The Conjecture That Brought Disaster! (Revised; please pull down to refresh your bookshelf before entering this chapter)
Qi Hao stared at the flashing treasure chest icon, his finger hovering in midair. For a long time, he didn't tap it.
Something suddenly occurred to him.
Last time, he had seen a post on Tieba titled "A mystical guide to opening chests: how to improve your drop rates." The original poster had sworn that bowing three times before opening a chest would turn you into a luck emperor...
Qi Hao knew it was pure bullshit. Probability was probability; bowing three times wouldn't change the random number seed.
But what if?
Sometimes, when it was time to be superstitious, you just had to be a little superstitious.
Taking advantage of the empty dorm room, Qi Hao stood up and bowed three times toward the balcony.
With that done, he opened the chest.
The treasure chest icon enlarged and spun again.
Qi Hao's heart raced in time with the shifting colors.
He kept muttering, "Don't be white, don't be white, don't be white."
The white light lingered for an instant. He was just about to sigh and resign himself to it when the light suddenly flashed!
It was purple!
[Congratulations, host. You have obtained a purple treasure chest!]
Qi Hao nearly bit his tongue.
Purple! A purple treasure chest!
Had the mystical ritual actually worked?
"System, open the treasure chest!" Qi Hao looked expectantly at the icon before him.
[Opening...]
[Opened successfully!]
[Item obtained: Jacobian Conjecture (complete proof)]
[Description: This reward contains the complete proof of the Jacobian Conjecture, from the foundational lemmas to the final theorem. It takes a unique algebraic geometry approach, unlike any known method in the existing literature.]
Qi Hao stared at the words "Jacobian Conjecture" on the panel, stunned.
That name... Had he heard it somewhere before?
He remembered coming across a post on Tieba a while ago. Its title had been something like "Peking University genius washes dishes in America: a life ruined by a mathematical conjecture."
He had read it as entertainment gossip at the time, and he could no longer remember the details clearly.
Qi Hao opened his laptop and began searching.
The first result was an encyclopedia entry.
The entry was brief, only a few short paragraphs: "The Jacobian Conjecture, also known as Keller's Problem, was proposed in 1939 by the German mathematician Keller. It states that if F: Cⁿ→ Cⁿ is a polynomial mapping whose Jacobian determinant is a nonzero constant, then F must be a polynomial automorphism (that is, it has a polynomial inverse mapping)."
"More than seventy years have passed since the conjecture was proposed, and it remains neither proven nor disproven. The American mathematician Smale included it among the eighteen important mathematical problems of the twenty-first century."
He continued scrolling through the search results and found an old post on a Tieba forum called Mathematics Bar. Its title was:
[Popular science] Yitang Zhang and the Jacobian Conjecture: a genius's darkest hour
The post described in detail a piece of academic gossip that had long circulated in Huaguo's mathematical circles. Yitang Zhang was born in Shanghai in 1955 and entered Peking University's mathematics department as an undergraduate in the class of 1978. That class produced a number of figures who would later make waves in the international mathematics community, but Zhang was not among them.
In 1985, Yitang Zhang went to the United States to study for a doctorate in mathematics at Purdue University under Professor Tzuong-Tsieng Moh, a mathematician of Chinese descent. The subject Moh chose for his doctoral dissertation was none other than the Jacobian Conjecture.
Professor Tzuong-Tsieng Moh was a renowned scholar in algebraic geometry. He was himself deeply obsessed with the Jacobian Conjecture and had even published a paper claiming to prove one of its core foundational lemmas.
Trusting his advisor, and driven as well by the inborn pride of a genius, Yitang Zhang plunged headfirst into the problem.
That plunge lasted seven full years.
Yitang Zhang's talent was beyond question. He made astonishing progress on the Jacobian Conjecture and had even reached the threshold of a final proof.
But at the final stage of his derivation, to close the entire logical loop, he had to cite the core lemma his advisor Tzuong-Tsieng Moh had published years earlier.
Then tragedy struck.
When Yitang Zhang submitted his doctoral dissertation on the Jacobian Conjecture, the university's dissertation review committee discovered a problem with the crucial lemma he had cited, a result his advisor Tzuong-Tsieng Moh had published.
In other words, Tzuong-Tsieng Moh's theory was actually wrong!
Because the Jacobian Conjecture was a famous problem that had stirred the academic world, Yitang Zhang's work attracted the attention of quite a few mathematicians.
Once more people became involved, they confirmed the error in the lemma. How could Tzuong-Tsieng Moh take that lying down?
Humiliated and furious, he blamed Yitang Zhang for everything.
It was Yitang Zhang who had made him lose face.
In American academia, where lineage and seniority counted for so much, this was nothing short of a disaster.
Because of this, the relationship between advisor and student fell to freezing point. In 1992, Yitang Zhang managed to scrape through and earn his doctorate, but Tzuong-Tsieng Moh refused to write him a single letter of recommendation for a job.
In American academia, a graduate without a recommendation from his doctoral advisor might as well have "unemployable" branded onto him. No matter how talented you were, no university or research institution dared take you on.
And so, after graduation, this once-favored son of heaven couldn't even find the lowest-level doctoral job. To make ends meet, he could only work as an accountant at a Subway fast-food restaurant owned by a friend...
His former classmates and friends had long since become full professors with tenure at top universities, while he, a genius once considered a potential Fields Medal winner, scraped together a living doing odd jobs on the streets.
Another seven years passed.
For reasons Qi Hao didn't know, Yitang Zhang chose not to return to his home country.
Around 1999, through an introduction from an old friend, Yitang Zhang finally secured a temporary lecturer position at the University of New Hampshire.
The Jacobian Conjecture, which had caused the break between him and his advisor, remained unresolved to this day, and he never again touched research related to it.
The last line of the post read:
"The Jacobian Conjecture ruined the first half of Yitang Zhang's life, but who knows? Perhaps one day, fate will make it up to him in another way."
Seven years, and another seven.
How many stretches of seven years did a person have in a lifetime?
Especially the seven years when a mathematician was in his golden age, at his peak, and at his most creative!
He didn't know why Yitang Zhang had stayed in the United States rather than return to his home country after offending his advisor. Perhaps Zhang felt he hadn't done well enough to go back, or perhaps he was waiting for an opportunity.
Who knew?
People were always complicated, and mathematicians were no exception.
In the eyes of the general public, mathematicians were a group of ascetics above worldly affairs, with only truth for company.
Yitang Zhang's story laid bare before Qi Hao the dark side of academia, where seniority mattered and academic tyrants could even cover the sky with one hand.
There were quite a few comments beneath the post. Some cursed Tzuong-Tsieng Moh for being petty, while others criticized Zhang for not returning to his home country. Others jumped in to explain that when Zhang was at Princeton, he could go ten days without saying a word to anyone; if he came back, nobody would be able to stand him.
Without a doubt, the Jacobian Conjecture had brought Yitang Zhang plenty of trouble.
And now, the complete proof of the conjecture that had brought disaster upon Yitang Zhang lay quietly in Qi Hao's system inventory.