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Thinking and Explaining

What's a mathematician to do? [closed]

What is torsion in differential geometry intuitively?

nontrivial theorems with trivial proofs

Important formulas in combinatorics

Homotopy groups of Lie groups

Are there any very hard unknots?

A learning roadmap for algebraic geometry

What do the stable homotopy groups of spheres say about the combinatorics of finite sets?

When can a Connection Induce a Riemannian Metric for which it is the Levi-Civita Connection?

Why do Bernoulli numbers arise everywhere?

Why do combinatorial abstractions of geometric objects behave so well?

The concept of duality

Intuitive explanation for the Atiyah-Singer index theorem

What programming language should a professional mathematician know? [closed]

What is the motivation for a vertex algebra?

Why aren't representations of monoids studied so much?

Most intricate and most beautiful structures in mathematics

What universities have laid off tenured math faculty for financial reasons?

Derived algebraic geometry: how to reach research level math?

A dictionary of Characteristic classes and obstructions

What is Koszul duality?

Double affine Hecke algebras and mainstream mathematics

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Taking lecture notes in lectures

The 'real' use of Quantum Algebra, Non-commutative Geometry, Representation Theory, and Algebraic Geometry to Physics

Elegant proof that any closed, oriented 3-manifold is the boundary of some oriented 4-manifold?

Character table does not determine group Vs Tannaka duality