Chapter 11 - Verification
Chapter 11 - Verification
Formulas filled the three chalkboards in the MIT mathematics lab.
The left board held the common coordinate system, the middle board held thresholds and connections, and the right board was lined with long, unorganized formulas.
Siwoo stood on a step stool, staring at the last line.
Chalk dust coated his fingertips, and dozens of papers were piled on the desk.
Most were covered in traces of being erased and rewritten, and Siwoo didn't move for a long time, still holding the chalk.
"...This is it."
It was the part that had been off for the last few days.
If he aligned the baseline, it would connect, but the meaning would waver slightly at the final stage; he could see the path within the common coordinate system, but it wouldn't lead to the end.
Just one part, the final connection; that was where it kept blurring.
Siwoo drew one more small line at the bottom right of the board, and instead of erasing the blank space he'd left, he pushed it to the side.
One dot, one arrow, and a new baseline.
Only the sound of chalk echoed in the lab, and the entire chalkboard looked like a single painting.
"...It actually works."
Siwoo immediately checked the clock.
It was still within the allotted research time.
He took a slow breath, climbed down to the desk, took out a sheet of paper, and wrote the title.
[Hodge Conjecture Proof Draft]
The formulas weren't as long as he thought; in fact, they had shortened.
The unnecessarily roundabout lemmas were removed, and as the parts he had pushed aside as exceptions entered the connection, the structure became simple.
If this was really correct, it meant there had been a door right in the middle of the path countless mathematicians had taken a detour around.
Siwoo wrote the formulas until the last page and immediately sent an email to Jonathan.
-Draft
The moment he pressed the send button, the lab door opened, and the person standing there was Andrew.
He was walking in with coffee but stopped when he saw Siwoo's face.
"Siwoo."
"Yes?"
"Did you find something?"
Siwoo pointed to the email sent screen.
"I sent it."
"Sent what?"
"The draft."
"...What draft?"
"The Hodge Conjecture."
Andrew couldn't say anything for a few seconds.
Then he immediately took out his phone.
"Professor. You need to come to the lab right now."
20 minutes later, Jonathan Reed opened the lab door and walked in.
His tie was a bit crooked, and traces of having rushed over remained on his face, but his eyes were sharp.
He took the printed draft without a word, and after 30 minutes passed, Jonathan said in a low voice.
"Wait."
Andrew asked immediately.
"Is there a problem?"
Jonathan didn't answer.
He went back to the front page and read the same part again.
"Andrew."
"Yes."
"Call Bradley."
"Contact Elliot, the department chair, and the president's office as well."
Andrew's face stiffened.
"Is it that serious?"
"I don't know yet."
"Then why?"
"That's why we need to call them faster."
People began to gather in the MIT mathematics department conference room.
-Hodge Conjecture Proof Draft
As soon as Bradley saw the title, he rubbed his face.
"Even the title is bad for the heart."
Elliot asked.
"Have you read it?"
"Not yet."
"I only read the first three pages."
"How was it?"
Elliot remained silent instead of answering, and Jonathan stood up from his seat.
"There is only one thing to do today."
"Find the flaws."
The air in the conference room changed immediately.
"Do not assume it is correct."
"Do not show consideration because he is a genius, and forget the child's age."
"Treat it like a paper and tear it apart."
Bradley nodded.
"That's right."
Andrew looked back at Siwoo.
Siwoo was sitting in the corner of the conference room, and Hyejin and Taesik were sitting in the back.
Siwoo looked calm, and seeing that, Jonathan asked.
"Siwoo. Are you okay with this?"
"Yes."
"We are going to try to find the parts that are wrong."
"That's the right thing to do."
Bradley looked at Siwoo.
"Why do you think so?"
"Because I might be wrong."
The review began, and the first hour was quiet.
The sound of turning pages, the sound of marking with pens, the occasional short breath; the professors each picked out parts that looked weak.
Bradley latched onto the definition of the connection, and Elliot looked at the consistency of the baseline alignment.
Andrew checked for points of conflict with existing papers, and Jonathan followed whether the overall structure was preserved until the end.
After an hour, the first question came out.
"Here."
Bradley pointed to the middle of the draft with his finger.
"You said this connection is preserved, right?"
Siwoo nodded.
"Yes."
"But under these conditions?"
"That's not the same connection."
"What?"
"It looks similar, but the coordinate system is different."
Bradley narrowed his eyes.
"Then you have to move it?"
"Yes."
"Where should it be moved to?"
