Chapter 337 - 127: No Choice but to Double the Efforts!

Words : 966 Updated : Oct 7th, 2025

Chapter 337: Chapter 127: No Choice but to Double the Efforts!United States, City of Cambridge, Areston Community. This community is very close to both MIT and Harvard University, with a quiet environment, good schools, and its own park. However, Zhang Xinwen chose to live here because, compared to other middle-class residential areas in Cambridge or Boston, the housing prices here are lower, and the living conditions are not bad, making it quite cost-effective. Moreover, many of the residents in the community are staff from MIT and Harvard, which adds a sense of security. There’s no denying that although being a university professor in the United States carries a certain social status, it does not belong to the high-income group, especially when you’re not very famous yet. It’s well known that this country really takes "birds of a feather flock together" to the extreme. Middle-class and poor communities are mixed together, with knowledge and crime often just a street apart. Everyone seems to be used to these things. In any city here, even in Washington, the capital, or New York, a world financial center, certain areas also face higher crime rates and social issues. Relatively speaking, Cambridge, with MIT and Harvard, is very safe. Especially at night, the community is very quiet, even tranquil. It’s unusual for people in middle-class communities to go out at night. There’s no noise from automobiles on the streets, and certainly no mysterious gatherings of unknown origins. If a family makes noise recklessly, they’re likely to receive a visit from 911. At such early hours, the phone’s ringtone can be especially jarring. That’s exactly what woke Zhang Xinwen, as he just opened his eyes, he heard the woman beside him complaining. "Who is it? Who’s calling at this hour? How many times have I told you, turn your phone to silent mode when sleeping," she said, turning on the light angrily and getting up, blanket in hand, leaving the room. Zhang Xinwen just felt a headache. Reaching middle age, marital disputes seemed to become more frequent, and even a mathematics professor wasn’t immune. They had just argued before sleep and managed to placate her, but one phone call threatened to escalate the conflict again. Shaking his head helplessly, he picked up the phone and got angry upon seeing the number. If it were a colleague’s number from Cambridge, that’d be fine—it would at least prove someone else was working late. But this was a number from Huaxia. Don’t they respect the time zones? Cambridge EDT is 12 hours behind CST! It’s already 12:50 AM in Cambridge now, has Li Lixing gone mad? Answering the call with resentment, he didn’t even have a chance to speak when the person on the other end hastily said, "Professor Zhang, check your email, Qiao Yu has solved it!" Dazed, Zhang Xinwen instinctively asked, "Qiao Yu? What has he solved?" "What else could it be? Of course, the problem we’re dealing with! I can’t talk now, I still need to notify Ronald!" "Beep beep beep..." The busy tone in the handset left Zhang Xinwen in a daze for a while. What... He just hung up? He was planning to scold this guy who disturbed his sweet dream and destroyed his marital relationship, but he just hung up? Wait a minute... Qiao Yu has solved that problem? His mind finally fully activated, Zhang Xinwen suddenly jolted awake, quickly threw on some clothes, hurried to his small study, and turned on the laptop to login to his email. Indeed, there was an email from Li Lixing from Huaqing, with a tiny image attached. Curiously, Zhang Xinwen clicked it open, and the minimalistic proof process burrowed strongly into his mind. After reading it carefully, Zhang Xinwen felt somewhat unreal. The problem that had troubled them for more than half a year, Qiao Yu solved it in just six lines? With a sigh of admiration that lasted less than two seconds, Zhang Xinwen grabbed a pen, pulled out a stack of paper from the desk, and started deriving. For example, the proof of the invariance in the fifth line. The prover here ensured that the average value of a global function under the influence of a transformation group is a characteristic layer. This is crucial because it proves that the constructed characteristic layer W essentially captures the significant features of the global function, rather than changing with the group. The logic of the proof is that through the average action of the transformation group, the resulting result still belongs to the characteristic layer can be guaranteed. But Qiao Yu’s expression was: Using the principle of categorical contraction, it can be proven: ∀g∈G,g⋅Φ(f)=Φ(f). Therefore, Φ(f) is an invariant function and can be considered an automorphism of the Whitaker Layer. This is obviously too concise. Using the principle of categorical contraction, this statement seems simple but is quite a troublesome task to prove. First, the average must be defined: Φ(f)=1/∣G∣g∈G∑g⋅f, then the invariance needs to be verified: g·Φ(f)=g·｛1/∣G∣g∈G∑g⋅f｝... Time passed as Zhang Xinwen furiously wrote, unknowingly filling three whole pages of scratch paper with calculations, arriving at the same conclusion as Qiao Yu’s proof process. "Yes!" Zhang Xinwen couldn’t help but shout in excitement, causing a burst of barking outside, which startled him into quickly shutting his mouth. Fortunately, apart from the dog barking twice, there was no other sound indoors or outdoors. Feeling relieved but still excited, Zhang Xinwen calmed himself. For any mathematician, having something that they had been pondering for more than half a year suddenly resolved is impossible not to excite. Joy was quickly followed by a stroke of fear. Good thing Elder Yuan made the decision to pull Qiao Yu into their research group...

Chapter 337 - 127: No Choice but to Double the Efforts!

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