Chapter 81

Tong Gexiao was truly enraged by Li Yi's unreasonable demands, so the fourth test paper she gave to Li Yi was not a student's test paper at all, but a set of exercises on Riemannian geometry.

Riemannian geometry is a branch of mathematics that extends beyond the Euclidean geometry system, with fundamental axioms that differ from normal geometry.

Euclidean geometry tells us that through a point not on a given line, there is exactly one line parallel to the given line. However, in the world of Riemannian geometry, through a point not on a given line, there are no lines parallel to the given line. This means that in this geometric system, any two lines in the same plane will intersect.

In such a mathematical framework, which is different from the real world and has distorted rules, all problems become ambiguous and require a significant amount of mental effort.

Tong Gexiao is very fond of Riemannian geometry. She is pursuing an in-service doctoral degree at the Capital Normal University, and her dissertation focuses on Riemannian geometry. This means that the questions on this test paper are research topics for doctoral students in mathematics.

Moreover, for Tong Gexiao, who is an in-service doctoral student, this set of Riemannian geometry exercises is quite challenging. She couldn't solve the first few questions and had been struggling with them for several days. Just as she encountered the arrogant Li Yi, she threw the entire set at him.

Aren't you capable? You even dare to make such demands to your teacher! If you are so capable, then solve Riemannian geometry. If you can solve this, the teacher will admit defeat!

In Tong Gexiao's view, no matter how skilled Li Yi is in mathematics, he cannot solve Riemannian geometry. As a high school student, being able to solve Olympiad math problems is already exceptional. If he could solve problems that even doctoral students can't, that would be unbelievable.

However, Li Yi exceeded her expectations once again!

To Li Yi, the Riemannian geometry problems were actually kindergarten-level math problems, not much different from the previous test papers.

Think about it, kindergarteners might find "two plus two equals four" much harder than "one plus one equals two" because they have to count two more fingers, but adults wouldn't see any difference between these two problems. At Li Yi's level, Riemannian geometry and "one plus one equals two" are both basic concepts.

Upon receiving the questions, he wrote down the answers as smoothly as flowing clouds, without a single pause!

Tong Gexiao, with wide eyes, watched Li Yi rapidly write down the equations, her mouth almost dropping open in shock!

Oh my God, the first question is solved like this, so ingeniously, how did I not think of it!

The second question requires such a function transformation, how brilliant!

The third question... Wait, I don't understand this step at all, what's the logic behind it?

When Li Yi finished the entire set of questions, Tong Gexiao was still staring intently at the third question, trying to figure out how Li Yi solved it!

"This mainly involves tensor analysis methods..." Li Yi, seeing Tong Gexiao's puzzled expression, explained casually.

"Oh!" Tong Gexiao suddenly understood, so that's how it works!

Then her gaze towards Li Yi completely changed. Who is this person? He can handle Riemannian geometry so effortlessly? Even undergraduate students in mathematics wouldn't be this good!

And such a genius is actually her student, and his math scores are always in the single digits. Can you believe it?

Li Yi didn't take Tong Gexiao's surprise seriously at all. He pointed to the remaining questions and said, "Do you have any more questions you don't understand? I can explain them to you."

Seeing a student about to explain the questions to her, Tong Gexiao, even if she really didn't understand, felt embarrassed to ask. Recalling her earlier words that if Li Yi could solve the questions correctly, she would let him do whatever he wanted, her face turned as red as the evening sky.

"He must have been joking, he must have been..." Tong Gexiao kept reassuring herself.

Li Yi seemed to have forgotten his earlier teasing and said calmly, "Do you have more questions?"

Tong Gexiao, seeing Li Yi's smug expression, felt a surge of anger. She loudly replied, "Yes!"

She grabbed a blank sheet of paper and quickly wrote on it. Li Yi glanced over and saw, wow, the Goldbach Conjecture!

