Chapter 259 - 247: To the Next Generation, Good Luck

Chapter 259: Chapter 247: To the Next Generation, Good Luck

"...The next update might be a little late. I need to chew through this paper first."

"Bye, everyone."

The video ended, and the comment section below instantly exploded.

"Holy crap, even the vlogger is reacting like this?"

"Wait, is the *Mathematical Annals* a big deal? A professor at my university submitted to the *Mathematical Annals* too, and even got published in the A-series."

A second later, someone in the replies immediately shot back.

"Bro, you’re talking about the domestic *Mathematical Annals*."

"The vlogger is talking about the *Annals of Mathematics*—the one from Princeton."

"It’s the top of the four major journals in mathematics. Other top journals publish one or two hundred papers a year; this one only publishes about forty."

"Every single paper is worthy of being written into a textbook."

"Speaking of which, is this Li Dong from Yan University the same guy who was on the Broadcast before?"

"Yeah, yeah, yeah, that’s him! The one who made a huge leap forward on the Montgomery couplet."

"What is the guy above me talking about? Is this a ’try not to laugh’ challenge? It’s called Montgomery’s Conjecture on Association, not ’couplet’!"

"..."

The outside world was in an uproar.

But the true insiders hardly made a peep on social media.

They all knew what this paper meant.

Because this wasn’t a single-point breakthrough.

It was an architectural-level breakthrough.

Just like back in 1974, when Deligne cracked the Weil conjectures.

After that one paper was published, for the next thirty years, the entire fields of Algebraic Geometry and arithmetic geometry gave rise to a steady stream of results: Faltings’s proof of the Mordell conjecture, Fermat’s Last Theorem, Wu Baozhu’s fundamental lemma...

A whole string of Fields Medal-level achievements, all of which had sprouted from the toolbox of that one paper.

As for Li Dong’s paper, if it truly held up...

...it would be that kind of foundational existence for the Langlands Program.

The insiders dared not speak out because they still needed to chew through it a few more times.

But just then...

Two hours after the main text of the paper was posted, the official website of the *Annals of Mathematics* took the rare step of adding an editor’s note.

The note was very short, just a single line of text:

[At the request of the reviewer, their peer review report has been published alongside the paper under their name, to serve as an attached commentary.]

For those who followed the *Annals* year after year, this single line of text was like a clap of thunder.

The peer review process for the *Annals* had been strictly anonymous since its inception.

For over a hundred years, from Serre to Deligne, from Terence Tao to Faltings, countless top-tier reviewers had left their marks on it.

But all of them spoke as an "anonymous referee."

In over a hundred years, the number of people willing to publish their review reports under their own name could be counted on one hand.

And the person who signed it this time was—Robert Langlands himself.

The old man who had personally written down the "Langlands Program" in 1967.

...

A few more words must be said here.

Everyone in this field knows that Langlands is an extremely stingy person when it comes to praise.

He had never been stingy about writing down his own original ideas, but he had always been very reserved in his evaluation of others’ work.

Whenever young colleagues received a review from Langlands, if they could just read the opening phrase, "This is interesting work in the direction of...," they could already close their laptops and go out for a celebratory glass of champagne.

Because that meant it had passed.

More often, what he wrote was...

"The author’s calculations, from what I could verify, are correct."

"Whether they constitute meaningful progress on this conjecture is another question, which I will leave to the editorial board."

This was his review for a 2007 paper that used the trace formula to improve the GL(3) case.

That paper was later published in *JAMS*, and the author eventually earned tenure as a professor.

There was another, even more famous, comment.

"The paper’s use of the trace formula is meticulous."

"I do not see its results as a substantial extension beyond existing work."

"This does not mean the paper should not be published. My meaning is that readers should not harbor expectations for it beyond what it is."

From anyone else, such comments would be considered daggers.

Coming from Langlands, it was already considered "mildly polite."

Everyone in the circle knew that his highest praise for a paper was to add a single sentence after a positive evaluation:

"The author should be encouraged."

(The author should be encouraged.)

That was all.

...

So this time.

When his review report was posted on the official *Annals* website as a signed appendix, nearly everyone in the world working on the Langlands Program clicked on it the moment it appeared.

The report wasn’t long, less than a thousand words in total.

But its first paragraph left everyone who clicked on it dumbfounded.

"I am writing this review report under my own name."

"This goes against your journal’s custom and is something I have not done in over twenty years."

"Editor, please understand. When an old man knows he will not have many more opportunities like this, please allow him this small indulgence."

"I have read this paper three times."

"The first time was to verify its arguments. They are correct."

"The second time was to confirm my own astonishment. It did not fade."

"The third time was to imprint its construction upon my heart, for I am old, and I wish to carry this construction with me for the rest of my days."

It was not until the second paragraph of the review that Langlands began to discuss the paper itself.

He didn’t comment on it Chapter by Chapter as per the review process. Instead, using a tone as if he were lecturing students, he placed the paper within the fifty-year context of the Langlands Program.

"Between 1967 and 1970, I hastily scribbled down a set of conjectures in letters and lecture notes, which later became known as the ’Langlands Program’."