Scholar’s Advanced Technological System

Looking at the expanded task bar for about five minutes, the Ark eventually chose to use the reward task card.

The plan for mass projectors, although on the schedule of work of the Moon Orbit Construction Committee, does not know when to wait to get this thing built.

In the meantime, he could do something else first.

Anyway, the work on the moon is hanging up, and the task is whether or not to run there, at best just postpone it a little bit back.

[Golden reward task open!

[Note: The throne of the old era has stood for a century and a half, and the beginning of the new era will surely take the end of the old era as its prelude! The first step on the road to the future starts with mathematics…]

[REQUIREMENT: Prove Lehman's guess within three years!

[Mission Reward: 10,000 points, 2 million math experience, a "legend” task card.

“… to prove Lehman's conjecture within three years? ”

He looked at the contents of the holographic panel from scratch and said to himself thoughtlessly.

“Although this is the finest crown in mathematics, three years...”

“You underestimate me. ”

Finally, a look at the mission statement and requirements was confirmed, the ark smiled slightly, and the index finger gently paddled over the holographic screen, turning off the updated taskbar.

It's not easy to prove Lehman's guess, even if it proves Lehman's guess, it's just opening a road to the top of the mountain, and it takes a lot of work to climb the top.

But even so, what?

Never had a problem bothering him for three years...

The Ark had no doubt that he would be able to solve the problem within three years.

This is both a mathematical intuition and the confidence he has long had in mathematics!

“The ‘legend' task card is really exciting...”

Now that it's all a legend, it's more advanced than a golden task card.

Though I don't know exactly what's hidden on the back of the card, when I think of the word legend that defines it, the heart of the Ark flourishes...

……

After leaving the system space, the ark sitting in the office slowly opened its eyes and returned to God from a closed eye support.

Familiar warm currents gradually climb up to the brain along the spine, and as one of the sensations immersed in the hot spring spreads along the nervous network towards the limbs, the ark feels unprecedented spiritual rise, unprecedented clarity in the field of thought.

It feels like…

Another step closer to Almighty God.

It didn't take too long to transform the brain, and the warm currents climbing the spine were scattered.

Moving her shoulder gently, she felt the weight on her shoulder, and the ark reached up and found herself with a blanket over her shoulder.

He glanced at the only person in the office and saw the little girl's face blushing, stubbornly saying.

“… I saw that you slept well, so I put it on for you. ”

Looking at Han Mengqi, who was hastily explaining, Ark laughed and said.

“Thanks.”

“You're welcome... well, you set up my problem, I'm done. ”

Hot forehead was about to come out of steam, Han Mengqi staggered her gaze against the ark, stepped on a small step and handed out the almost full stack of A4 paper in her hand.

“I don't know if that's right, but... I figured it out myself. ”

“Show me. ”

No more bullshit, the ark took the stack of A4 paper from the little girl's hand and swept it roughly.

The line at the beginning of the article is the title he gave her last month.

[For any real number s > 1, define zeta (s) = Σ1 (m ^ s), and validate zeta (2n) as an excess number.

The line of sight continued to go down, and it took about five minutes, and the ark looked at the end of this five- or six-page calculation process from scratch, and gave a more pertinent assessment.

“Very standard method of proof. ”

Looking away from the proof process in hand, the ark looked at the calendar and returned the proof process to Han Mengqi, who was waiting for the result.

“Surprisingly, I thought you'd spend more time proving it. I didn't expect you to do it this year. ”

When he heard the compliment, the squeezed lip couldn't help but be a little proud, and Han Mengqi hummed softly.

“… I'm smart. ”

The ark smiled lightly.

“I'll personally confirm that. ”

Looking at the ark ready to ask the question, Han Mengqi struck a hundred and twenty points of spirit and waited hard to say.

“Ask! ”

“Page 3, line 16. ”

Brushing and rolling the paper sounded, Han Mengqi quickly found the position of the row.

A slightly cooler cup of coffee on the table was lifted and the ark paused for a moment, continuing: "Explain in detail how zeta (2n) was introduced from Formula 2 to exceed the number. ”

When he heard the question, Han Mengqi's heart relaxed.

Prior to her arrival, she was ready to be made difficult by the Ark. I didn't think the Ark had taken such a particularly difficult question to make her difficult, but asked a very basic question.

Taking a deep breath, she paused for a moment to continue.

“… the conversion of Euler formula 2 is available, for any integer n > 1, with zeta (2n) = b (n) π ^ (2n). ”

“where b (2n) is a rational number of columns, i.e. the Bernoulli number. It is clear that zeta (2) is π ^ 2 times a special rational number, zeta (4) is π ^ 4 times a special rational number… so we know perfectly well that zeta (2), zeta (4) … are all rational numbers. And because π is an excess number, these function values are, of course, an excess number. ”

After listening to Monkey Han, the ark nodded in praise of the location.

“Nice.”

“But don't be too proud, it's just a question of whether you did it yourself. The next question is the real challenge. ”

Looking at Han Mengqi, the ark dropped the coffee cup in his hand and continued to ask.

“Now that you have proven zeta (2n) to be outnumbered, what I would like to ask is zeta (3)? ”

Such a simple question…

Han Mengee lifted her chin with pride.

However, she was stunned just as she was preparing to answer the question.

zeta (3)!

zeta (3) …

Huh?

What the hell is this thing?!

Looking at Han Mengqi, Ark chuckled and asked.

“Can't you answer that? Zeta (3) always seems easier than zeta (2n), doesn't it? The latter has an unknown number in brackets. ”

“Hmm...” The mumps drummed up, chewing on Han Mengqi's lower lip to meditate, but he couldn't say a word.

It took a while to ask in a probing tone.

“Is it also… beyond the number? ”

The ark laughed and asked, "Oh? Why?”

Han Mengqi answered honestly: "… guessed. ”

Looking at the little girl with her head down honestly, the ark laughed and paused for a moment to continue.

“It's not surprising that you don't know, because Euler, who wrote the Euler formula, doesn't either. It was not until 1978 that the French mathematician R.Ap 'ery proved that zeta (3) was not a rational number, and we still do not know whether zeta (5) was a rational number. ”

As soon as the Ark asked its own question, there was no answer at all, Han Monkeyton said in a drummed manner.

“What... take this unanswered question... to bully me. ”

“There's an answer,” he said after looking at Han Mengqi, and Ark smiled, changing his serious tone, "any mathematical question has an answer, we just don't know yet. And when you become a PhD from a master's degree, the challenge is here, and you have to learn to find your own way to the maze exit, propose IDEA, and then make it happen. ”

After hearing the words of the Ark, Han Mengqi first slightly stunned.

Then she reacted violently, with a surprise expression on her face.

“Wait, wait, you mean, decided to take me as an apprentice?! ”

The ark nodded with a smile.

“After you've successfully answered the first question, I've actually decided. ”

“As for the second question, it's your research topic. ”

Saying, the ark stood up from behind the desk and walked to the blackboard of the office, picking up a piece of chalk with half a piece of chalk, writing it on the blackboard, talking.

“The transcendence of the values of the Lehman zeta function at odd integer points has been a classic problem in the analytical mathematics community. According to the Euler formula and the nature of the Bernoulli number, zeta (2n) is easily proven to be an excess number, so it is assumed that for any integer n > 1, zeta (2n +1) is also an excess number. ”

“The best result so far is that countless zeta (2n +1) are irrational, yet the difference between mathematically infinite and infinite is also so far apart. ”

“If you can take a step in this direction, even a small step, as long as it is an achievement that is recognized by academia. ”

“Then you'll graduate from me. ”