The Goldbach Conjecture is a hypothesis proposed by the 18th-century German mathematician Goldbach, but he couldn't prove it. He wrote to the famous mathematician Euler for help, but Euler couldn't prove it either, even until his death.

To this day, the Goldbach Conjecture has been circulating in the mathematical community for nearly three centuries, and countless mathematicians have studied it, but none have been able to prove it.

After writing the Goldbach Conjecture, a hint of smugness flashed in Tong Gexiao's eyes. Aren't you capable? Let's see if you can handle this!

"If you can prove this problem, the teacher doesn't need to give you that. I would even sell myself to you!"

"This problem is quite complex, and there isn't enough space on this paper!" Li Yi sighed, looking at the blank sheet of paper. "I'll write an electronic document for you when I have time!"

"Alright, stop pretending, the teacher knows you can't do it." Tong Gexiao raised her chin, finally finding a bit of self-respect.

Li Yi said, "I really can do it, but the proof is indeed complicated. I won't write it for you today. Here, give me all the paper you have, and I can write the solution to another difficult problem for you."

"Another one?" Tong Gexiao blinked.

"Yes, don't you like Riemannian geometry? Then I'll prove another concept proposed by Riemann, the Riemann Hypothesis!"

"The Riemann Hypothesis?" Tong Gexiao was almost jumping in shock.

The Riemann Hypothesis is a conjecture about the distribution of the zeros of the Riemann zeta function ζ(s), proposed by the mathematician Riemann in 1859.

Compared to the Fermat Conjecture, which took over three and a half centuries to be solved, and the Goldbach Conjecture, which has stood for over two and a half centuries, the Riemann Hypothesis has only a record of one and a half centuries, but its importance in mathematics far exceeds these two more well-known conjectures. It is the most important and eagerly awaited unsolved problem in mathematics today.

"What, you don't want it?" Li Yi reached out and pinched Tong Gexiao's cheek.

Fortunately, all the classmates in the class were intimidated by Tong Gexiao and were answering questions with their heads down, not daring to look up. Otherwise, they would have fainted on the spot when they saw Li Yi pinching the teacher's face like he was teasing a child.

However, this extremely over-the-top action didn't elicit any reaction from Tong Gexiao. She was already stunned by Li Yi's bold claim.

"Here, all of it!"

Tong Gexiao handed over the entire stack of scratch paper to Li Yi and opened her eyes wide, wanting to see if this guy was really going to do something incredible!

That's the Riemann Hypothesis! One of the most important unsolved problems in mathematics. If it were truly solved, wouldn't it guarantee a Fields Medal or a Wolf Prize in Mathematics?

It's worth noting that the Nobel Prize only includes physics, chemistry, biology or medicine, literature, and peace. In 1968, an economics prize was added, but there is no prize for mathematics.

In this context, two international mathematics awards have been established: the Fields Medal, awarded by the International Mathematical Union at the International Congress of Mathematicians held every four years; and the Wolf Prize in Mathematics, established by the Wolf Foundation and awarded annually. These are the "Nobel Prizes" of the mathematics community.

In addition, at the beginning of the 21st century, the Scientific Advisory Board of the Clay Mathematics Institute selected seven problems that could guide the advancement of mathematics and have a significant impact on its development, known as the "Millennium Prize Problems." Solving any of these problems would earn a million-dollar reward!

The Riemann Hypothesis is one of the seven Millennium Prize Problems!

If Li Yi could solve the Riemann Hypothesis, it would definitely cause a sensation worldwide!

Seeing Li Yi pick up a pen and start writing equations on the white paper, Tong Gexiao's heart was pounding. Rationality told her that Li Yi couldn't possibly achieve such a feat, but the incredible test papers he had just solved made her think he might be capable!

After finishing one sheet of scratch paper, Li Yi casually handed it to Tong Gexiao to read, then took another blank sheet and continued writing. Before long, the stack of papers in Tong Gexiao's hands had grown thick!

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