nhaliday + quantifiers-sums   6

soft question - Thinking and Explaining - MathOverflow
- good question from Bill Thurston
- great answers by Terry Tao, fedja, Minhyong Kim, gowers, etc.

Terry Tao:
- symmetry as blurring/vibrating/wobbling, scale invariance
- anthropomorphization, adversarial perspective for estimates/inequalities/quantifiers, spending/economy

fedja walks through his though-process from another answer

Minhyong Kim: anthropology of mathematical philosophizing

Per Vognsen: normality as isotropy
comment: conjugate subgroup gHg^-1 ~ "H but somewhere else in G"

gowers: hidden things in basic mathematics/arithmetic
comment by Ryan Budney: x sin(x) via x -> (x, sin(x)), (x, y) -> xy
I kinda get what he's talking about but needed to use Mathematica to get the initial visualization down.
To remind myself later:
- xy can be easily visualized by juxtaposing the two parabolae x^2 and -x^2 diagonally
- x sin(x) can be visualized along that surface by moving your finger along the line (x, 0) but adding some oscillations in y direction according to sin(x)
q-n-a  soft-question  big-list  intuition  communication  teaching  math  thinking  writing  thurston  lens  overflow  synthesis  hi-order-bits  👳  insight  meta:math  clarity  nibble  giants  cartoons  gowers  mathtariat  better-explained  stories  the-trenches  problem-solving  homogeneity  symmetry  fedja  examples  philosophy  big-picture  vague  isotropy  reflection  spatial  ground-up  visual-understanding  polynomials  dimensionality  math.GR  worrydream  scholar  🎓  neurons  metabuch  yoga  retrofit  mental-math  metameta  wisdom  wordlessness  oscillation  operational  adversarial  quantifiers-sums  exposition  explanation  tricki  concrete  s:***  manifolds  invariance  dynamical  info-dynamics  cool  direction 
january 2017 by nhaliday

bundles : abstractmathproblem-solving

related tags

additive-combo  adversarial  algebraic-complexity  aphorism  better-explained  big-list  big-picture  binomial  books  cartoons  clarity  coarse-fine  communication  complexity  concentration-of-measure  concrete  cool  counterexample  cs  dimensionality  direction  draft  dynamical  entropy-like  estimate  examples  existence  explanation  exposition  extrema  fedja  fourier  giants  gowers  ground-up  hi-order-bits  homogeneity  identity  info-dynamics  information-theory  inner-product  insight  integral  intuition  invariance  isotropy  lens  levers  lifts-projections  limits  list  local-global  logic  magnitude  manifolds  math  math.AT  math.CA  math.CV  math.FA  math.GR  mathtariat  measure  mental-math  meta:math  metabuch  metameta  neurons  nibble  operational  org:mat  oscillation  overflow  p:someday  p:whenever  pdf  philosophy  polynomials  positivity  probabilistic-method  probability  problem-solving  proofs  q-n-a  quantifiers-sums  reference  reflection  retrofit  s:*  s:**  s:***  s:null  scholar  signum  soft-question  spatial  stat-mech  stirling  stories  structure  sum-of-squares  symmetry  synchrony  synthesis  tcs  tcstariat  teaching  tensors  the-trenches  thinking  thurston  tidbits  tightness  tricki  tricks  uniqueness  unit  vague  visual-understanding  wiki  wisdom  wordlessness  worrydream  writing  yoga  🎓  👳 

Copy this bookmark: