“Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” —Archimedes
Archimedes was talking about physics, but academics have always understood the metaphor intuitively. We speak of “high-leverage activities,” of people who “punch above their weight,” of the importance of “strategic positioning.” We recognize that effort alone doesn’t determine outcome, but where and how you apply effort matters enormously.
But when we think carefully about Archimedes’ claim, there are four questions embedded in it, not two:
- What lever do you have?
- Where do you place it?
- What are you trying to move?
- Where do you stand?
The first two are obvious. The third is less so, we often skip it or answer too vaguely. The fourth is the subtlest: Archimedes needed a fulcrum, a fixed point from which to exert force. Without stable ground, no amount of lever or clever placement accomplishes anything.
In an academic career, that fulcrum is something like judgment, your values, your sense of what actually matters, your ability to distinguish the important from the merely urgent. It’s the thing that holds steady while everything else moves.
Let’s take each in turn.
What Lever Do You Have?
Your lever is your current inventory of assets: time, expertise, relationships, reputation, resources, institutional position. This inventory changes dramatically over a career.
The graduate student’s primary lever is time and intellectual energy, thousands of hours to invest in deep skill-building, relatively unconstrained by competing obligations. The assistant professor trades some of that time for new levers: a research program, initial grants, the ability to mentor students. The associate professor accumulates methodological expertise, a network of collaborators, perhaps some editorial or service roles that confer information and influence. The full professor or department chair holds institutional levers, convening power, resource allocation, the ability to shape hiring and direction.
Each stage has levers the others lack. The mistake is often wanting the levers you don’t yet have while undervaluing the ones you do. The graduate student who neglects deep work in favor of networking is misallocating; so is the senior professor who competes with their students for theorem-proving rather than opening doors only they can open.
Where Do You Place It?
This is the question of strategy. The same lever, placed differently, yields entirely different results.
Consider problem selection. A talented young mathematician can place their lever on a fashionable problem in a crowded area, one with high visibility, many competitors, incremental progress likely. Or they can place it on a neglected problem in an unfashionable area, one with lower visibility, but the potential for outsized impact if the area turns out to matter. Neither choice is universally correct. But it is a choice, and it has consequences that compound over years.
Or consider collaboration. You might place your lever on a large team project where your contribution is one of many, or on a solo paper where the risk and reward are entirely yours, or on mentoring a junior person whose success becomes part of your legacy. Each placement moves something different.
Some high-leverage placements in academic mathematics:
- Developing a method others adopt. If your technique becomes standard, every paper using it extends your influence without additional effort from you.
- Writing the definitive exposition. A well-written survey or textbook teaches while you sleep. It compounds.
- Mentoring the right people well. Your students’ careers become a form of intellectual legacy that outlasts any single paper.
- Strategic service. Editing a key journal, running a seminar series, leading a professional organization. These are expensive in time but provide information and influence unavailable otherwise.
- Building infrastructure. The dataset you curate, the code you make reusable, the protocols you document all reduce friction for future work, yours and others’.
Some low-leverage placements, or leverage that backfires:
- Accumulating debt faster than you can service it. Saying yes to every collaboration, committee, and mentoring request spreads you thin until nothing gets real attention.
- Building a group around a wrong direction. Leverage amplifies mistakes. If your research program turns out to be misguided, you’ve wasted not just your time but your students’ and postdocs’ time too.
- Letting reputation outrun judgment. Influence can entrench bad ideas as easily as good ones, and can insulate you from the criticism you need most.
- Mistaking activity for contribution. Many papers, many students, many projects. But the thinking thins out. You become an administrator of research rather than a researcher.
What Are You Trying to Move?
Here is where honesty becomes important. “Impact” is too vague. Move what, exactly?
Your own career? That’s legitimate, especially early on since you need a job, tenure, the security to do longer-term work. But it’s a different target than moving a field’s direction, or moving a student from potential to achievement, or moving an institution toward better functioning.
The targets sometimes align and sometimes conflict. The paper that advances your career most might not be the one that advances the field most. The service that helps your department might slow your research. The mentoring that transforms a student’s life might never appear on your CV.
Part of building a good career is getting clear on what you’re actually trying to move at any given stage, and, importantly, accepting that the answer may change. The assistant professor fighting for tenure is legitimately focused on career survival. The full professor with security who remains focused only on personal accolades has perhaps lost the plot.
Where Do You Stand?
Archimedes needed a place to stand, a fixed point, a fulcrum. Without it, the lever is useless.
In an academic career, this is something like: your values, your sense of what actually matters, your ability to distinguish the important from the merely urgent.
Without a stable fulcrum, leverage becomes chaos as you move many things, but in no coherent direction. The academics who seem to use leverage best are those who have genuine clarity about what they’re trying to accomplish, and who protect that clarity against the constant pressure to do more, say yes, optimize for legibility.
The lever is your assets. The placement is your strategy. The thing you move is your purpose. But the fulcrum, the place you stand, is your judgment.
Get clear on all four, and you might not move the world. But you’ll move something that matters to you, and you’ll know why.