About Navigating Proof Space
Welcome to a space where mathematics meets the mathematical life.
What This Blog Is About
Navigating Proof Space explores the intersection of rigorous mathematics and the realities of building a career in our field. Here you’ll find discussions of harmonic analysis, functional analysis, and related areas of mathematics, alongside honest conversations about the challenges and opportunities of academic life.
The Mathematical Focus
My primary research interests lie in harmonic analysis, the study of functions through their frequency components, and its connections to partial differential equations, operator theory, and complex analysis. This blog will dive deep into these areas, exploring both classical results and recent developments. Whether you’re encountering Fourier transforms for the first time or working on cutting-edge problems in time-frequency analysis, there will be something here for you.
The Career Perspective
Mathematics doesn’t happen in a vacuum. Behind every theorem is a mathematician navigating funding applications, job markets, collaboration challenges, and the constant balance between curiosity-driven research and practical constraints. This blog addresses these realities with the same rigor we bring to our mathematical work.
Who Am I?
I’m Brett Wick, a Professor of Mathematics at Washington University in St. Louis. My research focuses on harmonic analysis, particularly applications of these ideas to operator theory, complex analysis and function theory. I’ve been fortunate to work in this field for over two decades, experiencing the full spectrum of mathematical life: from graduate school uncertainty to the challenges of building a research program.
Who This Is For
- Graduate students navigating their first encounters with advanced analysis;
- Early career mathematicians building research programs and making career decisions;
- Established researchers interested in fresh perspectives on familiar territory;
- Anyone curious about the intersection of mathematical beauty and mathematical reality.
What You Can Expect
Posts will range from technical mathematical discussions to practical career advice, from explorations of classical theorems to commentary on current trends in our field. The tone will be conversational but substantive—this is a place for serious mathematical thinking expressed in accessible language.
Join the Conversation
Mathematics is collaborative by nature. Comments, questions, and different perspectives are not just welcome—they’re essential. Whether you’re sharing an elegant proof technique or asking for career advice, this community is here to support mathematical growth in all its forms.
Questions about the blog? Want to suggest a topic? Feel free to reach out at bwick[at]wustl[dot]edu or leave a comment on any post.