Tag: big-picture

277 Thinking and Explaining 2010-09-14T02:13:50.010

177 Intuitive crutches for higher dimensional thinking 2010-05-26T09:49:53.130

176 Fundamental Examples 2009-11-11T07:52:13.173

168 Your favorite surprising connections in Mathematics 2010-02-08T00:10:18.557

132 Analytic tools in algebraic geometry 2010-08-06T01:55:24.553

127 Proposals for polymath projects 2015-09-30T07:00:32.040

124 Examples of eventual counterexamples 2010-02-16T13:00:56.847

113 What is an integrable system 2009-11-21T17:18:12.360

112 Experimental Mathematics 2010-01-17T07:59:45.013

104 What makes four dimensions special? 2010-11-28T08:51:17.653

98 Why are modular forms interesting? 2010-05-14T10:25:10.187

94 What recent discoveries have amateur mathematicians made? 2010-10-30T14:20:24.430

86 How do you decide whether a question in abstract algebra is worth studying? 2010-09-24T06:17:01.583

74 Why is it a good idea to study a ring by studying its modules? 2009-11-12T19:55:23.767

74 How to find ICM talks? 2010-04-01T13:28:59.223

73 Why do Bernoulli numbers arise everywhere? 2011-04-11T02:41:06.740

71 Theorems that are 'obvious' but hard to prove 2011-01-09T11:19:49.657

71 What notions are used but not clearly defined in modern mathematics? 2011-02-25T20:43:24.550

67 Examples of major theorems with very hard proofs that have NOT dramatically improved over time 2013-12-20T07:14:00.630

64 How does "modern" number theory contribute to further understanding of $\mathbb{N}$? 2012-12-01T20:58:40.857

63 Why is Set, and not Rel, so ubiquitous in mathematics? 2013-02-07T00:51:04.703

61 Logic in mathematics and philosophy 2011-04-20T12:13:02.563

59 Collection of equivalent forms of Riemann Hypothesis 2010-09-25T12:29:06.333

58 Is there a high-concept explanation for why characteristic 2 is special? 2009-10-17T18:55:01.043

58 How does one find out what's happening in contemporary mathematics research? 2014-06-20T00:26:13.090

55 What precisely Is "Categorification"? 2009-11-10T11:22:23.160

55 The concept of Duality 2011-08-26T00:22:59.143

53 Why certain diophantine equations are interesting (and others are not) ? 2010-10-16T19:53:37.300

52 When has discrete understanding preceded continuous? 2017-05-28T23:45:42.027

51 Grothendieck's manuscript on topology 2011-11-28T14:32:44.623

50 What is the significance of non-commutative geometry in mathematics? 2012-02-11T07:58:49.377

49 What's wrong with the surreals? 2010-06-24T01:00:12.753

49 Atiyah-Singer theorem-a big picture 2016-03-08T19:42:16.803

48 What's a groupoid? What's a good example of a groupoid? 2009-10-19T00:53:47.793

48 Sheaf cohomology and injective resolutions 2009-10-19T03:38:52.007

48 What is a cumulant really? 2013-10-14T03:58:36.457

47 Equality vs. isomorphism vs. specific isomorphism 2010-05-12T12:02:18.367

47 What is the high-concept explanation on why real numbers are useful in number theory? 2011-04-14T02:40:59.847

47 What advantage humans have over computers in mathematics? 2016-03-13T00:13:58.960

46 Describe a topic in one sentence. 2009-10-22T16:28:18.433

45 "Algebraic" topologies like the Zariski topology? 2010-02-05T21:24:16.047

45 Modern algebraic geometry vs. classical algebraic geometry 2010-07-13T02:04:00.650

44 What is a cohomology theory (seriously)? 2009-11-19T16:26:06.903

44 Does any research mathematics involve solving functional equations? 2011-01-27T01:02:30.407

44 What do theta functions have to do with quadratic reciprocity? 2013-01-28T00:47:24.660

42 current status of crystalline cohomology? 2010-01-13T11:42:50.327

41 Mathematics of path integral: state of the art 2010-03-27T09:19:00.690

41 Where can square roots come from when they are not distances? 2016-03-13T21:48:24.987

38 What are examples of good toy models in mathematics? 2009-10-20T03:34:54.547

38 Universal definition of tangent spaces (for schemes and manifolds) 2009-11-04T22:47:03.137

38 Why is it useful to study vector bundles? 2009-12-05T05:02:04.017

36 The 'real' use of Quantum Algebra, Non-commutative Geometry, Representation Theory, and Algebraic Geometry to Physics 2010-02-08T19:43:03.990

