## 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

### 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

### 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

### 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

### 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

### 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

### 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

## 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, ...

gr.group-theory pr.probability finite-groups topological-groups

### 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

### 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 \zeta_X(s) = \prod_{p\ \mbox{prime}}\zeta_{X\vert\mathbb{F}_p}(s), ...

ag.algebraic-geometry schemes zeta-functions euler-product