Category: Miscellaneous

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…

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…

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…

“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…

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…

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…

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.…

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…