This post is based on my experience as an editor for several journals. My opinion on Introductions to papers has evolved since serving in this role.
The Uncomfortable Truth
Here’s something that might make pure mathematicians cringe: getting your paper into a top journal has more in common with getting views on YouTube than you’d think. Both depend on capturing human attention in an environment of overwhelming choice, and both rely on the same cognitive psychology principles that govern how our brains decide what’s worth our time.
Before you close this tab in disgust, consider this: editors at mathematics journals face hundreds of submissions. They make initial decisions quickly sometimes in minutes, not hours. They’re not evaluating theorems at this stage, they’re deciding whether to even send your paper to referees. And in that crucial moment, your introduction is doing the same job as a YouTube thumbnail and opening hook.
The Cognitive Science Behind Editorial Decisions
The Paradox of Choice and Cognitive Load
When facing too many options, humans don’t carefully evaluate each one. Instead, our brains switch to what psychologists call “satisficing”, using quick heuristics to filter options rapidly. A journal editor with 150 submissions isn’t that different from someone scrolling through YouTube recommendations. Both are in cognitive overload, and both will use mental shortcuts to decide what deserves attention.
This isn’t laziness; it’s neurological necessity. The prefrontal cortex can only handle so much decision-making before it starts taking shortcuts. Your beautifully crafted proof in Section 4 is irrelevant if the editor’s brain has already decided by paragraph 2 that this paper isn’t exciting enough for their journal.
The Curiosity Gap: Your Most Powerful Tool
Psychologist George Loewenstein identified something YouTubers now exploit millions of times per day: humans have an almost compulsive need to close gaps between what they know and what they want to know. When we sense that we’re missing information, our brains release dopamine in anticipation of getting it.
Consider these two introduction openings:
Version A: “We study the boundedness properties of singular integral operators on weighted Hardy spaces.”
Version B: “A fundamental mystery in harmonic analysis is why certain operators that should explode actually remain bounded. Despite forty years of intensive study since Stein’s groundbreaking work, the weighted case has resisted all attempts, until now.”
Version B creates a curiosity gap. It promises to resolve a tension. The editor’s brain is now primed to want the resolution, making them more likely to keep reading or send to referees.
The YouTube Connection: Same Brain, Different Content
The parallels with successful YouTube videos are almost embarrassing in their directness:
The Hook (First 5 Seconds = First Paragraph)
- YouTube: Creators know they have 5 seconds before viewers click away.
- Papers: Editors decide within the first paragraphs whether to continue reading.
- Psychology: The primacy effect means first impressions dominate judgment.
Social Proof
- YouTube: “10 million subscribers can’t be wrong!”.
- Papers: “Building on work of Terence Tao and recent Fields medalist…”.
- Psychology: Authority bias and social validation shortcuts.
The Payoff Structure
- YouTube: Reveal just enough to maintain interest, full payoff at the end.
- Papers: State the theorem clearly but not technically, save the clever proof idea for later.
- Psychology: Variable reward schedules maintain attention better than immediate gratification.
The Story Arc
- YouTube: Setup → Conflict → Resolution.
- Papers: Important problem → Previous attempts failed → Our breakthrough.
- Psychology: Narrative bias, our brains evolved to process stories, not abstract facts.
A Template That Works
Based on these principles, here’s a structure that maximizes your chances of avoiding desk rejection:
Paragraph 1: The Universal Hook
Start with the broadest possible framing. Connect to a classical problem everyone recognizes. You want non-specialists nodding along.
“Understanding when [general phenomenon] occurs has been central to [broad area] since [classical reference].”
Paragraphs 2-4: Building Tension
Create the curiosity gap. What specific aspect remains mysterious? Who tried and failed? Why did standard approaches fail?
“While substantial progress has been made in [setting], the case of [your setting] has proved remarkably resistant to attack. The techniques of [famous person 1] break down because… The approach of [famous person 2] requires assumptions that…”.
The Reveal: Your Contribution
Don’t bury it, but frame it as resolving the tension you’ve built.
“Our main result shows that [phenomenon] holds under [conditions], resolving the conjecture posed by [someone recognizable] and opening the door to…”.
The Innovation Paragraph
This is what top journals really want, new tools others can use.
“The key innovation is a new technique combining [unexpected area A] with [area B], which bypasses the traditional barrier of…”.
Future Impact
Help editors envision citations and follow-up work.
“This approach suggests new attacks on [related important problem] and raises natural questions about…”.
The Uncomfortable Reality
It feels wrong that groundbreaking mathematics needs the same attention-grabbing tactics as “You Won’t Believe What Happened Next!” videos. But we’re not submitting to Platonic ideals; we’re submitting to human editors who go home tired, check their phones too much, and have the same cognitive limitations as everyone else.
The mathematics community likes to imagine that quality rises to the top naturally, that good mathematics speaks for itself. While this is definitely true in some cases, it also slightly ignores how human attention actually works. Your profound result can’t impact the field if no one reads it because the introduction didn’t create sufficient motivation to continue.
The Senior Researcher Exception
You’ve probably noticed that famous mathematicians can get away with terse, technical introductions that would doom anyone else’s paper. This isn’t just unfair bias, it’s another cognitive shortcut. When an editor sees a familiar prestigious name, their brain fills in the motivation automatically. They know this person’s work matters because past work has mattered (availability heuristic plus confirmation bias).
Most of us don’t have that luxury. The introduction has to do all the contextualizing work explicitly.
Practical Exercise
Take your next strong result and write two introductions:
- Your usual version, mathematical, precise, technical.
- A “marketing” version using every psychological principle above.
Show both to colleagues. Watch which one makes them want to read the paper, even outside their specialty. That’s the version that might finally get you past the desk rejection at the journal you have been aiming for.
The Bottom Line
These aren’t cheap tricks or “selling out.” They’re recognition that mathematical communication happens between humans, and humans have predictable psychological patterns that determine what we pay attention to. You can rage against this reality, or you can use it to ensure your mathematics gets the audience it deserves.
Your theorems might be eternal and objective, but the decision to publish them is utterly human. Write your introductions accordingly.
Remember: The editor deciding your paper’s fate might have just come from a boring committee meeting, might be thinking about lunch, and definitely has 20 other papers to evaluate today. Your introduction is not just competing with other mathematics, it’s competing with everything else demanding their attention. Make it count.