“Embrace the suck” is military slang for accepting that some situations are going to be difficult, uncomfortable, and uncertain, and learning to operate effectively anyway. It’s about finding ways to function when conditions are far from ideal, when you don’t have complete information, and when there’s no clear path forward.
Mathematical research is full of suck. You’ll spend months working on problems that lead nowhere. You’ll use techniques you don’t fully understand. You’ll follow hunches that feel promising but that you can’t yet articulate clearly. You’ll read papers where you understand maybe 60% of the content but sense that the remaining 40% contains something important.
The students who thrive in research are those who learn to embrace this mathematical suck. They become comfortable being uncomfortable. They can work productively at the edge of their understanding, following promising leads even when they can’t explain exactly why those leads seem promising.
Others struggle with this ambiguity. They interpret uncertainty as personal failure rather than the natural state of being at the research frontier. They want complete understanding before taking any steps forward. They’re waiting for clarity that rarely comes in research mathematics.
This difference in tolerance for uncertainty predicts research success better than raw mathematical ability. Here’s why:
Research happens in the unknown: By definition, research problems don’t have known solutions. If you could solve them with existing tools and complete understanding, they wouldn’t be research problems. You’re always working with partial information and provisional understanding.
Breakthrough insights come from liminal spaces: The most important mathematical discoveries often emerge from fuzzy intuitions about connections between areas you understand incompletely. If you insist on complete clarity before pursuing these hunches, you miss the productive uncertainty where new ideas emerge.
Mathematical creativity requires experimental thinking: Like scientists testing hypotheses, mathematicians try approaches that might not work. This requires willingness to invest time and effort in directions that may prove fruitless. Students who need guaranteed success struggle with this aspect of research.
The best mathematical remixes come from partial understanding: Recognizing that “this problem feels like that other problem” from a different field often requires working with incomplete analogies. Complete understanding of both areas might actually obscure the useful connections.
The irony is that undergraduate mathematics education often rewards the opposite mindset. Students learn to expect well-posed problems with definite answers, complete algorithmic solutions, and clear criteria for success. Then graduate school suddenly demands comfort with ill-defined problems, uncertain outcomes, and provisional methods.
So how do you develop comfort with mathematical suck? Some strategies that help:
Reframe uncertainty as normal: Mathematical research isn’t like problem sets. Confusion, false starts, and partial understanding aren’t signs of failure, instead they’re the natural state of working at the frontier of knowledge.
Practice working with incomplete tools: Use theorems before you understand their proofs. Apply techniques before you master their derivations. Build tolerance for working with tools you don’t fully control.
Study mathematical history: Understanding how mathematical ideas actually developed, usually through false starts, partial insights, and gradual clarification, helps normalize uncertainty and shows that even great mathematicians worked with incomplete understanding.
Collaborate with others: Working with people from different mathematical backgrounds exposes you to different comfort levels with uncertainty and shows that everyone is working with incomplete knowledge in some areas.
Set process goals, not just outcome goals: Instead of “solve this problem,” try “understand why technique X might be relevant” or “explore the connection between areas Y and Z.” Process goals let you make progress even when the ultimate solution remains elusive.
Develop multiple projects: Having several research directions reduces the psychological pressure on any single project. If one direction hits a wall, you can shift focus while your subconscious continues working on the stuck problem.
The students who learn to embrace mathematical suck don’t just become better researchers, they become better mathematical citizens. They’re more willing to attend talks outside their area, more open to collaboration across fields, more comfortable exploring new territories.
They also become better at the mathematical remixing we’ve discussed throughout this series. Comfort with uncertainty enables the experimental thinking needed to spot connections across fields, the willingness to work with partial analogies, and the persistence needed to develop fuzzy intuitions into rigorous results.
Mathematical research will always involve uncertainty, incomplete understanding, and periods of confusion. The question isn’t whether you’ll encounter the suck, it’s whether you’ll learn to embrace it as a natural part of the process. Those who do often find that the most rewarding discoveries emerge from the places where they were most uncomfortable.
In the end, mathematical research isn’t about eliminating uncertainty, it’s about learning to live with it.