The Universal Laws of Metric Corruption
In 1975, economist Charles Goodhart articulated a principle that should be carved above every department chair’s door: “When a measure becomes a target, it ceases to be a good measure.” Around the same time, psychologist Donald Campbell observed something similar, noting that “the more any quantitative social indicator is used for social decision-making, the more subject it will be to corruption pressures and the more apt it will be to distort and corrupt the social processes it is intended to monitor.”
These two laws describe subtly different pathologies. Goodhart’s Law is about optimization making measures useless; when people know they’re being evaluated by a metric, they naturally optimize for that metric rather than the underlying quality it was meant to measure. Campbell’s Law emphasizes active corruption and distortion under pressure, particularly when stakes are high. Together, they explain why so many well-intentioned measurement systems in academia have become elaborate theaters where we perform success rather than achieve it.
The Academic Manifestation: Publish or Perish
Nowhere are these dynamics more visible than in the “publish or perish” culture of academic research. Papers were meant to measure productivity and scientific contribution. Citations were supposed to indicate impact. Grant funding was intended to enable important research. Each metric began as a reasonable proxy for something we valued.
But once careers began depending on these numbers, the distortion began. We now have salami-slicing (splitting one result into multiple papers), citation rings (groups that cite each other regardless of relevance), and entire research programs designed around fundability rather than intellectual merit. The h-index, created to measure sustained scientific impact, became something to game through strategic self-citation and collaborative publication strategies.
The credential arms race represents these same dynamics at a different scale. As bachelor’s degrees became universal, master’s degrees became necessary. As PhD programs expanded, postdocs became de facto requirements. In mathematics, where everyone has a PhD, the race shifts to other signals: the prestige of journals, the fame of advisors, the exclusivity of seminars. Each escalation makes sense individually but creates collective inefficiency; we spend ever more time signaling ability rather than developing it.
Why Metrics Aren’t All Bad
Before condemning all metrics, we must acknowledge an uncomfortable truth: they often work. Papers really do force us to finish proofs and communicate clearly. Citations genuinely indicate that work is being used. Prestigious journals maintain high standards way more often than not. Grant proposals force us to articulate why problems matter.
The metrics weren’t chosen randomly. They emerged because they correlate with valuable academic activity. A young mathematician with strong publications has demonstrated real capability. The pathology isn’t in having metrics, instead it’s in over-optimizing for them. There’s a vast difference between publishing solid papers and salami-slicing everything, between earning citations through good work and gaming citation rings, between getting grants to enable research and becoming a grant-writing machine.
Metrics serve as useful navigational tools, like a compass that tells you direction but not whether there’s a cliff ahead. The wisdom lies in knowing when they’re pointing toward genuinely good practice and when they’re pulling you away from it.
The Compound Failures of Metric Optimization
Ignoring Goodhart and Campbell’s warnings leads to predictable failure patterns. The Publication Maximizer fragments every result into minimum publishable units, eventually owning papers no one reads. When promotion committees start discounting quantity, they lack any signature deep contribution. Worse, they’ve trained themselves to think in publication-sized chunks and lost the ability to see bigger mathematical structures.
The Citation Gamer joins citation rings and aggressively self-cites until someone examines the actual network. The Grant Writer becomes so skilled at proposals that it becomes their primary competency, with mathematical ability atrophying. The Trend Chaser jumps from hot topic to hot topic, never developing deep expertise in anything.
But the deepest failure is skill atrophy. When you optimize for metrics, you develop the skills that game metrics, not the skills that do mathematics. It’s like training for a marathon by only practicing your starting sprint. Eventually, you can’t actually run the distance.
Finding Ungamed Signals: The Meta-Game
As traditional metrics degrade, finding ungamed signals becomes its own game. These signals share certain characteristics: they’re expensive to fake in the right currency, emerge from complex interactions, can only be observed indirectly, or reveal themselves through time delays.
In mathematics, genuinely solving a long-standing open problem can’t be gamed; either you solved it or you didn’t. The way other mathematicians spontaneously build on your work, not just cite it, is harder to fake than citation counts. Which graduate students choose to work with you when they have options? Who seeks you out for collaboration organically? What happens when you give a talk; do people ask genuine mathematical questions or polite ones?
Time-delayed revelations connect to what’s called the Lindy Effect, the idea that the future life expectancy of ideas is proportional to their current age. Papers that remain useful after 10 years likely will for another 10. Work that creates new language or frameworks, that makes previously impossible things possible, that keeps appearing in different disguises across areas, these tend to have staying power. The challenge is that betting on potential “Lindy winners” means accepting that most bets will fail, and you won’t know which ones for years.
The Art of Costly Verification
When people are gaming metrics, evaluation requires what economists call “costly verification”, assessment methods that require genuine effort and can’t be easily faked. This means actually reading papers rather than counting them, asking about mathematical ideas rather than achievements, looking for consistency between informal mathematical conversation and published work.
