires further research, but at least we have a direction."

Witten's eyes lit up. "Great idea, let's do it!"

Four men spent the entire day in the conference room discussing and conducting several experiments. They finally reached a consensus: to solve the general solution of the Navier-Stokes equations, they first needed to prove the correctness of the proposition regarding the Infinite Flow Algorithm for Partial Differential Equations. The proof of the Infinite Flow Algorithm should begin with either the Direct Increment Method or the Decrement Method. This proof process would be extremely complex and computationally intensive. The subsequent error analysis would be based on massive amounts of data, which would be difficult for ordinary Computer Science to handle, requiring the use of supercomputing.

In any case, having a clear direction is better than being completely clueless.

Communication is very important. Some issues require collective discussion. By combining the highlights of each person's academic ideas, a powerful collective wisdom can be formed.

Before Witten came to China, Shen Qi's initial solution to the Navier-Stokes equations was a combination of local Gauss integral and Multi-scale Increment Method. This was a level above the algorithm that Xiao Junlong discovered by breaking a paper cup, but it still had a troublesome problem: the algorithm's instability.

Shen Qi, while chatting and discussing with Witten and the others, came up with an even more brilliant move: cutting off the enemy's supply lines.

Witten is a top expert in mathematical algorithms. He created his own mathematical algorithm system to better explain String Theory, for which he won the Fields Medal.

Next, Shen Qi proposed that Witten design the algorithm framework, with Zhou Yu'an and Xiao Junlong assisting, and the NS Equation project entered a substantial progress stage.

The Navier-Stokes equations project has clarified its direction and established its main focus. With Witten leading the team and Shen Qi coordinating behind the scenes, and Zhou Yu'an and Xiao Junlong being the center's most capable mathematical generals, it is an elite team with excellent work style.

Witten might be able to help a little with the project of Mathematical Grand Unification, but at his age, Witten's energy is limited, so don't expect the old man to achieve great things everywhere.

Around 4 or 5 p. m., Shen Qi drove to the entrance of the School of Mathematical Sciences to wait for Ou Ye to get off work.

"Without a great general at hand, Li Zhenqiang is the vanguard." Shen Qi sighed as he sat in the car. The Mathematical Grand Unification is very difficult. It's not that Li Zhenqiang is not good. Li Zhenqiang is also a fierce general. In the Three Kingdoms period, Li Zhenqiang was equivalent to Liao Hua, with a martial prowess of close to 80.

In addition to Liao Hua, Shen Qi also needs at least one super general of the "Five Tiger Generals" level with a combat strength of 95 or above for the project of Mathematical Grand Unification.

"Without a doubt, my wife is this super warrior." Shen Qi knows Ou Ye well; she's due to give birth in a little over three months.

During pregnancy and breastfeeding, it is difficult for Ou Ye to participate in physical activities.

"I'll fill in my wife's number theory gaps first, and once she's back to normal, she can take over." Shen Qi waited in the car until 5:15, Ou Ye still hadn't come out.

Ou Ye is usually very punctual when she leaves work; she leaves the office at 5:00 and arrives at the entrance of the School of Mathematics before 5:05.

"Will nothing happen?" Shen Qi asked nervously; expectant fathers are particularly sensitive at this stage.

Shen Qi turned off the engine, got out of the car, entered the Mathematical Sciences Department, and easily found his way to Ou Ye's office.

"You're so stupid!" came Ou Ye's voice from the office.

Thank goodness, my wife is alright, she's working overtime... Shen Qi felt relieved. He peeked through the crack in the door and saw that Ou Ye was disciplining a little girl, making her cry. The little girl looked so pitiful, sobbing.