Siwoo drew a line on the chalkboard.
One arrow, one dot, and a small baseline.
"Here."
Bradley looked at the chalkboard and shut his mouth, and Elliot came over to the side to look with him.
"...It explains it."
Bradley said in a low voice.
"Move on to the next."
Second question, third question, fourth question, the questions continued.
Siwoo couldn't answer every question.
A few times he said he didn't know, and a few times he said he hadn't looked at it yet.
But the core didn't collapse.
The parts he didn't know were peripheral, and the central structure kept holding up.
The afternoon review was rougher.
Now the professors didn't bother with etiquette and went in aggressively on purpose to find flaws.
"Isn't this circular logic?"
"No. It breaks here first."
"Then why is this lemma necessary?"
"Because it's not."
"If you remove that, the back part will collapse, won't it?"
"It won't collapse."
"Why is that?"
Siwoo walked to the chalkboard and wrote a few lines, and the professor who asked the question shut his mouth.
"...It doesn't collapse."
The atmosphere changed. They had to find where it was wrong, but they couldn't see any wrong places.
At first, it was a meeting to find flaws, but by the afternoon, everyone was looking at the same point.
7 PM, the conference room door opened, and Harold Grant entered.
He didn't even take off his coat and immediately demanded the draft.
"Where is it?"
Jonathan handed over the draft without a word, and Harold sat down and started reading from the first page.
The conference room became quiet again, and every time he turned a page, people's gazes moved with it.
10 minutes, 20 minutes, 40 minutes, an hour passed, and he didn't say a word.
And only after reading the last page did he take off his glasses.
"This makes no sense."
The conference room froze, and Jonathan asked quietly.
"Is it wrong?"
"No."
That one word shook the entire conference room.
"Then?"
Harold exhaled slowly.
"It seems correct."
No one could speak.
They all knew how heavy those words were.
"It seems correct." To a mathematician, those words were almost taboo.
It was a phrase never easily uttered before complete verification, but Harold Grant had said it.
Siwoo asked quietly.
"Are there no wrong parts?"
Harold looked at him.
"I haven't found any yet."
"Then you can just look for more."
Harold was dazed for a moment, then laughed.
"Yes. I suppose I can look for more."
He turned toward Jonathan.
"We must inform Clay."
"They have already been contacted."
"Then we must call the official review team."
The president asked.
"What about the announcement?"
Harold said firmly.
"Not yet."
"Why not?"
"This is too big of an event. If we release it to the world without verification, the child will be torn apart."
Hyejin's face stiffened, and Harold turned his head toward her.
"Ma'am, we must protect him."
"Protecting the child is just as important as verifying the proof."
Hyejin looked at him for a long time, then said briefly.
"Please keep that promise."
"I promise."
That night, the lights in the MIT president's office were turned on again.
Hodge Conjecture Proof Draft, proposal for a private international verification procedure; the president read the document and looked at Jonathan.
"We really have come this far."
"It's not the end yet."
"But... we are close to the end."
Andrew said in a low voice.
"The Clay review team departs tomorrow."
The president closed his eyes, and the history of MIT and countless geniuses passed through his mind.
There had been countless discoveries, but nothing like this.
An eight-year-old child creates a draft proof for a Millennium Prize Problem, American mathematics elders cannot find a flaw, and the Clay Mathematics Institute moves for an official review.
"Do not let it leak to the press under any circumstances."
"It is already being controlled."
The next morning, the Clay Mathematics Institute's review team boarded a plane to Boston.
And for the first time, MIT wrote this sentence in an internal document.
[Yoon Siwoo's draft is classified as a candidate for the Hodge Conjecture proof]
The Clay Mathematics Institute review team arrived at MIT.
The conference room door closed immediately, and the review began.
The review team's questions poured in, and Siwoo answered them one by one.
The review team checked again and again.
And at dawn, the last page was turned, and the conference room became quiet.
The head of the Clay review team took off his glasses and said.
"Are there any questions?"
No one answered.
"Are there any counterarguments?"
Still, no one answered, and the head slowly exhaled and looked at Jonathan.
"Congratulations."
"The Hodge Conjecture has been solved."
Bradley leaned back in his chair.
Andrew covered his face, and the president had no words.
Harold stared at the chalkboard for a long time.
Decades? No, a problem that had held out for over a hundred years had just ended.
At that moment, Siwoo asked quietly.
"So, is it over now?"
"...Yes."
That dawn, MIT created a top-secret document.
[Hodge Conjecture Verification Complete]