334: Chapter 334 Because I'm afraid of dying!

Perhaps it was because Biology had been upgraded to LV5, increasing his Intelligence by four points and raising it to 215.

Or perhaps it was because he hadn't touched the P vs NP problem for a long time, and while re-examining it, Zhao Yang felt his thoughts flowing like a fountain.

Looking at the research materials before him, countless inspirations began to emerge in Zhao Yang's mind. The obstacle that had stumped him for several months—the gap between the sensitivity of Boolean functions and the lower bound of circuit complexity—suddenly began to loosen at this moment.

Zhao Yang realized that he had been trying to force a breakthrough using Fourier analysis, but this path naturally had bottlenecks for circuit classes other than AC0.

The truly promising direction was not spectral analysis, but rather using polynomial methods from Algebraic Geometry to map the computational process of Boolean functions onto a high-dimensional algebraic variety, and then judging the minimum depth of the corresponding circuit by studying the geometric properties of this algebraic variety.

Thinking of this, Zhao Yang became excited. He grabbed a stack of scratch paper and began to derive it.

First was the construction of the mapping itself: how to convert an arbitrary Boolean circuit into a system of polynomial equations? This step referenced some techniques from the dimension reduction mapping in the Kakeya Conjecture, but it required a significant amount of adaptation.

Then, the logic gates of a Boolean circuit are not continuous geometric objects; one must use polynomials to simulate the AND, OR, and NOT operations.

He quickly wrote down a few lines of definitions on the paper, using polynomial ideal theory to handle the algebraization of the logic gates.

Then came utilizing the lower bound of the dimension of the algebraic variety to correspond to the lower bound of circuit complexity. The inspiration for this step came directly from his treatment of the high-dimensional tube overlap problem when proving the Kakeya Conjecture. If the dimension of the algebraic variety is below a certain threshold, then the corresponding system of polynomial equations cannot have a solution, which means the computational capability of the original circuit is strictly limited.

Conversely, if one could prove that the dimension of the algebraic variety corresponding to a certain NP-complete problem must exceed this threshold, that would be equivalent to proving it cannot be computed by polynomial-sized circuits.

Zhao Yang wrote from the afternoon until the early hours of the morning. The scattered draft paper on his desk grew, with some being crossed out and rewritten, and others folded at the corners and set aside to be verified later.

This state of abundant inspiration disappeared the following afternoon. He encountered a new obstacle while handling an elimination step in polynomial ideal theory.

The elimination theorem over algebraically closed fields does not fully apply to finite fields with positive characteristic, and the foundation of circuit complexity happens to be finite fields.

Zhao Yang stared at the lines of derivation on the paper for a long time, then put down his pen. He realized that this problem could not be solved in a short time by a flash of inspiration.

But he had indeed taken a solid step forward on this problem. The shift from Fourier analysis to polynomial methods, and the construction of the mapping from Boolean functions to algebraic varieties—these two steps were the core skeleton of the entire proof framework. With the skeleton built, the remaining filling, while tedious, had a clear direction.

Zhao Yang let out a long sigh, leaned back in his chair, and picked up his water cup to take a sip. He didn't continue to grind away at the obstacle. Based on his experience, he knew very well that when encountering a bottleneck that hadn't loosened after more than two hours of thinking, the best method was to shift his attention. Letting the brain's background processing mode digest the massive amount of information he had just fed it was often more effective than forcing it.

He casually opened his email, wanting to see if there were any new messages today. Lying in his inbox was an email from the Wolf Foundation, sent a few hours ago. He opened it and saw that he had won this year's Wolf Prize in Mathematics, and the foundation was inviting him to Tel Aviv to attend the award ceremony.

The Wolf Prize. Zhao Yang scanned the email from beginning to end, then closed the window. He had no objections to the prize itself; the Wolf Prize in Mathematics ranked just behind the fields medal and the Abel Prize in the mathematics world, and many Fields Medalists had also received the Wolf Prize later on.

But the award ceremony was in Tel Aviv, which made him lose interest. He didn't have any good feelings toward Israel, and more importantly, Tel Aviv was too sensitive a place.

According to the Intelligence Shin-chan had uncovered last time, there was more than one foreign faction interested in him!

The spy network that had been rooted out at the Aerospace Center before was just the tip of the iceberg.

According to some materials he had seen, he had already been targeted by certain organizations when he went to India to attend the International Congress of Mathematicians, but at that time, there was protection from the Ministry of State Security, plus many accompanying personnel, and Zhao Yang had almost never left his hotel, giving those organizations no opportunity, which was why nothing had happened.

The situation in Tel Aviv was far more complex than in Hyderabad, and plus, the country of Israel... those who know, know. Zhao Yang did not intend to take that risk.

He continued to browse other emails. Xue Qikun had sent a new set of superconducting sample test data, saying that the critical temperature had increased by a few percentage points again.

Liang Mengsong had sent the yield report for the fourth mass production batch of the 32nm production line, with data stable at over ninety-three percent. Chen Haifeng had sent the Spark Technology monthly financial briefing, with global revenue maintaining growth for the third consecutive month. Zhao Yang replied to them one by one, and just as he was preparing to go eat, his phone rang.

It was a call from Terence Tao.

"Zhao, have you received the email about the Wolf Prize?"

Terence Tao asked Zhao Yang.

"Are you going to Tel Aviv?"

"How did you know?"

Zhao Yang was somewhat surprised. The results of the Wolf Prize were confidential; before the official announcement, only the foundation internally and the recipient themselves would receive notification.

"Do you even need to ask? This year's Wolf Prize in Mathematics—apart from you, it's impossible for there to be any other candidate."

Terence Tao said matter-of-factly.

"You proved the twin prime conjecture and Goldbachs Conjecture, and you even solved the Kakeya Conjecture while you were at it. If the Wolf Prize isn't given to you this year, that can only mean the people on the selection committee collectively need to get their eyesight checked."

Zhao Yang smiled: "Then you can accept it on my behalf, and while you're at it, bring the prize money back for me."

The other end of the line was quiet for a few seconds. Terence Tao's tone became helpless: "Why do you have me accept everything on your behalf? Last time, the Cole Prize medal sat in my office drawer for several months before I brought it to Yanjing for you. You're having me accept the Wolf Prize too?"

"Last time was on the way; this time it's intentional. Anyway, you're going to attend the award ceremony, right?"

Terence Tao was silent for a moment, then sighed: "I did receive an invitation, but I'm attending as a past recipient, which is different from you. You are this year's recipient; in principle, you must be present in person."

He paused, his tone becoming a layer more serious.

"Zhao, why do you dislike attending academic conferences so much? You only went to the International Congress of Mathematicians once; you didn't go to accept the Cole Prize, and you won't go to accept the Wolf Prize either. I know you don't like socializing, but this isn't just socializing—it's a way to stay connected with the entire mathematical community. You stay in Yanjing by yourself, and many colleagues want to communicate with you but can't find the opportunity."

Zhao Yang thought for a moment and said: "I'm afraid of death."