MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

When is an erratum necessary?

A typo, a spelling error etc., in a published article, is definitely not enough for issuing an erratum. If a mistake destroys a main result, then an erratum is definitely necessary, and the proof ...

soft-question journals  
asked by Hao Chen 29 votes
answered by Carlo Beenakker 17 votes

A point set of power series with coefficients in {-1, 1}. Connected or not?

Let $z$ be a fixed complex number with $|z|<1$ and consider the set $$X_z := \Big\{\sum\limits_{i=1}^{\infty} a_i z^i \ \Big|\ a_i\in \{-1,1\} \forall i\Big\}.$$ What can be said about the set $M$ ...

cv.complex-variables ds.dynamical-systems sequences-and-series fractals complex-dynamics  
asked by Kirby Lee 25 votes
answered by Douglas Zare 21 votes

Rational points on the "quintic circle" $x^5 + y^5 = 7$

I suspect that the curve $x^5 + y^5=7$ has no $\mathbb Q$ points, and a brief computer search verifies this hypothesis for denominators up to $10^4$. What techniques can be used to show that there are ...

nt.number-theory arithmetic-geometry diophantine-equations rational-points  
asked by pre-kidney 18 votes
answered by Michael Stoll 35 votes

Deep/precise relationship between two approaches to FLT for polynomials, $n = 3$

David Speyer commented the following here. I saw Brian Conrad give an excellent one hour talk to undergraduates where he proved that there do not exist nonconstant, relatively prime, polynomials ...

ag.algebraic-geometry nt.number-theory polynomials elliptic-curves riemann-surfaces  
asked by Kevin Dong 17 votes
answered by Joe Silverman 4 votes

Is there any pattern to the continued fraction of $\sqrt[3]{2}$?

Is there any pattern to the continued fraction of $\sqrt[3]{2}$ ? Wolfram Alpha returns for cube root of 2: $\sqrt[3]{2}=$ [1; 3, 1, 5, 1, 1, 4, 1, 1, 8, 1, 14, 1, 10, 2, 1, 4, 12, 2, 3, 2, 1, 3, ...

nt.number-theory continued-fractions  
asked by john mangual 17 votes
answered by joro 12 votes

Examples of Noetherian overkill

I have read in many places that the noetherian hypothesis is often overkill - both in commutative algebra and in ($\overset?=$) algebraic geometry. In particular, I've read that coherence and finite ...

ag.algebraic-geometry ac.commutative-algebra commutative-rings coherent-rings  
asked by Arrow 17 votes
answered by Georges Elencwajg 4 votes

Can a stochastic Turing machine output a consistent extension of PA with positive probability?

Suppose that we interpret the output tape of a Turing machine as an assignment of true or false to all sentences of PA, taking the $n$th output bit as the truth value of the sentence with Goedel ...

computability-theory computer-science foundations  
asked by Abram Demski 14 votes
answered by Bjørn Kjos-Hanssen 11 votes

Greatest hits from previous weeks:

Why can't a nonabelian group be 75% abelian?

This question asks for intuition, not a proof. An earlier question, Measures of non-abelian-ness was thoroughly answered by Arturo Magidin. A paper by Gustafson1 proves that, for a nonabelian group, ... pr.probability finite-groups topological-groups  
asked by Joseph O'Rourke 50 votes
answered by Geoff Robinson 49 votes

Has philosophy ever clarified mathematics?

I've recently been reading some standard textbooks on the philosophy of mathematics, and I've become quite frustrated that (surely due to my own limitations) I don't seem to be gleaning any ...

ho.history-overview math-philosophy  
asked by Daniel Moskovich 69 votes
answered by djechlin 92 votes

Can you answer these?

Arithmetic zeta function and local zeta functions

For the arithmetic zeta function of (say) a nonsingular projective variety $X$, one has the following Euler product \begin{equation} \zeta_X(s) = \prod_{p\ \mbox{prime}}\zeta_{X\vert\mathbb{F}_p}(s), ...

ag.algebraic-geometry schemes zeta-functions euler-product  
asked by THC 8 votes

Which ordering of factors is needed to obtain this kind of determinantal inequalities?

Let $A$ and $B$ be $n\times n$ Hermitian positive definite matrices. The curious determinantal inequality given here, which can be stated as $$\det (A^{4}+ ABBA+BAAB+B^{4})\ge\det(A^{4}+ ...

linear-algebra matrices inequalities matrix-analysis  
asked by Wolfgang 7 votes

Theories introduced by a class of forcing notions

The following notion is introduced by Mohammad Golshani. Let $V$ be a model of set theory and let $\mathcal{P}$ be a class consisting of non-trivial forcing notions in $V$. Let $$Th(V, ...

lo.logic set-theory forcing modal-logic  
asked by Rahman. M 4 votes
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