Category: Career Advice
-
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…
-
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…
-
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…
-
The No Free Lunch Theorem: Why There’s No Universal Strategy for Career Success or Research Productivity
Introduction: A Theorem That Changes Everything In 1997, David Wolpert and William Macready proved something that should fundamentally change how we think about optimization, careers, and life strategies: the No Free Lunch (NFL) theorem. While originally formulated for machine learning and optimization algorithms, this mathematical principle reveals a profound truth that extends far beyond computer…
-
Navigating the Easy-Hard-Impossible Trichotomy in Mathematical Analysis
In mathematical research, problems naturally fall into three categories: the easy, the hard, and the impossible. While this trichotomy applies across all areas of mathematics, it takes on distinctive characteristics in analysis, harmonic analysis, complex analysis, operator theory, and function theory, where geometric intuition and functional-analytic structure create their own patterns of tractability and obstruction.…
-
The GPS Model of Mathematical Research: Recalculating Without Regret
The Core Analogy When you take a wrong turn while using GPS, something interesting happens: the system doesn’t scold you or declare “wrong way!” It simply recalculates from your new position, treating your current location, however you arrived there, as a valid starting point for moving forward. This immediate, judgment-free recalculation offers a powerful model…
-
From the Gridiron to the Whiteboard: Applying Bill Walsh’s Philosophy to Mathematical Research
Since we are now in the middle of football season and I enjoy watching games on Sunday afternoon while thinking some about my work, I thought I’d attempt to connect leadership ideas to mathematical research. Bill Walsh’s “The Score Takes Care of Itself” offers more than just football wisdom. The legendary San Francisco 49ers coach…
-
The Psychology of Mathematical Introductions: Why Your Paper Needs a Hook Like a YouTube Video
This post is based on my experience as an editor for several journals. My opinion on Introductions to papers has evolved since serving in this role. The Uncomfortable Truth Here’s something that might make pure mathematicians cringe: getting your paper into a top journal has more in common with getting views on YouTube than you’d…
-
The Math Poster Survival Guide: What Works and What Doesn’t
I just attended the recent poster session at the AMS Central Sectional Meeting at Saint Louis University. It was a great event that helped to showcase the research of many early career researchers. In viewing some of the posters, some thoughts occurred to me about what works, what doesn’t and things people might want to…
-
How to Give a Good 20-Minute Math Talk (By First Learning What Not to Do)
We’ve all been there. You’re sitting in a conference room at an AMS Sectional meeting, coffee in hand, ready to hear about some exciting new results in harmonic analysis. Twenty minutes later, you emerge confused, overwhelmed, and unsure what the speaker actually proved. The talk has ended, but you couldn’t tell anyone what it was…