Think about how you approach a new problem. Do you immediately dive deep into the first promising lead, chasing it as far as it goes before backing up? Or do you scan the landscape first, surveying all available options before committing to any single path?
These two approaches map neatly onto two well-known algorithms from computer science: depth-first search (DFS) and breadth-first search (BFS). And it turns out they’re not just useful for traversing graphs — they describe something real about how people think, create, and solve problems.
The Two Modes
A depth-first thinker picks a direction and commits. They drill down, following one thread of reasoning to its conclusion before considering alternatives. They’re goal-oriented, fast-moving, and often intuition-driven. When faced with a maze, they sprint down the first corridor and only backtrack when they hit a wall.
A breadth-first thinker fans out. They explore all nearby options before going deeper into any one of them. They build a solid foundation of understanding around their starting point, methodically expanding outward. In the same maze, they’d peek down every corridor at each junction before choosing one.
Neither approach is inherently better. Depth-first gets you to solutions faster — if your initial direction happens to be right. Breadth-first is more thorough and reliable, but slower. As Kevin Lawler puts it: “Depth-first strategies may get you there faster; the tradeoff is that there’s less guarantee the path holds.”
The Creativity Connection
Here’s where it gets interesting. This distinction maps closely onto a well-established concept in psychology: divergent vs. convergent thinking, first described by J.P. Guilford in 1956.
Divergent thinking — generating many different ideas and possibilities — is essentially breadth-first cognition. It’s the brainstorming phase, the creative exploration, the “what if?” mode. Convergent thinking — narrowing down to a single best answer — is depth-first. It’s the analytical, logical, efficient mode.
This gives us a rough (and admittedly imperfect) mapping:
| Breadth-First | Depth-First | |
|---|---|---|
| Cognitive style | Divergent | Convergent |
| Strength | Creativity, exploration | Efficiency, precision |
| Risk | Never finishing | Going deep in the wrong direction |
| Feels like | Brainstorming | Problem-solving |
| Classic domain | Art, design, strategy | Mathematics, engineering |
Don Norman, the famous cognitive scientist, made a fascinating observation that connects these styles to emotion: a relaxed, happy state of mind tends to put the brain into breadth-first mode — more conducive to creative, out-of-the-box thinking. Tension and pressure, meanwhile, activate depth-first mode, narrowing focus and increasing dopamine-driven goal pursuit.
This suggests the connection isn’t just a neat analogy. There may be a genuine neurological basis for these two modes of cognition, with emotional state acting as the switch between them.
Most of Us Are a Mix
The reality, of course, is that nobody is purely one or the other. We oscillate between breadth and depth constantly, often without noticing. As Fang Jin writes: “We can be quite aggressive sometimes, and when we do that we are more like a depth-first person. Of course we can get exhausted easily, so we sometimes retrospect a bit… and then we switch to breadth-first.”
The best problem-solvers, creative and mathematical alike, know when to switch modes. They brainstorm broadly (BFS) to generate options, then drill down (DFS) to evaluate the most promising ones. Research on mathematical creativity confirms this: the interplay between divergent and convergent thinking is what produces solutions that are both novel and useful.
The practical takeaway? Know which mode you default to. If you’re a natural depth-first thinker, you might benefit from forcing yourself to survey more options before committing. If you’re a breadth-first thinker, you might need to resist the temptation to keep exploring and actually commit to going deep on something.
And if you’re building a team, as Mark Hudnall argues, seek out people who think differently than you: “People who think differently than you see things that you can’t.”
Breadth-First Concept, Depth-First Execution
Perhaps the most elegant synthesis comes from Arpit Mathur, who suggests: concept in breadth-first mode, execute in depth-first mode. Explore widely when you’re defining the problem. Then go deep when you’re solving it.
That might just be the optimal algorithm for human thinking.
Further Reading
- Jim Mason, “Depth-First Versus Breadth-First Thinkers — Which Kind Are You?” — Medium / Age of Awareness (2021)
- Fang Jin, “Are you depth-first person or breadth-first person?” — Medium / Geek Culture (2021)
- Mark Hudnall, “Depth-first and breadth-first thinkers” (2015)
- Kevin Lawler, “Breadth- and Depth-First Thinking”
- Arpit Mathur, “On Breadth First and Depth First Thinking” — Code Zen (2010)
- Vink et al., “Creativity in mathematics performance: The role of divergent and convergent thinking” — British Journal of Educational Psychology (2022)
- Asana, “Convergent vs. Divergent Thinking: Finding Balance”
