Tag: Research Advice
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The Mathematician’s Paradox: Why Chasing Trends Might Create More Lasting Mathematics Than Pursuing Eternal Truths
A counterintuitive guide to navigating academic mathematics using the Lindy Effect Every mathematics graduate student eventually faces the same existential question: Should I work on classical problems that have captivated mathematicians for centuries, or chase the latest trends, be they in machine learning, quantum computing, or cryptography? The answer, surprisingly, might challenge everything you’ve been…
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The Politics of Giving Credit
I recently had an unusual experience. I received critical feedback about a paper; not for failing to cite someone, but for citing them too generously. A colleague objected to a sentence in my introduction that described another researcher’s contributions as “important” to a body of theory. The objection wasn’t that the characterization was inaccurate. It…
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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 Secretary Problem and Academic Careers: Why Your Research Path is More Forgiving Than You Think
The Classic Problem: When You Only Get One Shot Imagine you’re a department chair tasked with hiring the best possible secretary from a pool of 100 applicants. The rules are harsh: you interview candidates in random order, must decide immediately after each interview whether to hire them, and once rejected, a candidate is gone forever.…
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Putting Strategy into Practice: A Tactical Guide for Mathematical Careers
We’ve explored two frameworks for thinking strategically about mathematical research: explore-exploit from foraging theory and sow-reap from agricultural thinking. But frameworks are only useful if they can guide real decisions. How do you actually implement these ideas in the messy reality of a mathematical career? The challenge is that mathematical research involves more uncertainty, longer…
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From Foraging to Farming: The Sow vs. Reap Framework for Mathematical Careers
In our previous post, we explored how the explore-exploit dilemma from foraging theory illuminates strategic choices in mathematical research. But as we dug deeper into this analogy, its limitations became apparent. Mathematical research isn’t just about finding existing resources – it’s about creating new forms of understanding that didn’t exist before. This suggests we need…
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The Explorer’s Dilemma: When to Dive Deep vs. Branch Out in Mathematical Research
Every mathematician faces a fundamental strategic question that rarely gets discussed explicitly: when should you continue mining your current area of expertise, and when should you venture into unfamiliar mathematical territory? This decision shapes careers, determines research impact, and often means the difference between sustained productivity and intellectual stagnation. The framework I want to explore…
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Don’t Rank Fish by Their Tree-Climbing: Finding Your True Reference Class in Mathematical Research
“Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.” — Often attributed to Einstein The academic world loves metrics. Publications per year. H-index at tenure. Median time to PhD. Grant dollars secured. We aggregate, average, and…
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The Invisible Mathematicians: How Survivorship Bias and Statistical Illusions Distort Academic Career Advice
Why everything you think you know about success might be wrong There’s a joke that goes something like this: “Looking at successful careers for career advice is like asking lottery winners for financial planning tips.” The joke is funny because it’s uncomfortably true, and it points to a deeper problem: our understanding of what leads…
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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…