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.
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.

Institutes

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