HuckFinn

BERKELEY, CA — In what experts are calling "honestly kind of embarrassing for the rest of us," a PhD student with admittedly "not much research to do" has accidentally revolutionized 2,500 years of mathematical methodology by picking up some books and thinking "what if we did it the other way."

Lijie Chen, a complexity theorist now at UC Berkeley, made the groundbreaking discovery during the summer of 2022 while experiencing what researchers technically term "the existential void between dissertation defense and gainful employment." Rather than confronting the yawning abyss of academic job markets, Chen opted to read some metamathematics papers, a decision that has since upended the foundational assumptions of human logical inquiry.

"Because I was graduating, I didn't have much research to do," Chen explained to reporters, apparently unaware that this sentence would haunt established mathematicians for generations. "I was figuring I should learn something new."

The breakthrough centers on "reverse mathematics," a technique where researchers swap axioms and theorems — essentially doing proofs backwards. After 50 years of the world's smartest people failing to prove computational problems are hard, someone finally thought to check if the puzzle box opened the other way. It did.

At the bedrock of the discovery lies the Pigeonhole Principle, which states — and readers may want to sit down for this — that if you have 11 pigeons and 10 holes, at least one hole contains more than one pigeon. This observation, achievable by any preschooler with a muffin tin and too many grapes, has been formally named, rigorously proven, taught in graduate seminars, and cited in thousands of peer-reviewed papers. It is, researchers confirm with straight faces, "a surprisingly powerful tool." Every three-year-old who has ever tried to put five stuffed animals in four cubbies has independently derived this theorem without federal funding.

Marco Carmosino, a complexity theorist at IBM who reviewed the paper, expressed what sources describe as "shock that an unemployed graduate student and an undergraduate accomplished anything at all."

"I was surprised that they were able to get this much done," Carmosino stated, in a quote that Chen's mother has reportedly already framed. "People are going to look at this and they're going to say, 'This is what got me into metamathematics.'"

The paper has sent shockwaves through the "famously intimidating" field of metamathematics — a discipline where mathematicians use mathematics to study mathematics. Imagine a restaurant critic who reviews only his own reviews. A lifeguard who watches himself watching the pool. An accountant who audits exclusively his own audits of his audits. This is not only permitted in academia but is considered so rigorous that practitioners speak of it in hushed tones, as though they've discovered a door in reality that loops back into itself. They have tenure.

In a move that would get you fired from literally any other job, metamathematicians deliberately choose "weaker axioms" because stronger ones make things too easy. Imagine a surgeon requesting a duller scalpel for "more nuanced cuts." A pilot disconnecting autopilot because "the plane was flying too well." A firefighter bringing a smaller hose to "really understand the fire." Mathematicians alone have discovered that handicapping yourself is not incompetence but methodology, and have named this approach "elegant." HR has not been consulted.

The research also addresses the "equality problem" in communication complexity, which asks whether two people holding strings of numbers can determine if they're identical without comparing them. After decades of work, complexity theorists have triumphantly proven that they cannot — confirming that if you want to check if two things are the same, you have to actually look at them.

Millions in grant money have verified what every person who has ever said "wait, read yours out loud" already knew. The paper has been cited 847 times. A follow-up study confirming you have to open a book to read it is currently under peer review.

The field has now spent 50 years "seeking rigorous answers" to why their proofs haven't succeeded, effectively studying why they can't solve problems, then pivoting to study why they can't study why they can't solve problems. Grants have been renewed.

Chen, for his part, seems unperturbed by the magnitude of his accidental contribution. When reached for comment, he was reportedly "reading some papers" and "figuring he should learn something new."

His collaborator, Jiatu Li, was an undergraduate at the time of the discovery. Li could not be reached for comment, as he was busy being 22 and having already contributed more to mathematics than most tenured professors.