[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"origin-scholar-s-advanced-technological-system":3,"chapter-scholar-s-advanced-technological-system-scholar-s-advanced-technological-system-chapter-845":6},{"origin":4,"title":5},"english","Scholar's Advanced Technological System",{"chapter":7,"nextChapterSlug":19,"prevChapterSlug":20,"totalChapters":21,"novelImage":22},{"id":8,"novel_id":9,"title":10,"slug":11,"index":12,"content":13,"wordcount":14,"created_at":15,"updated_at":15,"volume":16,"translator":17,"content_hash":18},1330717,1769,"Chapter 845 - Three Years!","scholar-s-advanced-technological-system-chapter-845",845,"\u003Cp>Lu Zhou stared at his mission panel for five minutes, and in the end, he decided to activate the mission card.\u003C\u002Fp>\n\u003Cp>Even though the Lunar Orbit Committee planned on building a mass driver on the moon, he had no idea how long it would take.\u003C\u002Fp>\n\u003Cp>He should be using this time to complete another mission instead.\u003C\u002Fp>\n\u003Cp>After all, the lunar mass driver was advancing forward by itself, so the mission could be picked up again at any time.\u003C\u002Fp>\n\u003Cp>[Golden reward mission: Activated!\u003C\u002Fp>\n\u003Cp>[Description: The beginning of a future era starts with mathematics...\u003C\u002Fp>\n\u003Cp>[Requirements: Solve the Riemann hypothesis within three years!\u003C\u002Fp>\n\u003Cp>[Mission rewards: 10,000 general points, two million mathematics experience points. “Legendary” mission card.]\u003C\u002Fp>\n\u003Cp>“... Solve the Riemann hypothesis in three years?”\u003C\u002Fp>\n\u003Cp>Lu Zhou finished reading the translucent mission panel and muttered to himself, “I know this is the crown of mathematics, but three years...\u003C\u002Fp>\n\u003Cp>“Is more than enough time.”\u003C\u002Fp>\n\u003Cp>Lu Zhou double-checked the mission requirements again. He then tapped the screen and closed his mission panel.\u003C\u002Fp>\n\u003Cp>Solving the Riemann hypothesis wasn’t an easy task. Even though he already solved the Quasi Riemann hypothesis, climbing the final part of the mountain would take a lot of effort.\u003C\u002Fp>\n\u003Cp>But why was Lu Zhou so confident?\u003C\u002Fp>\n\u003Cp>Because there had yet to be a problem that took him more than three years to solve...\u003C\u002Fp>\n\u003Cp>Lu Zhou had no doubt that he could solve this problem within three years.\u003C\u002Fp>\n\u003Cp>This was both his mathematics intuition and his self-confidence from being the king of modern mathematics!\u003C\u002Fp>\n\u003Cp>“The ‘legendary’ mission card sounds exciting...”\u003C\u002Fp>\n\u003Cp>Surely legendary is better than golden, right?\u003C\u002Fp>\n\u003Cp>Lu Zhou didn’t know what was hidden behind that mission card, but the word legendary made him thrilled...\u003C\u002Fp>\n\u003Cp>...\u003C\u002Fp>\n\u003Cp>After Lu Zhou exited the system space, he opened his eyes and woke up in his office.\u003C\u002Fp>\n\u003Cp>He felt a warm sensation climbing from his spine to his brain. It was like his neurons were immersed in a spa of knowledge. He never felt better before.\u003C\u002Fp>\n\u003Cp>It felt like...\u003C\u002Fp>\n\u003Cp>He was one step closer to becoming the omniscient God.\u003C\u002Fp>\n\u003Cp>It didn’t take long for the information to enter his brain, and the warm sensation in his spine gradually subsided.