In our time-compressed lives, this seems impossible. But it’s where community becomes crucial. Form reading groups where each person deeply understands different papers. Build trusted networks where you know whose judgment aligns with yours. Use mathematical conversations as efficient verification; a 30-minute discussion reveals more than any CV.
The principle extends to self-assessment. Document your failed attempts privately, they often contain seeds of later success. Share negative results informally even if they’re not publishable. Recognize that “failed” attempts that clarify why something is hard are genuine contributions. The survivorship bias in academia means we never see the brilliant mathematicians who spent years on approaches that didn’t work and left the field. Valuing our own negative results helps maintain perspective.
Navigating the Optimization Trap
Avoiding metric optimization while maintaining a viable career requires strategic thinking. Some approaches that work:
Maintain a shadow research program: Keep working on what genuinely interests you alongside what you need for career advancement. Sometimes these converge beautifully. That risky, interdisciplinary project, like using genetic algorithms to prove inequalities in harmonic analysis, might transform your field or might just teach you something fascinating. Either outcome has value.
Find your “enough”: This evolves throughout your career. Early on, “enough” might mean “get a permanent position.” Mid-career might be “have intellectual freedom.” Later might be “develop the next generation.” The key is recognizing when you’re optimizing for metrics past the point of diminishing returns for your actual goals. Regularly ask yourself questions like: “If I had tenure tomorrow, what would I work on?” Then move incrementally toward that while maintaining viability.
Practice strategic opacity: Don’t always announce what you’re working on. This protects you from both competition and the pressure to produce premature results. Some of the best work happens in private, revealed only when ready.
Build dual citizenship: Maintain credibility in the metric-driven system while developing a parallel identity in something the system can’t fully capture. Become the person who explains difficult concepts beautifully, who connects pure math to applications, who asks questions that reshape fields. This gives you flexibility; when metrics matter, you can point to traditional achievements, but your real impact comes from the ungameable contribution.
Control What You Can Control
Perhaps the deepest wisdom for navigating the measurement trap is focusing on what you can control: your weekly progress. You can’t control whether AI will transform mathematics, whether your unconventional approach will work, or how metrics will shift. But you can control whether you understood one new concept this week, proved one lemma, or wrote one clear page.
This weekly-progress approach is surprisingly ungameable. You can’t fake having deeply understood something week after week; the mathematical coherence either builds or it doesn’t. Small progress accumulating over a semester creates major advances that, remarkably, tend to satisfy traditional metrics as a natural byproduct. The papers and citations accumulate organically when you’re doing real mathematics, without the distortions that come from optimizing for them directly.
It’s like focusing on the derivative (weekly change) rather than trying to optimize the integral (career-total metrics). The local optimization is more tractable and, paradoxically, often leads to better global outcomes.
The Tension of Living in the System
There’s an essential tension in all of this: we must simultaneously play the game and see through it. Early in our careers, we often must follow metrics more closely; we’re learning the craft, building credibility, proving we can succeed in the standard framework. Only later do we gain the security and perspective to question and diverge.
This creates a paradox in mentoring. Do we tell young mathematicians what we know, that metrics are flawed proxies? Or do we let them follow the path as we did, gaining the credibility that will later allow them to question? Perhaps the answer is to teach them to use metrics as navigational tools while maintaining awareness that they’re not the destination.
The real tragedy of the measurement trap isn’t just individual. When everyone optimizes for the same degraded metrics, genuine breakthrough work becomes rarer. Fields stagnate, public trust erodes, and funding dries up. We risk creating a generation of mathematicians skilled at gaming metrics but lacking the deep technical strength and taste that leads to important work.
Looking Forward: The Persistence of Real Work
Despite these challenges, there’s reason for cautious optimism. Focusing on genuine mathematical progress, understanding, proving, connecting, teaching, almost automatically generates traditional metrics as a byproduct. This suggests the system hasn’t completely decoupled from its purpose. The metrics work as outputs of good mathematics, even as they fail when used as targets.
Moreover, technological shifts like AI might disrupt ossified metrics before they become completely corrupted. When the game fundamentally changes, old measures become irrelevant before they can be gamed into meaninglessness. The challenge is developing capabilities that aren’t yet measured while maintaining enough traditional success to stay in the game.
Perhaps the best we can do is maintain dual citizenship: succeed enough in the metric-driven system to earn freedom, while preserving the intellectual courage to work on what matters. Control what we can control, our daily and weekly progress toward genuine understanding. Build communities that value costly verification over easy metrics. And remember that while metrics might determine careers, they don’t determine mathematical truth.
The measurement trap is real, but it’s not inescapable. By understanding how metrics corrupt and maintaining vigilant awareness of their limitations, we can navigate the system without losing sight of why we chose mathematics in the first place: not for the h-index or the grants, but for the beauty of understanding something true about the universe, one proof at a time.