Writing
94 posts · Page 6 of 7
How to develop genuine mathematical intuition beyond memorizing formulas, with strategies for visualization, analogy, and deep understanding across different branches of mathematics.
The extraordinary story of Srinivasa Ramanujan, who rose from poverty in colonial India to produce some of the most beautiful and mysterious formulas in the history of mathematics, only to die at the age of thirty-two.
We explain Gödel's two incompleteness theorems — why any consistent formal system strong enough to express arithmetic contains true statements it cannot prove, and why it cannot prove its own consistency.
An in-depth look at George Pólya's four-step problem-solving method, with concrete mathematical examples showing how to apply each step in practice.
A practical guide to navigating arXiv, the world's largest mathematics preprint server: how to search, browse, set up alerts, read preprints, and use arXiv as a tool for mathematical research.
The remarkable story of Emmy Noether, who overcame institutional sexism to transform abstract algebra and whose theorem linking symmetry to conservation laws remains one of the deepest results in mathematical physics.
A comprehensive guide to preparing for graduate school in mathematics — what to study, how to strengthen your application, and what to expect when you arrive.
We state and prove both parts of the Fundamental Theorem of Calculus, explore why it is the single most important result in analysis, and trace its historical development from Newton and Leibniz to Riemann and Lebesgue.
Practical strategies for taking notes in mathematics lectures, including what to write down, how to organize your notes, and how to review them effectively.
Everything you need to know about Mathematics Stack Exchange: how to ask good questions, write great answers, use MathJax, build reputation, and get the most out of the largest online math community.
The story of Alexander Grothendieck — a stateless refugee who became the most revolutionary mathematician of the twentieth century, rebuilt algebraic geometry from the ground up, and then walked away from it all.
We present Cantor's diagonal argument proving that the real numbers are uncountable, explore its consequences for set theory, and examine how it forever changed our understanding of infinity.
A practical guide to writing a master's thesis in mathematics — from choosing a topic and working with your advisor to structuring the document, writing proofs, and surviving the process.
A comprehensive guide to writing clear, rigorous mathematical proofs, covering proof techniques, structure, common patterns, and advice from experienced mathematicians.
Explore the extraordinary life and work of Terence Tao — from child prodigy competing in the International Mathematical Olympiad at age ten to Fields Medalist and one of the most prolific mathematicians alive.