\u003C\u002Fp>\n\u003Cp>Lu Zhou moved his shoulders and felt something weighing on him. He reached out and felt a blanket.\u003C\u002Fp>\n\u003Cp>He looked at the girl in the office. The girl blushed and said, “I saw you were sleeping, so I put the blanket on you.”\u003C\u002Fp>\n\u003Cp>Lu Zhou looked at Han Mengqi and smiled.\u003C\u002Fp>\n\u003Cp>“Thank you.”\u003C\u002Fp>\n\u003Cp>“You’re welcome... Oh, the question you assigned me, I finished it.”\u003C\u002Fp>\n\u003Cp>Han Mengqi was turning bright red. She tried to avoid eye contact as she walked up and handed him the stack of A4 papers.\u003C\u002Fp>\n\u003Cp>“I don’t know if it’s right, but... I thought of it myself.”\u003C\u002Fp>\n\u003Cp>“Let me see.”\u003C\u002Fp>\n\u003Cp>Lu Zhou took the stack of A4 papers from the girl and glanced at it.\u003C\u002Fp>\n\u003Cp>The title was the question he assigned her.\u003C\u002Fp>\n\u003Cp>[For any real number s u003e 1, define ζ(s) = Σ1 \u002F (m ^ s)... Prove that ζ(2n) is a transcendental number.]\u003C\u002Fp>\n\u003Cp>Lu Zhou spent five minutes looking through the first couple of pages. He then gave her an evaluation.\u003C\u002Fp>\n\u003Cp>“Standard proof.”\u003C\u002Fp>\n\u003Cp>Lu Zhou looked at the calendar, then looked at Han Mengqi.\u003C\u002Fp>\n\u003Cp>“I’m surprised. I thought it would take you more time to prove it, I didn’t expect you to finish it this year.”\u003C\u002Fp>\n\u003Cp>Han Mengqi couldn’t help but smile proudly. She pouted and replied, “I’m actually pretty smart.”\u003C\u002Fp>\n\u003Cp>Lu Zhou smiled.\u003C\u002Fp>\n\u003Cp>“I agree with that.”\u003C\u002Fp>\n\u003Cp>Lu Zhou looked like he had some questions, so Han Mengqi energetically spoke first.\u003C\u002Fp>\n\u003Cp>“Go ahead, ask away!”\u003C\u002Fp>\n\u003Cp>“Line 16, page three.”\u003C\u002Fp>\n\u003Cp>Han Mengqi quickly found the line on her A4 copy.\u003C\u002Fp>\n\u003Cp>Lu Zhou picked up the room temperature coffee cup on his table and took a sip. He paused for a second before saying, “Explain in detail on how you introduced the ζ (2n) from equation 2 as a transcendental number.”\u003C\u002Fp>\n\u003Cp>After hearing this question, Han Mengqi was relieved.\u003C\u002Fp>\n\u003Cp>She did a ton of preparation before coming to Lu Zhou, so she didn’t expect Lu Zhou to ask a fairly basic question.\u003C\u002Fp>\n\u003Cp>She took a deep breath and replied, “This can be obtained by transforming equation 2 using Euler’s formula. For any integer nu003e 1, ζ (2n) = b (n) π ^ (2n).\u003C\u002Fp>\n\u003Cp>“B(2n) is a sequence of rational numbers, which is, Bernoulli numbers. Obviously ζ (2) is π ^ 2 times a special rational number, and ζ (4) is π ^ 4 times a special rational number... So it is obvious that ζ (2), ζ (4)... are rational numbers. And because π is a transcendental number, the function values are also transcendental numbers.”\u003C\u002Fp>\n\u003Cp>After hearing Han Mengqi’s explanation, Lu Zhou nodded with approval.\u003C\u002Fp>\n\u003Cp>“Not bad.\u003C\u002Fp>\n\u003Cp>“Don’t be happy just yet, that was just to prove you wrote the thesis yourself. The following question is the real challenge.”\u003C\u002Fp>\n\u003Cp>Lu Zhou put down his coffee cup and spoke.\u003C\u002Fp>\n\u003Cp>“Now that you have proven that ζ (2n) is a transcendental number, I want to ask, what about ζ (3)?”\u003C\u002Fp>\n\u003Cp>What a simple question...\u003C\u002Fp>\n\u003Cp>Han Mengqi proudly raised her chin.