417: Chapter 867 Someone claims to have solved the Hodge Conjecture?

Zhao Yang had just returned to his room and put down his luggage; he hadn't even opened his suitcase yet when Pierre Deligne came knocking at the door.

He followed Pierre Deligne to a small conference room on the top floor of the hotel, and when he pushed the door open, several people were already sitting inside.

Faltings was sitting in a single sofa by the window, leaning on his cane, while Terence Tao was leaning against a desk, holding a cup of coffee. There were also several other professors Zhao Yang had met before at Princeton and Cambridge; some were flipping through their conference schedules, while others were talking in low voices.

Seeing Zhao Yang enter, Faltings tapped his cane against the floor as a way of greeting.

"You finally decided to make the trip yourself. I heard from Terence Tao earlier that you might come, but I thought he was just trying to comfort us. You didn't go to accept the Cole Prize or the Wolf Prize, so for a while, I thought you were going to pull a Perelman and never leave your house again."

"Prof. Perelman didn't care to accept them; I just purely didn't want to go out."

Zhao Yang smiled and sat down nearby.

"So, what made you change your mind this time?"

"If I didn't come, the IMU would probably have sent someone to Beijing to corner me. The chairman of this conference had Terence Tao pass on a message beforehand, saying that if I didn't show up, they would consider moving the award ceremony to Beijing."

Everyone in the room laughed.

After chatting for a while about recent developments in mathematics, the conversation naturally turned to Zhao Yang.

Faltings set down his teacup, looked at Zhao Yang, and said, "Zhao, the papers you've published in the last few years have almost all been in the field of Biology. Aside from the Kakeya paper you collaborated on with Terence Tao, you've had almost no new independent results in mathematics. I'm not saying Biology isn't important, but if your talent were to shift entirely to Biology, it would be a huge pity for the entire mathematical community."

"Prof. Faltings, I haven't stopped doing mathematics. The research group for the Warings Problem is still making progress, my students have just finished compiling the interim results into a draft paper, and I'm also involved in the Hodge Conjecture work with Terence Tao. It's just that I haven't published any new mathematical results as the first author recently."

"But your energy is spread too thin. Aerospace, batteries, medicine, materials, and now you're supervising students too; mathematics probably only occupies a small part of your time now."

Faltings said, his tone serious, though his eyes held a complex expression.

"Although you might find an old fossil like me annoying, there are some things I still want to say: don't waste your mathematical talent. You are the most mathematically gifted person I have ever met. Mathematics is the foundation of everything! If you stop doing mathematics, it would be a huge loss for the entire mathematical community, and for you personally, it would be a regret!"

Zhao Yang thought for a moment and replied earnestly, "Prof. Faltings, I know you have my best interests at heart. But I see it a bit differently. Mathematics has never been weakened for me. When I conduct research in other fields, I am fundamentally still using mathematical tools to solve practical problems. The superconducting model uses Topology, Directed Evolution uses partial differential equations—I have never left mathematics; I've simply applied it to more areas."

Terence Tao set down his coffee cup and added, "I can vouch for that. The mathematical model in his Directed Evolution paper, if taken alone, would be of a weight suitable for a top-tier applied mathematics journal. While I was helping him organize the manuscript for the Hodge Conjecture, I noticed that the method he used to process data in his Biology paper is the same framework he used for the normal cone boundary estimation in his proof of P vs NP."

Faltings was silent for a moment, then slowly nodded.

"Perhaps you're right. But regardless, I still hope to see your name in mathematical journals."

He paused, then changed the subject. "Since we've brought it up, tell me about your sixty-minute report. What are you planning to talk about?"

"It's related to the Hodge Conjecture; it's some interim results that Prof. Terence Tao and I have been pushing forward together."

The conference room went quiet for a moment. The professors exchanged glances, and Faltings raised his eyebrows, his expression slowly shifting from serious to expectant.

"The Hodge Conjecture? Is that the direction you were discussing with Terence Tao before?"

"Yes. The core idea is to use the polynomial ideal and algebraic variety dimension estimation tools I used in my proof of P vs NP to re-examine the algebraic cycle problem in the Hodge Conjecture. It's currently still at the interim progress stage; we are still some distance away from a final proof."

Faltings nodded, his tone much softer than before.

"Every time you say the words 'interim progress,' I never know whether I should believe you. The last time you said 'interim progress' was before your report on the P vs NP problem in Hyderabad. That 'interim progress' later turned into a complete proof of a Millennium Prize Problem."

He paused and looked at Zhao Yang seriously. "But regardless, I will definitely be there to listen to this report."

The group chatted for a while longer before going their separate ways.

Zhao Yang didn't return straight to his room. He stood in the hotel lobby for a moment, then followed the signs toward the venue. The main venue for the conference was in the convention center next to the hotel, where the multi-story halls were divided into various large and small lecture halls.

Outside the main hall was an open lounge area with several rows of sofas and coffee tables. Nearby, there were a few booths with display boards set up by amateur mathematics enthusiasts, covered in printed mathematical manuscripts.

Zhao Yang had originally just been wandering around, but when he walked to the lounge area, he saw Wang Hong. She was standing in front of a booth, leaning over and looking at something intently. The stall owner was a middle-aged man in his fifties wearing thick glasses.

The table in front was covered with printed paper manuscripts, and there was a huge poster with "A Complete Proof of the Hodge Conjecture" written in Korean and English. Next to it were a few photos of the stall owner with a deceased mathematician.

Zhao Yang walked up next to Wang Hong and glanced down at the pages of the manuscript spread out on the table. Wang Hong was staring at the manuscript intensely, her brows furrowed, as if she were calculating something.

She was looking at it so intently that she didn't even notice when Zhao Yang arrived.

"No need to calculate."

Zhao Yang spoke up suddenly.

Wang Hong was startled; she looked up to see it was Zhao Yang and breathed a sigh of relief.

"Teacher Zhao, what are you doing here? This person says he has proven the Hodge Conjecture. I've been looking at it for a while, but it feels a bit off; there are so many problems with it..."

"This person is a fraud, or rather, a crank."

Zhao Yang said directly.

The stall owner clearly understood Chinese, or at least understood the word "fraud."

Hearing Zhao Yang's words, he jerked his head up, his face flushing crimson.

"What right do you have to call me a fraud? I have spent twenty years studying the Hodge Conjecture. All my manuscripts are here, and all the derivation steps are public. These two are famous deceased mathematicians; they both looked at my preliminary concepts back then and encouraged me to continue. You didn't even look at it carefully, and the moment you open your mouth, you call me a fraud?"

Zhao Yang pointed to the third page of the manuscript spread out on the table.

"Take another look at this page yourself. In the premise you introduced in the first step, you equate the algebraic cycle of the Hodge class to a specific type of element in the cohomology ring, which is correct in itself. But in the fourth step, when deriving the Chern class of the vector bundle, you secretly changed the rational coefficients of the algebraic cycle to integer coefficients. Your construction is trivial under rational coefficients, and the conclusion only holds after changing them to integer coefficients. However, you haven't provided any argument for the transition from rational coefficients to integer coefficients. I have seen this exact same routine in at least three submissions from cranks."

The stall owner froze. He looked down at the page Zhao Yang was pointing to, and the expression on his face began to shift uncertainly.

Several students wandering nearby heard the commotion and gathered around to watch the spectacle.

Soon, someone recognized Zhao Yang.

"That looks like God Zhao!"

"It is! It's God Zhao!"