Benjamin Dickman
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 13h comment How has “what every mathematician should know” changed? Related to $\pi$ and its being irrational (as well as the infinitude of the primes): See MO 21367 and the fascinating answer of François G. Dorais. Nov 18 revised Has the Fundamental Theorem of Algebra been proved using just fixed point theory? Finally found that Kulpa paper! Many thanks to K. Szumiło. Nov 12 comment Proofs without words See also: MESE 220. Nov 9 comment A different kind of divisor sums I think your initial recording of the sequence got cut off, since it ends with a $1$ (which won't be the case for any $n > 1$). Also, any prime $p$ will have only divisors $1$ and $p$ hence only sums $2$, $1+p$, and $2p$; in particular, the sequence will record a $3$ at the primes. To this end, I wonder whether considering the sequence for $n$ composite could be helpful? (Though one could similarly argue that $p^2$ a squared prime will only have sums $2$, $1+p$, $1+p^2$, $2p$, $p+p^2$, and $2p^2$, which are distinct, and thus explain the $6$ that arises for your fourth and ninth entries...) Nov 2 comment Forcing is intuitionistic Have you checked Kreisel (1961) "Set-theoretic problems suggested by the notion of potential infinity"? As mentioned in MO 124011, Kreisel claimed he had a form of forcing in his interpretation of intuitionism in that paper. (Cf. the historical treatment of forcing by G.H. Moore.) Oct 13 comment Simple bijection between reals and sets of natural numbers Do the interleaved blocks really go back to Dedekind? (I first saw this construction in the "Foundations" text by RL Wilder...) Oct 13 comment Where does the name $NE(X)$ come from? I googled cone of curves NE(X) "notation" and found: Numerically effective (Considering the effort expended, I don't think this is worth posting as an answer...) Oct 13 reviewed Approve When are simple foliations strictly simple? Oct 12 comment How does a mathematician choose on which problem to work? @quid I do not intend this as a "finalized product" and I hope that, if the edit is seen as unhelpful, then someone [with the requisite reputation] will simply revert it (see: Requests for reopen votes here). Essentially, I agree with (e.g.) Joel / Misha / Alexandre in their comments above, and I thought the example Richard Stanley provided from his own work to be wonderfully informative. Oct 12 revised How does a mathematician choose on which problem to work? i have substantially edited this question in response to its being re-closed: I removed some of the more general questions from the body, and tried to focus on the title question. If anyone feels that the change is too great, or otherwise inappropriate, I only ask that you revert the edit. Oct 12 awarded Nice Answer Oct 11 comment How does a mathematician choose on which problem to work? The collection of questions is too broad: the OP begins with How does mathematical research work?; clearly this is too much. But I think the spirit of the question is reasonable, and maybe it would be better if phrased directly at mathematicians: What is a problem [big or small] that you solved or are working on, how did you choose this problem, and why did/do you continue to work on it? Perhaps it is true that mathematicians ("by definition") know how to choose problems [proof: they choose problems]; but knowing (cognitive) differs from articulating how you know (metacognitive). Oct 11 answered How does a mathematician choose on which problem to work? Oct 8 comment Is this notion of 'closed subset' of a semigroup action something people have thought of? The mention of saturated reminds me of the question blip that was MO 126742... Oct 6 awarded Enlightened Oct 6 awarded Nice Answer Oct 5 comment Are there irreducible polynomials with all zeros on two concentric circles? @Wolfgang I wondered how I could've gotten an up-vote at MO 114745 (your Salem Polynomials link -- to a question from Nov. 2012) and it led me to this post under Linked. So I thought I'd try to hunt down something of relevance. I'm glad you found it helpful! Oct 5 answered Are there irreducible polynomials with all zeros on two concentric circles? Oct 4 comment Monic polynomial with integer coefficients with roots on unit circle, not roots root of unity? (Inspired by MO 219963 linking back here today: Though I imagine it very unlikely, one may wonder, Why do I have an answer with the same Kronecker reference that re-appeared in a comment eight hours later? Well, when I posted this response, I found Dmitri's informative answer was already added twelve minutes ahead of mine (!) and, unfamiliar with MO, I thought the norm would be to delete my answer upon this realization. It was quite some time later that I finally restored it...) Sep 17 comment Is this integral representation of $\zeta(2n+1)$ known? Around the same time as the former paper there is also ζ(n) via hyperbolic functions (D'Avanzo & Krylov, 2010) which cites the paper of Silagadze. I point this out because it was (perhaps) a bit easier to find given the OP's presentation using sinh, cosh, tanh: google ζ(n) hyperbolic and it ought to be the first result. [Edit: Separately, why on earth is Suvrit's answer voted down?!]