Mathematics

Math Forums

• Stack Exchange Mathematics — Q&A site for math enthusiasts and professionals.
• Stack Exchange MathOverflow — Q&A site for professional mathematicians.
• MathOverflow Meta

Math Blogs

• n-Category Café — Blog on higher category theory and related topics.
• The n-Category Café Archive — Archived posts from the n-Category Café.
• Pak, Igor (Igor Pak's blog) — Combinatorics, and opinions about mathematics.
• Hard Arithmetic — Alex Youcis on arithmetic geometry.
• Xena Project — Kevin Buzzard on formalizing mathematics in Lean.
• Tao, Terence (What's new) — Research updates, expository notes, and lecture material.
• Not Even Wrong — Peter Woit on physics and mathematics.
• Stacks Project Blog — Johan de Jong on the Stacks Project and algebraic geometry.
• Mumford, David — Essays on mathematics, vision, and its history.

Advices

• The "Three Things" Exercise for getting things out of talks — by R. Vakil.
• Advice for Ph.D. students in math — by B. Poonen.
• For potential Ph.D. students — by R. Vakil.
• On preparing and studying for seminars — by T. Ochiai. (in Japanese)
• On writing mathematical papers — by T. Ochiai. (in Japanese)
• How to prepare for seminars — by Y. Kawahigashi. (in Japanese)

Literatures

• nLab — Wiki for research-level mathematics, physics, and philosophy.
• The Stacks Project — Comprehensive reference for algebraic geometry.
• Banana Space (香蕉空间) — Chinese-language mathematics wiki, written textbook-style.
• ProofWiki — Collaborative mathematics encyclopedia.
• Open Problem Garden — Collection of open problems in mathematics.
• The Art of Problem Solving — Resources for math competition preparation.
• Homotopy Type Theory Book — Book on Homotopy Type Theory.
• Algebraic Geometry — Online book on algebraic geometry.
• A. Gathmann's Notes on Algebraic Geometry
• Math 216: Foundations of Algebraic Geometry — Course notes by R. Vakil.
• Linear Algebra Done Right — by S. Axler.
• K. Conrad's Notes
• A. Landesman's Notes

YouTube Channels

• 3Blue1Brown — Visual explanations of math concepts.

Tools

• q.uiver.app — Draw commutative diagrams and export them to LaTeX.

Conferences

• Mathmeetings.net — Listing of mathematics conferences, workshops, and seminars.

Long Lists

• Teach Yourself Logic: The Study Guide and Book Notes
• Book recommendation: introduction to model theory
• Best algebraic geometry textbook? (other than Hartshorne)

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