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.
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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.
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.
A focused guide to the difference between homomorphic, homeomorphic, and isomorphic, with examples from algebra and topology.
A professional introduction to morphisms, homomorphisms, homeomorphisms, isomorphisms, and the general idea of structure-preserving maps across mathematics.
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.
A clear explanation of why the determinant of a matrix tells us how a linear map scales area, volume, and orientation.
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.
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.
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.
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.
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.
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.
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.
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.
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.