bio  website  isomorphismes.tumblr.com 

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 nonmathematical things, using modern mathematical shapes.
Besides this broad personal project, I am also interested in applying modern mathematics to economic theory.
1d

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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.…

1d

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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 
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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 
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Homological algebra and calculus (as in Newton)
It sounds like an isomorphism theorem for functors: replacing map(•) with surj(bij(inj(•))) .

Jun 7 
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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 
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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 
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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 
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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 
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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 
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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 
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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 
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Coboundaries and Gluing in Cech Cohomology  Intuition?
Here's my drawing of a coboundary: tmblr.co/ZdCxIyJEnZC based on Ghrist's EAT. 
May 9 
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Teaching homology via everyday examples
Was it from Chichilinsky? papers.ssrn.com/sol3/papers.cfm?abstract_id=1375205 
Mar 31 
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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 
Mar 23 
answered  How does an academic mathematician educate him/herself about job opportunities outside academia? 
Feb 15 
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How to respond to “I was never much good at maths at school.”
The stronger I bear in mind that my goal is to connect with someone and not to defend maths, the better I do. I look for any possible response except disagreeing with them. Also—someone who hates "maths" doesn't hate "representation theory" or "topology". "I think about knots all day" sounds much better than "Every day of my life is like the homework you hated". If it must be broached, I would emphasise the total lack of overlap between what I love and what they were forced to do as a youth. 
Feb 15 
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