bio  website  isomorphismes.tumblr.com 

location  Great Cacapon, WV  
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visits  member for  3 years, 9 months 
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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 nonmathematical things, using modern mathematical shapes.
Besides this broad personal project, I am also interested in applying modern mathematics to economic theory.
Sep 18 
answered  What is a good introductory text for moduli theory? 
Sep 11 
comment 
Heuristic behind the FourierMukai 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 timelogic, but meanwhile {T,F,?} should replace {T,F} in PC.) Or consider any linguistic ambiguity; vague predicates, ambivalent feelings, words that sortof fit the situation but notreally or maybekindasorta fit.…

Jul 24 
comment 
Au revoir, law of excluded middle?
I'm surprised that coming from philosophy you would say excludedmiddle 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 nonmathematician
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?
reread OP's question 
Jun 3 
revised 
Why is the gradient normal?
picture was gone 
Jun 3 
comment 
Why is the gradient normal?
@G.T.R. Thanks for headsup. I no longer remember what original image I was trying to use so I'll just add a few others. 
May 22 
comment 
Elementary+Short+Useful
Niles Johnson posted a very nice talk of this sort on youtube: nilesjohnson.net/hopf.html complete with excellent visuals (at the end) accompanied by highenergy music. Basically a Hopfsphere disco ball. 
May 22 
comment 
Elementary+Short+Useful
@PhilIsett One can easily show that the sum of two uniforms is triangular. One can also use Excel and thereby invoke some experimental mathematics. 
May 22 
comment 
Elementary+Short+Useful
...and if I wanted to introduce equivalencerelations to undergraduates, I'd definitely use the piano (modes, whitekeys & blackkeys, scales, the octave...) 
May 19 
comment 
Coboundaries and Gluing in Cech Cohomology  Intuition?
Penrose gave a concrete example of cocycle and coboundary in the tribar: jstor.org/stable/1575844 
May 19 
comment 
Coboundaries and Gluing in Cech Cohomology  Intuition?
Here's my drawing of a coboundary: tmblr.co/ZdCxIyJEnZC based on Ghrist's EAT. 
May 9 
comment 
Teaching homology via everyday examples
Was it from Chichilinsky? papers.ssrn.com/sol3/papers.cfm?abstract_id=1375205 
Mar 31 
comment 
Is there something like a Heyting Ring?
Don't join and meet each constitute group operations? 
Mar 25 
revised 
What are some examples of colorful language in serious mathematics papers?
corrected spelling 