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15h
comment Is there a general notion of semigroup action?
Welcome to MO, Robin!
1d
comment Machine learning approach
Please consider asking instead at stats.stackexchange. You should probably try to make your question more mathematically precise first.
2d
comment Is there a categorical proof of Gödel's incompleteness theorem?
This is not quite accurate. Lawvere exhibits a common structure of diagonal arguments in the language of category theory, but the part of Goedel's proof that invokes the diagonal argument comes after the demonstration that the formal theory of Peano arithmetic can itself be encoded in arithmetic -- and a full-fledged categorical account of the proof would also prove this fundamental arithmeticization. This Lawvere does not even pretend to do (and what Joyal actually does in the work referenced in the accepted answer).
Aug
28
comment A Book You Would Like to Write
I agree that the book is poorly titled...
Aug
28
comment Alternative definition of monoidal categories
@Turion String diagrams are sometimes relevant, but the private pictures I've developed for my purposes here are mostly decorated trees.
Aug
28
comment Alternative definition of monoidal categories
@Turion Thanks. Commutative diagrams are not so much the problem; it's other types of pictures I want to draw with little hassle.
Aug
28
comment Can there ever be symbolic formalism (of importance) without intuitive heuristics?
@მამუკაჯიბლაძე Feynman (see e.g. generallythinking.com/…) has remarked on how different "thinking about the same thing" can be for two different people. I believe you when you say you do not think verbally when you are not paying attention to it, but it's less clear that you can generalize that observation to cover everyone.
Aug
27
comment Examples of unexpected mathematical images
Sorry for not responding earlier. My comment was in reference to the wording of the OP, which asks specifically what mathematical insights did the image give rise to. I too take aesthetic pleasure in the pictures derived from applying the tracer to your parametric equations, but my reading is that the OP is interested specifically in examples which produced a mathematical insight, in order to be considered on-topic for MO.
Aug
24
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
Kieren, I hope you don't mind the edit. I just wanted to make sure the post was in the form of a question.
Aug
24
revised Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
put the post in the form of a question
Aug
24
comment Time in Girard's Geometry of Interaction
For me, reading Girard often feels like reading Derrida. In both cases I typically feel stupid for not being able to really follow the obscure allusions and suggestions, or else I get a feeling similar to taking a Rorschach test. Also I sense a kind of cultish mystique surrounding these men. I like it much more when Girard does some hard mathematics and produces a proof, as he has been known to do on occasion.
Aug
23
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
See also the meta thread: meta.mathoverflow.net/questions/1865/…
Aug
19
comment Survey of the history of calculus?
Might as well provide a link to Ehrlich's review of Bell's book: ohio.edu/people/ehrlich/Bell.pdf
Aug
17
comment How short can we state the Axiom of Choice?
Okay, thanks Frode. As a friendly suggestion: please consider editing your question to take into account Andreas's (correct) conjecture, and please consider removing the word "simple" (or "simply") since that's not so easy to measure, and specify shortness as the desired criterion. I think you then want to specify that you are looking for formulae written in the formal language of ZF -- in that case I think the question becomes crystal clear.
Aug
17
comment How short can we state the Axiom of Choice?
Even if Paul's suggestion is not expressed in the formal language of ZF, it's quite obvious how one would go about rewriting it in that language, and moreover: it's conceptually very simple. This raises the question of what is meant by "simplicity" in the Original Post. Or are we just counting the number of symbols in a ZF formula?
Aug
17
comment How short can we state the Axiom of Choice?
I didn't understand what you were driving at with "solutions that appeal to selection operators and their kins". It's the word 'kin' that seems vague -- is Paul's suggestion something you would disregard?
Aug
17
comment How short can we state the Axiom of Choice?
That was what I first thought of too. But I wondered whether this is the type of thing OP would disregard (I didn't understand his criteria).
Aug
17
comment How short can we state the Axiom of Choice?
Can you give just one example of a solution that you wouldn't disregard, whether long or not or simple or not?
Aug
17
comment Pseudomodules, “general coherence theorem”
As for the first question: you might check out ncatlab.org/nlab/show/actegory and the references therein (which might have an answer to your second question as well; I'd have to check the Kelly-Janelidze article as a likely candidate).
Aug
17
comment Examples of unexpected mathematical images
And so? What mathematical insights did this give rise to?