Category: Research Insight
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The Mathematical Proof That You Can’t Have It All: Arrow’s Impossibility Theorem and the Academic Career
Or: Why Your Career Anxieties Are Mathematically Inevitable Every mathematician knows that moment. You’re staring at your desk, covered with: Which do you tackle first? More fundamentally: How do you build a career that optimizes across all these dimensions? Here’s the liberating, terrifying truth: You can’t. And I mean that literally, as in, mathematically proven…
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The Measurement Trap: When Academic Metrics Stop Measuring Mathematical Truth
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…
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The Red Queen as Ally: Why Constant Change Keeps Mathematics Alive
In the first post of this series, we explored how the Red Queen Effect creates a relentless pressure in mathematical research, the need to constantly evolve just to maintain your position as the field advances around you. The natural response is to view this as an exhausting burden, something to be overcome or escaped. But…
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Navigating the Tension: Goal-Setting vs. Exploration in Mathematical Research
Recently, I’ve been thinking about a fundamental tension that every mathematician faces: the conflict between systematic goal-setting and open-ended exploration. This tension became particularly clear to me after reading Kenneth Stanley and Joel Lehman’s book “Why Greatness Cannot Be Planned: The Myth of the Objective.” The Stepping Stone Problem Stanley and Lehman argue that truly…