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ὰγεωμὲρητος μηδϵὶς ϵἰσίτω

The philosopher kings of Plato's Republic were to learn Geometry at the acme of their preparation to rule. The reasoning was not only due to Plato's geometrical view of Nature but also his view of abstraction.

Without taking sides on this particular philosopher—how much more would he have valued modern geometry? I'm interested in learning mathematics from this perspective: experiencing how "the most different" human language influences my thoughts about the everyday world.

(By the everyday world I mean love, money, and human diversity — things that seem far away from serious professional text.) In particular I'd like to be able to think up novel and creative ideas about non-mathematical things, using modern mathematical shapes.

Besides this broad personal project, I am also interested in applying modern mathematics to economic theory.


1d
awarded  Necromancer
2d
revised How to write popular mathematics well?
cut out extraneous info, not transition sentences
2d
comment How to write popular mathematics well?
Here is some evidence about pictures. I lifted some pictures from Allen Hatcher's AT book and posted them on a website frequented by teens. They were reblogged/liked ~800 times. How many teens do you think navigated to math.cornell.edu/~hatcher/AT/ATpage.html and read any of his wonderful book? (Probably more after seeing the picture.) This is the power of brevity with the internet as distribution.
Jul
1
comment Where does the notion of pseudoholomorphic curve come from?
Some context in the intro. of math.mit.edu/~vwg/…
May
25
revised How to understand a solenoid?
T₃: D² × S¹ or T₃ := D² × S¹ ? I can't tell if D²×S¹ is the domain of a mapping T₃ or is the object T₃ itself.
May
24
suggested approved edit on How to understand a solenoid?
May
15
comment Where does a math person go to learn quantum mechanics?
Thank you @Sky!
May
11
comment Where does a math person go to learn quantum mechanics?
Do you have a recommendation of where to get to the right level of representation theory?
May
1
comment Colloquial catchy statements encoding serious mathematics
@kjetilbhalvorsen Indeed, near-zero-Kelvin labs on Earth mean it's probably not.
Apr
30
comment Colloquial catchy statements encoding serious mathematics
I feel it should be a drunk spaceship, since birds fly at most over a thickened 2-sphere, and realistically over just a small patch.
Apr
30
comment Colloquial catchy statements encoding serious mathematics
I like it as a way to explain cohomology on a closed circuit graph, as an alternative to exactness ⇒ Green's theorem.
Apr
30
comment Do good math jokes exist?
mathoverflow.net/a/54520/11500
Apr
30
comment Examples of intuition from fields other than Physics to solve math problems
I don't know if this has solved any new problems to date, but Maldacena uses an economic analogy to explain some mathematics. So possibly in the future someone could use that analogy to reason about a larger system that's mathematically harder to swallow but where an argument like "That would change the arbitrage" was more intuitive.
Apr
28
awarded  Yearling
Apr
23
comment Intuition behind Alexander duality
I sometimes understand an idea better by seeing how it's used than by seeing it described. Here's Robert MacPherson using Alexander duality at minute 21; HTH someone.
Mar
24
comment Visualization of the real projective plane
ℝℙ¹ is the space of lines through the origin so I just imagine a line nailed into the origin spinning around. (Reminding myself when it reaches noon it's already been there at 6:00 since unlike a ray the line is bi-directional hence $a=-a$.)
Mar
23
comment Visualizing functions with a number of independant variables
Often in my experience it's not necessary to show 5-way interactions – a 5-input function is really separable, with interesting interactions being 2-way but rarely 3-way. It also pays, imo, to look for ways to reduce dimensionality when you don't absolutely have to use necessarily overwrought visualisation techniques (Chernoff-Fleury faces, symphonies) which, like a time-lapse not over time, are entertaining but not super clear.
Mar
22
comment Intuitive crutches for higher dimensional thinking
I like the idea of "more neighbours" in higher-D euclidean space. Geoff Hinton joked about being in a grocery store buying pizza. Tomato sauce and cheese were near the pizza-dough, but sardines were not. "Unfortunately it's not at 16-dimensional grocery store", because then everything related to pizza-dough could be next to pizza-dough. So I think of ℤ³ as a graph with each vertex having 6 edges. In ℤⁿ each node has 2n edges.
Mar
15
revised Motivation for concepts in Algebraic Geometry
improved formatting
Mar
15
suggested approved edit on Motivation for concepts in Algebraic Geometry