231: Chapter 231 Visiting Scholar Terence Tao

They might involve dark matter, high-dimensional space folding, or pure energy-state matter.

With current technological levels and instrument precision, it was simply impossible to reverse engineer them; he was still somewhat at a loss.

It seemed that industrial mass production of the energy potion would be impossible in the short term.

Zhao Yang closed the report, his expression returning to calm.

He wasn't in a hurry. The current technology tree hadn't reached that level yet, so forcing it was meaningless. As long as his subject levels continued to rise, pushing Physics and Chemistry to LV6 or even higher, one day he would be able to use pure scientific principles to analyze everything about the system!

He unplugged the mobile hard drive containing the test data and locked it in a drawer. Picking up the black signature pen on the desk, he pulled his attention back to the stack of A4 manuscript papers covered in formulas before him, continuing his work on Goldbach's Conjecture.

Time passed quickly in focused deduction.

During these past two months, Zhao Yang had cut off almost all unnecessary social interactions. Aside from his daily, unwavering ten-kilometer jog at a steady pace and a trip to the unmanned laboratory's control terminal to check progress, he spent all his time immersed in the private office allocated to him by the School of Mathematical Sciences, Peking University.

The "1+1" of Goldbach's Conjecture was a precipice that the mathematics community had failed to overcome for decades. Chen Jingrun's "1+2" back then was already the physical limit of the traditional Sieve Method. Zhao Yang knew very well that trying to break the parity barrier with old tools was purely a pipe dream.

Under these two months of high-intensity mental exertion, relying on his ultra-high IQ of 185 and LV5 mathematics level, Zhao Yang had also achieved some research results on Goldbach's Conjecture.

He built a brand-new mathematical bridge between the traditional Circle Method and the Sieve Method. He introduced a weighting function based on high-dimensional manifold topology, forcibly bypassing the parity entanglement of prime numbers distribution.

Of course, this wasn't yet the proof of Goldbach's Conjecture, but it was already considered a very good interim result.

Zhao Yang organized the forty-five-page manuscript into a standard LaTeX format; he had already posted the interim results on arXiv. Simultaneously, he also submitted this paper to "Inventiones Mathematicae," one of the four top journals in the mathematics world.

He gained thirty thousand mathematics experience points, which was decent, but it was still far from a mathematics level-up.

A few days after Zhao Yang published his paper, the School of Mathematical Sciences, Peking University released a major announcement: Professor Terence Tao, a top international mathematician and fields medal winner, would be coming to Peking University for a three-month visiting scholar exchange program.

Once this news came out, it sparked discussions online. Domestic academic circles and internet forums instantly exploded.

"What's the situation? God Tao is coming to Peking University for a three-month exchange? Usually, when big shots of this level come to the country, they stay for three to five days at most to give a lecture and then leave. Why stay so long this time?"

"Did the School of Mathematical Sciences, Peking University go all out? They even managed to invite God Tao for a long-term stay?"

"Have you guys not seen the latest academic updates? Who is currently at the School of Mathematical Sciences, Peking University? God Zhao! Terence Tao is definitely coming for Zhao Yang!"

"It's confirmed. A while ago, Zhao Yang just posted that paper on the topological weighted Sieve Method regarding Goldbach's Conjecture on arXiv. God Tao himself is a top grandmaster in the field of Analytic Number Theory; he definitely couldn't sit still after seeing that paper."

While Zhao Yang was browsing the web for information in his office, he was somewhat surprised to see this news.

But soon he logged into his email and saw an unread message sent by Terence Tao late at night.

"Zhao, I read your new paper posted on arXiv. Your idea of introducing high-dimensional manifold topology to handle the parity barrier is simply a stroke of genius. I spent three days deducing with your weighting function model on scratch paper.

However, regarding the selection of the integration path near the critical line of the complex plane, I believe there is still a logical leap in your proof. It's hard to explain clearly in an email. I have already applied for a three-month sabbatical from UCLA and will arrive in Yanjing next Tuesday. I need to discuss this framework with you in person."

After reading the email, Zhao Yang was thoughtful. Terence Tao's flight across the Pacific this time wasn't for any official academic exchange at all; it was purely for the Goldbach's Conjecture proof framework in his hands.

A few days later.

Zhao Yang and Professor Wang Wenyuan picked up Terence Tao at the airport.

The group exchanged pleasantries for a while.

Professor Wang Wenyuan hosted Terence Tao at a small internal restaurant within Peking University.

Terence Tao couldn't wait to start talking to Zhao Yang about his previous paper.

"Zhao Yang, regarding that error term convergence issue we discussed in the email."

Terence Tao spread the printed copy of the paper directly on the dining table, pointing to a set of integral formulas on one of the pages, his tone urgent.

"When you use contour integration here to handle the main term, you assume that the Dirichlet function has no zeros within the region. Although this complies with relevant theorems, when your topological space dimension is four or greater, this error will be multiplied by the weighting function."

Terence Tao picked up a pen and quickly wrote a line of equations in the blank space on the table.

"Look, if the character is quadratic, the constant here will cause the final error term to be unable to be absorbed by the main integration term. How did you solve this problem?"

Professor Wang Wenyuan sat nearby, holding a teacup, watching the two dive directly into a white-hot mathematical confrontation at the dining table.

For a moment, he couldn't get a word in at all and could only listen silently to their discussion.

Zhao Yang looked at the problem Terence Tao pointed out, his brain working rapidly.

This problem was indeed the deepest hidden thorn in the paper; ordinary reviewers wouldn't be able to see it at all. Only a top mathematician of Terence Tao's caliber could accurately pick out this flaw.

Zhao Yang didn't pick up a pen.

He looked at the line of formulas and, in a steady tone, directly provided the solution path from his mind.

"Professor Tao, you've overlooked the fundamental purpose of my introduction of high-dimensional mapping. I don't need to forcibly suppress this error term on the traditional complex plane."

Zhao Yang reached out his finger and tapped on the equation Terence Tao had written.

"When the dimension is four or greater, I didn't continue using traditional analytic continuation. Turn to page thirty-eight of the paper. I established an isomorphic modular form space there. I transformed the function corresponding to the Dirichlet character into a certain cusp form function through Automorphic Representation Theory."

Hearing the words 'Automorphic Representation Theory,' Terence Tao's eyes suddenly lit up.

He quickly flipped to the back, staring intently at the derivation Zhao Yang mentioned.

"In the isomorphic modular form space, using relevant conjectures, we can obtain a precise upper bound for the Fourier coefficients."

Zhao Yang stated calmly.

"This upper bound is sufficient to forcibly compress the magnified error term back. The logic is a completely closed loop."

Terence Tao stared at those two pages of derivation, his brain running at full speed.

The pen in his hand paused in the air for a moment.

Then, he took a deep breath and placed the pen back on the table.

"An ingenious conception."

Terence Tao looked at Zhao Yang and gave his evaluation.

"You've grafted tools from Algebraic Geometry into the Sieve Method of Analytic Number Theory. I had been looking for a way out within the traditional Circle Method framework and never thought to use automorphic forms to bypass the restrictions."

The look in his eyes as he watched Zhao Yang had changed from previous admiration to a kind of shock.

"This ability to break down disciplinary barriers and use top-tier tools from different fields with such ease is indeed startling."

"Let's eat, Professor Tao. The food is getting cold."

Zhao Yang calmly picked up his chopsticks.

This level of mental deduction was just a routine operation for him...