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I apologize for posting as an answer what should really be a comment, connected to one of Jacques Carette's comments on my earlier answer. Unfortunately, this is way too long for a comment. … So instead we construct models of ZFC, which are not so bad, and we rely on the interpretation to convert them into models of T. …

It seems people give a lot of credit to Bill Thurston. edit: Some time ago Riccardo Benedetti sent me some comments to append to my answer. … Finally a complete positive answer was given by A. …

I took The Princeton Companion to Mathematics (don't ask), converted the PDF to text, analysed the word frequency and isolated the names mentioned among the answers thus far. … Not to mention the fact that as Greg points out in a comment below, it is heavily biased in favour of those mathematicians after whom we name things. …

Let me convert my comments to an answer. … Thus, the expected density is $$ v_\infty = \prod_p (1-p^{-2})^{-1}(1-p^{-3})^{-1} = (\zeta(2)\zeta(3))^{-1} \simeq 0.5057390381 $$ agreeing with the answer that Francesco Polizzi just entered while I …

I'm converting the comment above to an answer: Shapiro made the following conjecture in the paper "The expansion of mean-periodic functions in series of exponentials" Comm. Pure and Appl. …

Update: See the comments for an extremely nice solution by George Lowther, plus my followup questions. I know of two results directly relevant to this problem. … (Warning: I converted from a different representation, and can't promise I didn't get a factor of 2 wrong or something like that.) …

Although the answers already given are correct, let me add some information (essentially just rephrasing the bracketed part of Thomas Scanlon's answer) that I've found useful for students who raised this … We have an explicit construction, which I'll call $C$, that will convert any element of $x$ into a choice function, namely sending any $y$ to $\{(x,y)\}$ (as in Charles Staats's comment on the original …

In response to Minhyong's request, I am reposting my comments above as an answer: As James Newton commented, if $L/K$ is unramified, then an irreducible $n$-dimensional representation (over $\mathbb C … [Added July 14, in response to Minhyong's question in the comments as to whether or not discrete series can convert into non-discrete series after applying some functoriality. …

Any comments or reference is appreciated! Please add some reference in your answer to support your claims, thanks a lot! … (2)And the infinitesimal generators of $\mathrm{Diff}(C)$ can be used to describe the velocity field along the curves in $Cur$. (3)Combined with Tobias' answer, [Mumford&Michor] also said symmetry is …

By popular demand, I am converting my comment above to an answer. Yes, the series converges. …

As of writing, I cannot see any way to answer this other than with a resounding yes. … (I say all of this as someone who, at least in recent years, has been converted.) …

Firstly, a general comment: as understanding of a mathematical problem deepens, it is common (and even expected) for the most mathematically natural formulation of a given problem (or class of problems … As mentioned in GH's answer, Iwaniec-Kowalski gives a more modern and advanced treatment of these topics. I also like Montgomery's CBMS book. …

(Converted from a comment to an answer as requested.) …

UPDATE 2: Qiaochu points out in a comment to his answer that the order of operations is not the most essential thing here. … UPDATE 3: For a very nice discussion of the ideas related to Theo's answer see http://golem.ph.utexas.edu/category/2008/12/groupoidification_made_easy.html …

I may as well convert my comment to an answer. The probability that a randomly chosen degree $d$ polynomial in $\mathbb{F}_p[u]$ is irreducible is $d^{-1} \cdot (1+O(p^{-d/2}))$. …