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bio website isomorphism.es
location Great Cacapon, WV
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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.


Oct
19
comment What's a groupoid? What's a good example of a groupoid?
I guess if this is true, then passing in (European) football also is more like a groupoid than a group. Only the person with the ball can pass to any teammate (or "negative pass" to any opponent). Yes?
Sep
30
revised How to write popular mathematics well?
head/heart
Sep
30
answered How to write popular mathematics well?
Sep
30
comment Cures for mathematician's block (as in writer's block)
Does it need to be science? I think it could be even further afield—history, art, anything that renews one's sense of curiosity and wonder at the world…
Sep
30
answered Category theory sans (much) motivation?
Sep
30
revised Mathematical definition of running
not Cartesian
Sep
30
comment Mathematical definition of running
@Noah Yes, you do remember that correctly. canyon23.net/math/1985thesis.pdf (found Kevin Walker's thesis via the E.A.T. book of Robert Ghrist. Dr Ghrist has done some work on robots not bumping into each other [braid theory] which may be what you had in mind?)
Sep
30
answered Mathematical definition of running
Sep
24
awarded  Autobiographer
Sep
18
answered What is a good introductory text for moduli theory?
Sep
11
comment Heuristic behind the Fourier-Mukai transform
also math.stackexchange.com/questions/1002/…
Sep
4
comment Wikipedia's definition of constant sheaf is wrong
@KevinBuzzard OK, but realistically people do expect Wikipedia to be right, and they expect maths textbooks to be right, and they expect the maths on Wikipedia to be right. It's up to people who know what a sheaf is (and what better forum to alert them) to correct WP, of course.
Jul
24
comment Au revoir, law of excluded middle?
I can't remember all of my original philosophical objections but for example "A sea battle will occur tomorrow" is neither true nor false today. (One could make a time-logic, but meanwhile {T,F,?} should replace {T,F} in PC.) Or consider any linguistic ambiguity; vague predicates, ambivalent feelings, words that sort-of fit the situation but not-really or maybe-kinda-sorta fit.…
Jul
24
comment Au revoir, law of excluded middle?
I'm surprised that coming from philosophy you would say excluded-middle is so undeniable. For me it was through philosophical objections that I wanted to deny EM (to deny that it must work in all cases ¬⊨P∨¬P; not to deny it in each case ⊨¬(P∨¬P)).
Jun
27
comment Algebraic Geometry for non-mathematician
The only "shortcut" I know of would be to play around with SURFER: imaginary.org/program/surfer. It shows you the roots of polynomials over 3 letters. Since varieties and algebraic curves are fundamental in AG this gives you a peek at the topic. Also an analytical statement about intersections (from eg lecture 1 of Vakil) can be envisaged with eg.
Jun
7
comment Homological algebra and calculus (as in Newton)
It sounds like an isomorphism theorem for functors: replacing map(•) with surj(bij(inj(•))).
Jun
7
comment Homological algebra and calculus (as in Newton)
When I think of ∂ I'm necessarily thinking about the fundamental theorem of calculus: take I=[0,1] then $\int_I D[f] = f \vert_{\partial I}$. So wouldn't ∂² then be evaluating $f$ on ∂(∂(I))=∅, which is a strange enough notion that I'm not sure what one would want to do to make sense of it. My way of thinking about it doesn't yield anything nice like $f''$ resulting from ∂∂I, which may make it a bad idea.
Jun
3
comment Badiou and Mathematics
on the arXiv: arxiv.org/abs/1406.0059v1 arxiv.org/abs/1301.1203 might be better than Wikipedia for a relatively technical yet also politically fraught subject.
Jun
3
revised Why is the gradient normal?
re-read OP's question
Jun
3
revised Why is the gradient normal?
picture was gone