\u003C\u002Fp>\n\u003Cp>However, when she was about to answer the question, she froze.\u003C\u002Fp>\n\u003Cp>ζ (3)!\u003C\u002Fp>\n\u003Cp>ζ (3)!\u003C\u002Fp>\n\u003Cp>What what what?\u003C\u002Fp>\n\u003Cp>What is that?\u003C\u002Fp>\n\u003Cp>Han Mengqi was muddled, Lu Zhou smiled and asked, “Can’t answer it? ζ(3) seems simpler than ζ (2n), right? It doesn’t even contain a variable.”\u003C\u002Fp>\n\u003Cp>“Yeah...” Han Mengqi pondered. She didn’t know what to say.\u003C\u002Fp>\n\u003Cp>After a while, she spoke in an uncertain tone.\u003C\u002Fp>\n\u003Cp>“Maybe... it’s also a transcendental number?”\u003C\u002Fp>\n\u003Cp>Lu Zhou smiled and said, “Oh really? Why?”\u003C\u002Fp>\n\u003Cp>Han Mengqi answered honestly, “It was a guess.”\u003C\u002Fp>\n\u003Cp>Seeing the girl lower her head, Lu Zhou smiled and spoke.\u003C\u002Fp>\n\u003Cp>“It’s not surprising you don’t know the answer. Because Euler also didn’t know. It wasn’t until 1978, when French mathematician R. Apery proved that ζ (3) is not a rational number. As for whether or not ζ (5) is a rational number, we still don’t know.”\u003C\u002Fp>\n\u003Cp>After Han Mengqi heard that there was no answer to the question, she pouted.\u003C\u002Fp>\n\u003Cp>“What is that... There isn’t even an answer to the question... You’re bullying me.”\u003C\u002Fp>\n\u003Cp>“There is an answer.” Lu Zhou smiled at Han Mengqi and said in a serious manner, “There’s an answer to every mathematics problem, we just don’t know it. When you become a PhD student, that is where the challenge is. You will have to find your own ideas for proofs, then find the proofs themselves.”\u003C\u002Fp>\n\u003Cp>Han Mengqi paused for a second.\u003C\u002Fp>\n\u003Cp>She immediately realized what was going on, and she looked ecstatic.\u003C\u002Fp>\n\u003Cp>“Wait a second, you’re saying that I can be your student!”\u003C\u002Fp>\n\u003Cp>Lu Zhou smiled and nodded.\u003C\u002Fp>\n\u003Cp>“I actually already made up my mind after you answered my first question.\u003C\u002Fp>\n\u003Cp>“The second question will be your research project.”\u003C\u002Fp>\n\u003Cp>Lu Zhou stood up from his desk and walked to the blackboard. He picked up a piece of chalk and wrote on the blackboard as he spoke.\u003C\u002Fp>\n\u003Cp>“The transcendence value of the Riemann zeta function at odd positive integers has always been a classic problem in analytical mathematical theory. According to Euler’s formula and the properties of Bernoulli numbers, we can easily prove that ζ (2n) is a transcendental number. Therefore, our hypothesis is that for any integer n u003e 1, ζ (2n + 1) is also a transcendental number.\u003C\u002Fp>\n\u003Cp>“The best result so far is that there are countless ζ (2n + 1), which are irrational numbers. However, the difference between infinities is still infinity.\u003C\u002Fp>\n\u003Cp>“If you can do good research in this area, even if it’s only a small proof, you will be recognized by the academic community.\u003C\u002Fp>\n\u003Cp>“By then, you will be able to graduate.”\u003C\u002Fp>",1281,"2026-06-05T19:44:57.547Z",1,"novelbin.me","c6b27a6cae0ee075d68e0b93be05c8ce870a611053081a41f7a919316b682e8e","scholar-s-advanced-technological-system-chapter-846","scholar-s-advanced-technological-system-chapter-844",1683,"https:\u002F\u002Fnovelzhen.com\u002Fimages\u002Fcovers\u002Fscholar-s-advanced-technological-system-cover.jpg"]