21 Answers votes newest views recent 12Proofs that require fundamentally new ways of thinking 5What are the most attractive Turing undecidable problems in mathematics? 1The phenomena of eventual counterexamples 3How should one present curl and divergence in an undergraduate multivariable calculus class? 1A Book You Would Like to Write (2) 4Describe a topic in one sentence. 5What notions are used but not clearly defined in modern mathematics? 17(Preferably rare) Audio/Video recordings of famous mathematicians? 16Good papers/books/essays about the thought process behind mathematical research 5What are some applications of other fields to mathematics? 23What does the adjective “natural” actually mean? 18The half-life of a theorem, or Arnold’s principle at work 2Toy Models of Quantum Mechanics 0What should be taught in a 1st course on smooth manifolds? 5Is there a mathematical axiomatization of time (other than, perhaps, entropy)? 8“Closed-form” functions with half-exponential growth 6New proofs to major theorems leading to new insights and results? 11Discrete Fourier Transform of the Möbius Function 13What a geometer should know … -1Dual Riemannian metric and the Dual Metric Form 2Does equality of Hodge star and symplectic star imply Kähler structure?