Shortest papers: the blank-page paper, a two-word proof, "Behold!"
What if the most brilliant piece of scientific literature you could ever write was just a blank page? Hey, I'm Salt. I'm Grace. Okay, a blank page as a published paper. How does that even get past an academic editor?
Well, in 1974, it did. A psychologist named Dennis Upper submitted a manuscript to the Journal of Applied Behavior Analysis. The title was The Unsuccessful Self-Treatment of a Case of Writer's Block. And the body of the paper was zero words. He submitted a blank sheet of paper to demonstrate writer's block.
You're kidding. Nope. The journal published it. They even printed a reviewer's note at the bottom praising Upper for submitting the most concise piece of research they'd ever seen. The reviewer said, um, they studied it with a magnifying glass and found no flaws.
That's a pretty good bit. But does a blank page count as real literature? It does, and that created a strange problem for modern researchers. Because in October 2024, an academic named Andy Wai Kan Yeung published an audit of Upper's paper. The blank page — well, he found it has dozens of formal citations in other journals.
Wait — what? Yeah, Salt, people are citing a blank page. Yeung's study showed that a lot of those citations are either satirical, or they're just erroneous. So this one joke from the seventies exposed the flaws in how we measure scientific impact today. It inflated citation metrics without anyone checking the substance.
So a visual gag basically broke the tracking system. Okay. But that's psychology. What about the hard sciences, where you need hard proof? You can't just submit nothing to a math journal.
No, but you can submit two sentences. Let's go back to November 1966. Two researchers, L. J. Lander and T.
R. Parkin, published a paper in the Bulletin of the American Mathematical Society. It was a single paragraph containing just one computer-calculated equation. Seriously? One equation.
What were they trying to prove with one equation? They weren't proving anything. They were disproving Leonhard Euler. Euler made a famous conjecture back in 1769 about the — about the sums of like powers. That conjecture stood as a rule for almost two centuries, because nobody could find a reason to doubt it.
Until Lander and Parkin. Right, because they got an early computer, and it churned the numbers until the machine spit out one set of integers violating the rule, so they just wrote down that single equation showing Euler was wrong, added a sentence saying here's the counterexample, and that was the paper. It broke the rule. Huh. Because proving a complex mathematical theory can require hundreds of pages of deep logic, but if you want to disprove one, you only need a single counterexample that breaks it.
You break it, you publish. And mathematicians have a tradition of pushing this boundary. Skip ahead to January 2005. John H. Conway and Alexander Soifer submitted a paper to The American Mathematical Monthly.
The text — the text was just two words long, sitting above two visual diagrams. Just two words? Yeah, they wrote "n can". What does that even mean? So they were answering this, um, very niche geometry problem about whether a certain number of triangles could cover a specific shape.
The first diagram showed the shape failing to cover it, and the second diagram showed a slightly different arrangement succeeding. Okay, so the pictures show the answer. Yes. The pictures showed the answer so clearly that the only words they felt they needed were "n can". But the journal editors refused to print it.
Rejecting a working proof over word count is absurd. Yeah, the editors pushed back. They, uh, told Conway and Soifer that the visual was nice, but a real paper needs an abstract and at least a paragraph of explanatory text. Did they add it? No, they fought them on it.
They argued that if the picture does the job, adding words doesn't make it better science, it just makes it bloated. They eventually got it published. I mean, Grace, if the geometry proves itself, why pad it out? Which is how the ancients used to work. If you look at early mathematical texts, they bypassed language all the time.
The Chinese Zhoubi Suanjing from roughly 200 BCE relies on visual proofs of the Pythagorean theorem with almost no written text attached. So they just drew the right angles and expected you to get it. Pretty much. And the 12th-century Indian mathematician Bhaskara the Second did, kind of the same thing. He just drew a diagram showing the squares and triangles interacting so you could see the relationships naturally.
His — his only written instruction for the whole proof was a single word. What was the word? It translates to "Behold!" or "Look!" See, that's the energy I want from modern researchers.
You drop the proof on the desk and just tell the reader to look at it. Have you ever tried to read a modern methodology section? We expect these sprawling, you know, hyper-wordy articles now. Yeah, it really does drag. You look at those ancient texts, or a two-sentence counterexample from the sixties, and you wonder if the wordy style of modern publishing is just obscuring scientific truth.
Like, maybe researchers today should spend a bit more time searching for their own "Behold!" moments instead of writing fifty pages of padding. I'd read a lot more math if they did. Thanks a lot for listening to Daybrain.
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