Mathematics
A Letter to My Younger Mathematical Self
A reflective letter to a younger self just beginning the study of mathematics — the things I wish I had known about learning, struggling, growing, and finding meaning in the subject.
Writing
Blog
94 posts · Page 1 of 7
Mathematics
The Cut Point Trick: A Fast Way to Tell Spaces Apart
A clear guide to cut points, why homeomorphisms preserve them, how the cut point trick works, and why higher-dimensional Euclidean spaces require stronger invariants.
Mathematics
Homomorphic vs Homeomorphic vs Isomorphic
A focused guide to the difference between homomorphic, homeomorphic, and isomorphic, with examples from algebra and topology.
Mathematics
What Is a Morphism? A Clear Guide for Students
A professional introduction to morphisms, homomorphisms, homeomorphisms, isomorphisms, and the general idea of structure-preserving maps across mathematics.
Mathematics
Unsolved Problems Waiting for the Next Generation
A tour of some of the most important unsolved problems in mathematics — from the Millennium Prize Problems to questions in every major area — waiting for the next generation of mathematicians.
Mathematics
Why the Determinant Measures Area and Volume
A clear explanation of why the determinant of a matrix tells us how a linear map scales area, volume, and orientation.
Mathematics
Brouwer's Fixed-Point Theorem: A Proof via the Fundamental Group
We prove Brouwer's Fixed-Point Theorem for the closed disk using the fundamental group and the non-existence of a retraction, deriving an algebraic contradiction.
Mathematics
Advice from Famous Mathematicians to Young Students
A collection of wisdom from some of the greatest mathematicians in history — practical advice, philosophical reflections, and encouragement for young people beginning their mathematical journeys.
Mathematics
The Beauty of Mathematics: Why Mathematicians Love Their Subject
An exploration of mathematical beauty — what it means, where it comes from, and why mathematicians describe their work in terms usually reserved for art, music, and nature.
Resources
How to Build a Personal Academic Website as a Math Student
A step-by-step guide to building a personal academic website as a mathematics student: why you need one, what to include, which tools to use, and how to host it for free using GitHub Pages, Hugo, or other platforms.
Mathematics
Mathematics in Developing Countries: Challenges and Opportunities
An examination of the state of mathematics in developing countries — the structural challenges, the remarkable individuals and institutions overcoming them, and the global efforts to build mathematical capacity.
Mathematics
Karen Uhlenbeck: Geometry, Physics, and the Abel Prize
The story of Karen Uhlenbeck, a pioneer of geometric analysis who overcame gender barriers in mathematics, made fundamental contributions to gauge theory and minimal surfaces, and became the first woman to win the Abel Prize.
Mathematics
Lagrange's Theorem: Why Subgroup Orders Divide Group Orders
We prove Lagrange's theorem — the fundamental result that the order of a subgroup divides the order of the group — and explore its many consequences, from Fermat's little theorem to the structure theory of finite groups.
Resources
Using GitHub for Mathematics Projects and Collaboration
A practical guide to using GitHub for mathematics: version control for LaTeX papers, collaborative research, sharing code and notes, building an academic portfolio, and contributing to open-source mathematical software.
Mathematics
Women in Mathematics: Progress, Challenges, and the Future
A look at the history and current state of women in mathematics — the pioneers who broke barriers, the challenges that persist, and the work being done to build a more inclusive field.