A heavy snow fell all night in New Jersey.
The heating at the Princeton Institute for Advanced Study kept the office as warm as spring, while outside, cold wind whipped snow particles against the thick glass.
Delian tossed the small nub of chalk in his hand into the chalkboard tray and dusted off his hands.
Chalk dust drifted slowly downward in the dim, yellow light of the wall sconces.
The chalkboard was densely covered with equations.
The derivations stretched from the far left of the board to the far right. The handwriting started out neat and fluid but grew progressively messier, coming to an abrupt halt before a large cluster of formulas—a chaotic jumble of compensation parameters and limit symbols.
Delian took two steps back, unfolded a wooden folding chair, and sat down.
He picked up the mug on the desk—the one with the Princeton crest on it—and took a sip of the black coffee, which had long since gone cold.
The bitter liquid slid down his throat but did little to clear his head.
"It’s no good. It’s still too bloated."
Delian stared at the cluster of formulas on the right side of the board, his brow furrowed.
His postdoc, David, stood at the other end of the chalkboard with an eraser in his hand, shoulders slumped.
In preparation for their formal submission to *Physical Review Letters*, they had already pulled several all-nighters in this office, trying to optimize this "patch." David had been slogging away in here for weeks, and the dark circles under his eyes were frighteningly deep.
"Professor, this renormalization scheme is logically self-consistent."
David pointed to a parameter on the board.
"As long as we introduce this infinity as a cancellation term, the boundary of the manifold can converge mathematically. The preprint has been online for two months, and none of our peers have raised any objections to this point."
"There are no objections because they can’t find a better way either. They’re just holding their noses and accepting it."
Delian placed the mug back on the desk with a soft clink.
"David, mathematics should be elegant. When you have to forcibly shove three compensation variables into an equation to keep it balanced, it’s like tying three crude hemp ropes to a delicate suspension bridge on the verge of collapse."
Delian leaned back in his chair and sighed.
"The bridge might not collapse, but it’s no longer a bridge. It’s become an ugly patch."
David didn’t argue.
He knew Delian was right.
The pinnacle of theoretical physics was simplicity. With this singularity problem, their current theory couldn’t get around the collapse into infinity caused by continuous calculus. The only way to brute-force a solution was with patches like this.
"Let’s take a break," Delian said, rubbing his temples. "My brain is fried. The more I stare at that board, the deeper I get stuck in this rut."
David put down the eraser, visibly relieved.
He walked over to the desk in the corner, sat down in a slightly cluttered leather swivel chair, and wiggled the mouse to wake the monitor.
The screen lit up, its blue glow illuminating David’s exhausted face.
"Check the email."
Delian said, still leaning back in his chair with his eyes closed.
"The preprint has been on arXiv for nearly two months now. Maybe an old friend can offer some advice, a new perspective."
David nodded and opened his inbox.
A dozen or so unread emails sat in his inbox.
Most were routine academic conference invitations. A few were from graduate students in other universities’ physics departments, typically asking for details about the derivation of a basic formula in the preprint. David usually handled these replies himself or simply archived them.
David scrolled down with the mouse wheel, scanning line by line.
His eyes stopped on one subject line.
The subject line was simple, with no polite prefixes. It just cited the ID of the preprint they had updated yesterday.
David glanced at the sender’s name.
"Zhuo Chen."
The email domain was .edu.cn.
"An email from Hua Country," David said casually. "Hua Country Science and Technology University."
Delian’s eyes remained closed, his fingers tapping lightly on the armrest of his chair.
"Keda? I have a few old friends over there who work in condensed matter. What’s the email say?"
David opened the email.
The body of the email was only two lines long, written in concise, standard academic English.
There was no flattery, no lengthy self-introduction. It simply pointed out a computational redundancy in the renormalization steps on page four of the preprint and included an attached PDF with an alternative approach.
"It’s just two sentences." David’s tone was a bit helpless. "He says we could try an algebraic substitution in step four and attached a two-page PDF."
"An algebraic substitution?"
Delian’s tapping fingers stopped.
He opened his eyes and looked toward David.
"Does he think this is high school algebra? Using algebraic substitution on a multidimensional manifold?"
"Probably a student from Hua Country who’s just getting into theoretical physics."
David shrugged, moving the mouse cursor over the PDF attachment.
"Every year, we get tons of emails from amateurs claiming to have disproven relativity or found the theory of everything."
"Open it anyway."
Delian stood up and stretched his stiff neck.
"It’ll be a change of pace, at least."
David double-clicked the attachment.
The PDF file popped up on the screen.
At the top of the page, there wasn’t even a title—just a massive matrix of integrals and limit symbols. It was the very singularity equation from the chalkboard that had been tormenting them all night.
David leaned back in his chair, propping his chin on one hand as his eyes followed the first line of equations down the screen.
The first two steps were standard assumptions.
Then came the third step.
The indifferent expression on David’s face vanished.

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