People from Huaguo Are Really Interesting!

Professor Alexei read the first two pages of the paper quickly.

The writing was unadorned, without the exaggerated rhetoric Americans were so fond of. It simply set out the problem, defined the notation, and developed the logic.

Alexei formed an initial impression: this author from Huaguo had received good training.

Then he turned to the third page.

The theorems began to come thick and fast, and numbered citations to the references appeared frequently.

Alexei did not rush on to the proofs. Following his usual reviewing practice, he turned first to the last page to look at the references.

His gaze fell on the lines of text.

Then his hand stopped.

Brudno, 1963, "On a Game Algorithm."

Alexei's eyes lit up at once.

He put down his teacup, unconsciously sat up straight, and leaned toward the screen almost involuntarily to examine the remaining references.

Adelson-Velsky, Arlazarov, Donskoy, and Landis.

Five papers, all from Soviet academic journals published between the 1960s and 1970s.

Professor Alexei took off his glasses.

For some reason, he laughed.

Huh, Soviet literature.

It's been such a long time since I've seen any.

In the mathematics department of Moscow State University in 1988, Alexei had been a second-year doctoral student. That winter, the department had organized an internal seminar on combinatorial game theory, and one of the speakers had been a student of Adelson-Velsky.

At that seminar, Adelson's student had presented the latest advances made by Arlazarov, Donskoy, and others in game-tree search algorithms. They had constructed a complete theoretical framework for analyzing the pruning efficiency of search trees in finite perfect-information games, including the derivation of a series of inequalities concerning absolute pruning bounds.

The talk had been given in Russian and written in Russian, and it had been published in a journal of the Soviet Union Academy of Sciences, with a print run of perhaps only a few hundred copies.

Had those results ever been translated into English?

Yes, but only a small portion. The Adelson team's 1975 paper on the Kaissa chess program had been translated into English and circulated in the West, but the more underlying, fundamental mathematical derivations-the theorems and lemmas that truly formed the skeleton of the theory-had, for the most part, never been translated.

Every scientist hoped their research results could benefit all of humanity, and the Adelson team was no exception.

But because they were Soviet, those results had become like treasure sunk in the deep sea, lying quietly somewhere, forgotten by all.

And now, in a paper submitted from Huaguo, Alexei saw that someone had salvaged the treasure.

Another paper he had read was Brudno's.

Alexei knew this one all too well.

The paper Brudno published was the first in human history to provide a rigorous mathematical proof of the Alpha-Beta pruning algorithm.

That was right, the first.

The Western academic world later generally credited the theoretical foundations of Alpha-Beta pruning to the classic paper by Knuth and Moore. That paper was indeed beautifully written, and its proof was exceptionally complete, but strictly speaking, Brudno had been the first!

But because Brudno had written in Russian and published in a Soviet journal, almost no one in the Western world had read it behind the Iron Curtain, so no one would give Brudno that honor.

That was the reality of those years. Mathematicians on either side of the Iron Curtain had independently climbed the same mountain. Those in the East had reached the summit first, but those in the West had not known it. Later, when those in the West reached it too, the whole world remembered only the West.

The West's strength had also led people to know only the achievements of those in the West.

Alexei could hardly say he was angry about it. After all, decades had passed, and he had long since grown used to it.

He did not know whether the Soviet Union's original convictions and ideals would endure.

But at that moment, looking at the paper's list of references, he did feel a surge of complicated emotions.

Someone remembered the Soviet researchers.

Someone not only remembered them, but had actually gone and read those papers, truly understood them, and produced new work building on them.

Alexei put his glasses back on and carefully read the paper from beginning to end.

It took him two hours.

His reviewing style was completely different from Kevin's. Kevin was the kind of young man who tended to go around an obstacle when he saw one, while Alexei was the kind of old-school scholar who had to turn over every stone to see what lay beneath.

He understood the central line of reasoning in the proof.

The author had indeed cited Adelson and his colleagues' classification theorem for symmetric game-tree structures, as well as Brudno's fundamental inequality concerning the relationship between pruning depth and branching factor.

Alexei noticed a crucial detail: the author was not simply lifting these old conclusions.

Building on those old conclusions, the author had constructed a new set of inequalities. By introducing a new concept he called the "state space compression operator," he had extended pruning bounds that originally applied only to fully symmetric game trees to a broader class of quasi-symmetric structures.

Alexei checked the proof of the central theorem repeatedly and found that the chain of logic was complete, with every step of the derivation supported. The author's understanding of the Adelson-Velsky framework was so deep that Alexei almost had the illusion that the author had attended that seminar all those years ago.

A person from Huaguo had dug up the Russian-language papers of Soviet mathematicians, understood them, put them to use, and built another story on top.

Alexei shook his head, the smile at the corners of his mouth deepening.

"People from Huaguo are really interesting."

Could the red spark really have been passed on?

He did not know who the author was. Otherwise, he would have loved to have a good conversation with him.

Since the author could cite Soviet literature, that proved his Russian was quite good.

It had been a long time since Alexei had spoken Russian with anyone.

He really missed that feeling.

The paper before him, however, was not perfect.

In the proof of convergence for the "state space compression operator" in Section 4, the author had skipped a step. Specifically, between Proposition 4.3 and Theorem 4.5, the author claimed that the compression operator was a contraction mapping under a particular norm, but the proof provided lacked an explicit estimate.

This was not fatal, however.

Alexei judged from experience that the estimate was most likely valid, but for a formally published paper, the gap needed to be filled.

Alexei opened the review system and began writing his report.

Reviewer 2's comments:

"This paper makes a novel and valuable contribution to the problem of absolute pruning in finite game trees. The author's command of the existing literature is impressive. In particular, the citations of Adelson and his colleagues' early work demonstrate that the author has a deep and comprehensive understanding of the field's historical development.

The proof of the central theorem is logically clear, and its conclusions are of theoretical significance.

However, one technical detail requires supplementation: between Proposition 4.3 and Theorem 4.5, a rigorous estimate of the compression operator constant is missing. I recommend that the author provide a complete proof in the revised manuscript.

Recommendation: Minor Revision."

Alexei submitted his comments.

The ultimate fate of this submission from Huaguo was no longer his to decide.

He hoped Reviewer 1 would appreciate the paper just as much.

But if Reviewer 1 was an American, it was hard to say what would happen.

As a reviewer, all he could do was give an honest, professional assessment.

The rest could only be left to the editor.