Writing
94 posts · Page 5 of 7
We trace the 358-year history of Fermat's Last Theorem — from Fermat's tantalizing margin note to Andrew Wiles's monumental proof via elliptic curves and modular forms — and explain the mathematical ideas that made the proof possible.
A guide to the difficult transition from computational mathematics to abstract, proof-based mathematics, with practical strategies for developing abstract thinking skills.
A practical guide to using Wolfram Alpha and Mathematica for mathematics: from quick computations and plotting to symbolic algebra, solving differential equations, and exploring mathematical concepts.
The life of Carl Friedrich Gauss, the child prodigy from Brunswick who became the greatest mathematician of his era, making foundational contributions to number theory, geometry, statistics, and physics.
We prove the Heine-Borel theorem — that a subset of Euclidean space is compact if and only if it is closed and bounded — and explore why compactness is one of the most powerful concepts in all of analysis.
A comprehensive guide to the best free and legally available mathematics textbooks online, covering every major subject from linear algebra and real analysis to topology and number theory.
A step-by-step guide to writing your first mathematics research paper — from understanding what constitutes a publishable result to structuring, writing, and submitting your work.
How examples and counterexamples drive mathematical understanding, with a catalog of famous counterexamples and strategies for constructing your own.
The life and staggering output of Leonhard Euler, the most prolific mathematician in history, whose work touched every branch of mathematics and established conventions we still use today.
We explain the Banach-Tarski paradox — how a solid ball in three-dimensional space can be decomposed into finitely many pieces and reassembled into two balls identical to the original — and explore the role of the Axiom of Choice.
A detailed guide to preparing for mathematics exams, covering study schedules, practice strategies, common pitfalls, and techniques for performing well under pressure.
A curated guide to the best YouTube channels for learning mathematics, from visual intuition builders to full university lecture series, organized by level and topic.
A comprehensive guide to the many career paths available to mathematics graduates — from finance and technology to government, consulting, and beyond.
The inspiring story of Maryam Mirzakhani, an Iranian mathematician who made groundbreaking contributions to the geometry of Riemann surfaces and moduli spaces, becoming the first woman to receive the Fields Medal.
We explore the Prime Number Theorem — the asymptotic law governing the distribution of prime numbers — its history from Gauss and Legendre to the landmark proofs by Hadamard and de la Vallée-Poussin, and the deep connection between primes and the Riemann zeta function.