36 Are there any "homotopical spaces"? 2010-04-17T15:00:07.727

36 Structures that turn out to exhibit a symmetry even though their definition doesn't 2013-12-13T19:56:24.080

36 Grothendieck says: points are not mere points, but carry Galois group actions 2016-03-17T20:58:55.953

35 How to unify various reconstruction theorems (Gabriel-Rosenberg, Tannaka,Balmers) 2010-02-24T12:18:05.960

35 What is Realistic Mathematics? 2010-08-07T16:07:35.080

35 Recent fundamental new directions in PDEs 2013-05-04T10:44:11.000

34 Intuition and/or visualisation of Ito integral/Ito's lemma 2010-06-28T06:32:45.603

34 Surprising and Useful Physical Intuition for Mathematical Objects 2011-03-28T14:41:02.217

34 Various flavours of infinitesimals 2011-07-05T20:12:44.387

33 What are some slogans that express mathematical tricks? 2009-12-14T14:52:24.670

33 On what kind of objects do the Galois groups act? 2011-07-06T09:25:30.853

33 Why is the definition of the higher homotopy groups the "right one"? 2017-10-21T17:39:31.130

32 What are interesting families of subsets of a given set? 2009-12-30T07:15:51.263

32 Underlying idea for (automorphic) L-function? 2014-11-23T12:24:31.500

32 Is algebraic geometry constructive? 2017-04-22T20:05:30.050

31 Doing geometry using Feynman Path Integral? 2010-03-27T07:36:05.257

31 Linear algebra in terms of abstract nonsense? 2016-07-02T13:29:03.497

30 Coefficients of Weil Cohomology Theories 2012-04-28T17:57:43.397

29 Why is it useful to classify the vector bundles of a space? 2010-02-24T07:40:28.040

29 Interesting mathematical topics arising from Biology 2011-09-01T21:34:42.027

29 "Softness" vs "rigidity" in Geometry 2012-12-11T21:50:40.823

28 Is there a common genesis for ADE classifications? 2010-07-24T22:04:26.980

28 How should one think about sheafification and the difference between a sheaf and a presheaf 2010-11-07T21:12:30.197

28 Continuous relations? 2014-08-22T17:00:39.867

27 What are some interesting problems in the intersection of Algebraic Number Theory and Algebraic Topology? 2012-07-26T21:43:56.347

26 Why are tensors a generalization of scalars, vectors, and matrices? 2010-03-18T11:52:54.993

26 Why are finiteness conditions important (and how to recognize them)? 2011-05-02T18:09:49.537

26 Characterizing specific "concrete" mathematical objects by abstract general properties 2011-12-18T00:52:32.497

25 Are infinite dimensional constructions needed to prove finite dimensional results? 2011-02-17T19:15:15.807

25 More on "Transalgebraic Theories" (a 19th century yoga)? 2011-10-23T10:08:17.517

25 A toolbox for algebraic topology 2012-07-13T12:53:24.533

25 Expert, Intuitive, Organizing Analogies 2016-03-20T15:01:20.383

24 Why the triangle inequality? 2011-05-20T09:47:54.363

23 Visualizing how Cech cohomology detects holes 2009-11-12T21:16:51.810

23 Contemporary mathematical themes 2013-08-08T14:33:21.643

23 Residual finiteness: why do we care? 2015-02-26T19:27:32.907

22 Heuristic behind the Fourier-Mukai transform 2009-12-26T23:59:36.100

22 Intuitive and/or philosophical explanation for set theory paradoxes 2010-06-18T19:08:53.807

22 Online math history lectures 2010-09-14T05:08:09.863

22 Narratives in Modular Curves 2010-12-01T20:42:22.400

22 Why are polynomials so useful in mathematics? 2014-06-13T01:10:17.903

22 Examples of intuition from fields other than Physics to solve math problems 2014-09-17T00:02:53.560

22 how do you visualize characteristic class? 2015-11-04T03:58:36.197

21 Natural setting for characteristic classes? 2010-04-27T03:22:41.690

21 Elevator pitch for the Virtual Fibering Theorem 2012-06-14T02:28:59.147

21 When must it be sets rather than proper classes, or vice-versa, outside of foundational mathematics? 2013-02-02T16:36:55.527

21 Current status of Grothendieck's homotopy hypothesis and Whitehead's algebraic homotopy programme 2017-04-09T11:27:52.743