147: Chapter 147 A Storm Rises in the Mathematics World

After uploading a copy to arXiv, it was time to submit.

Zhao Yang opened the editorial email of the Annals of Mathematics and selected the submission option.

Looking at the submission success page of the Annals of Mathematics submission system on the screen, Zhao Yang breathed a slight sigh of relief.

"I hope this paper gets accepted soon!"

His task deadline was only three months in total, and more than half had already passed.

This was a reward task, and Zhao Yang didn't want to miss it!

Sighing softly, Zhao Yang moved the mouse, clicked the 'X' in the top right corner, and closed the webpage.

Afterward, he opened his email again and sent that two-line email to Enrico Bombieri and Terence Tao.

Click send.

The progress bar flickered, indicating the sending was complete.

After finishing all this, Zhao Yang closed his laptop.

In Dorm Room 302, Sun Xu had already climbed into bed; he had to get up early the next day to help out at the cafeteria.

Li Tianqi and Wang Mian, who were nearby, had also stopped playing games, not wanting to disturb Wang Mian's sleep.

After glancing around the dorm, Zhao Yang looked at the digital watch on his wrist.

"It's only ten-thirty."

"I'll read for another hour and a half."

Zhao Yang pulled a book on Algebraic Geometry from the bookshelf and adjusted the angle of his desk lamp.

He opened the pages and was soon immersed in the ocean of mathematics.

Eastern Time in the USA, 9:31 AM.

Princeton, New Jersey, Institute for Advanced Study.

The lawn outside the window was still covered with a thin layer of frost.

Professor Enrico Bombieri walked into his office, hung up his overcoat, and habitually walked toward the Italian coffee machine in the corner.

As a fields medal winner and a leading figure in the field of number theory, his life was very disciplined.

The machine hummed, and the rich aroma of coffee filled the air.

Bombieri picked up his cup, sat behind the large mahogany desk, put on his reading glasses, and pressed the power button on his computer.

The screen lit up, and following his habit, he opened his email.

There were dozens of unread emails in his inbox.

Most were conference invitations, student inquiries, or manuscripts sent by peers.

His gaze swept over them quickly.

Suddenly, the mouse stopped.

Sender: Yang Zhao.

Subject: Proof of the twin prime conjecture

Bombieri's hand holding the coffee cup paused in mid-air.

He had an impression of this name.

About a month ago, Terence Tao had recommended a preprint on the Sieve Method on his blog, and the author was this Zhao Yang.

At the time, Bombieri had also read that paper; his assessment was that the techniques were skillful, the ideas were novel, and he believed that this young man from China should have achieved quite a bit regarding the twin prime conjecture.

But proving the twin prime conjecture?

The weight of those words was too heavy.

So heavy that the first reaction of this old professor, who had seen it all, was not surprise, but suspicion.

Every year, he received a dozen emails claiming to have proven the Goldbach conjecture or the Riemann hypothesis, most of which were the ramblings of amateurs.

But Yang Zhao was different.

He had a track record—the good kind of track record.

Bombieri put down his cup and clicked on the email.

The body of the email was very short, without any pleasantries.

It directly provided the link to the arXiv.

He clicked the link.

The browser redirected.

Title: "On the Boundedness of Prime Gaps"

Page count: 128 pages.

Bombieri did not download it immediately but read the abstract first.

"...By improving the GPY Sieve Method and introducing a new multi-dimensional variational weight function, we prove the existence of infinitely many pairs of prime numbers with a gap less than seventy million..."

"Seventy million?"

Bombieri narrowed his eyes.

This number seemed huge, but in the sense of number theory, it was not only finite but also a qualitative leap.

Before this, the bound was infinite.

As long as a finite bound was proven to exist, even if it were one hundred million, it was a breakthrough from 0 to 1.

This was the weak twin prime conjecture.

Moreover, the last sentence of the abstract read: "In Chapter 9 of the paper, we further optimized this method, pushing the bound to k=2."

Bombieri took a deep breath.

He pressed the download button and simultaneously picked up the phone on his desk.

"Mary, help me cancel all my appointments for the morning. Yes, all of them. No matter who comes, tell them I'm busy!"

Hanging up the phone, the printer started working.

Amidst the rustling sound of paper being fed, Bombieri's expression was unprecedentedly grave.

At the same time. Pacific Time in the United States, 6:31 AM.

On a street near the University of California, Los Angeles.

Terence Tao had just finished his ten-kilometer morning run.

Dressed in a sweat-soaked tracksuit, he stood on the lawn in front of his house, gasping for air.

He took out his BlackBerry to check his schedule for the day.

A new email notification popped up at the top of the screen.

From: Yang Zhao

Terence Tao paused for a moment.

He had been following Zhao Yang.

Since that last paper, he had always felt that this young man was still hiding something.

In that article about the Sieve Method, several steps were handled very subtly, as if deliberately bypassing a more direct path.

He opened the email.

A few seconds later.

Terence Tao suddenly looked up at the eastern sky, his eyes filled with shock.

"'On the Boundedness of Prime Gaps'... Did he really do it?"

Terence Tao quickly ran into the house without taking a shower.

At this moment, he couldn't care about the sweat and stickiness on his body and quickly opened the arXiv link on his computer.

Without downloading, he started reading the paper directly on the computer.

As the mouse scrolled.

Lemma 1... Lemma 2...

Construction function...

"A stroke of genius."

The amazement in Terence Tao's eyes grew stronger; the more he read, the more shocked he became.

Zhao Yang had introduced a brand-new algebraic geometry tool in the paper to handle the error terms of the Sieve Method.

"A very ingenious proof! Interesting! It is truly interesting!"

Terence Tao's eyes were full of excitement.

"I need to verify this. Now."

He grabbed a pen from the pen holder, pulled over a blank sheet of paper, and his brain began to spin at high speed as he started to calculate carefully.

Princeton University, New Jersey, USA, Annals of Mathematics editorial office.

This was the holy land of the global mathematical community; as long as one could publish a paper in the Annals of Mathematics, one would basically become a world-renowned mathematician overnight!

Charles Fefferman walked slowly into the office carrying a sandwich; he was the editor-in-chief of the Annals of Mathematics.

He was mainly responsible for editing in the direction of number theory.

Every day, his inbox was stuffed with various submissions claiming to have solved world-class problems.

Of course, 99% of these submissions were trash, and some couldn't even write basic calculus symbols correctly.

He sat down and opened the backend management system.

The latest submission appeared at the very top.

"On the Boundedness of Prime Gaps"

Author: Yang Zhao