Tag: mathematics
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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…
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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.…
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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…
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Commutators and Paraproducts in Nonhomogeneous Settings: Some Recent Progress
Notes on our recent work extending sparse domination and characterizing dyadic Hilbert transform commutators Background and Motivation Our recent paper addresses some long standing questions about commutators and paraproducts when the underlying measure lacks the doubling property. This is an area where classical intuition often fails, making it both challenging and interesting to work in.…
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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…
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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…
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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…
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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…
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The Psychology of Peer Review: Why Charitable Interpretation Matters in Mathematics
Based on a real experience; names changed to protect the innocent. Imagine this scenario: Dr. Smith submits a paper to a prestigious mathematics journal. The main theorem is groundbreaking, the proof technique is novel, and the implications are significant. But there’s a problem, the formal statement of the theorem is missing a crucial hypothesis, even…
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An Alphabet for Action: A-Z Action Verbs for Mathematical Research Success
In his motivational classic “Tough Times Never Last, But Tough People Do!”, Robert H. Schuller introduced a powerful concept he called an “alphabet for action”, an A-Z list of action verbs designed to inspire what he termed “possibility thinking.” Schuller’s insight was that having a comprehensive, memorable framework of action-oriented words could serve as a…