MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

construction of nonmeasurable sets

I have a history question for which I've had trouble finding a good answer. The common story about nonmeasurable sets is that Vitali showed that one existed using the Axiom of Choice, and Lebesgue et …

set-theory measure-theory ho.history-overview  
asked by Monroe Eskew 18 votes
answered by Bob Solovay 31 votes

$f(x)$ is irreducible but $f(x^n)$ is reducible

Does there exist an irreducible polynomial $f(x)\in \mathbb{Z}[x]$ with degree greater than one such that for each $n>1$, $f(x^n)$ is reducible (over $\mathbb{Z}[x]$)?

asked by user56292 18 votes
answered by Vesselin Dimitrov 31 votes

What arrangement of unit cubes minimizes surface area?

Question A. How does one arrange $n$ unit cubes to minimize surface area? Question B. How does one arrange $n$ unit cubes to form a rectangular prism of minimal surface area? Various curricular …

reference-request discrete-geometry  
asked by Benjamin Dickman 16 votes
answered by Joseph O'Rourke 4 votes

Probing the generalization of the abc conjecture to more than 3 variables

Browkin and Brzezinski, in "Some remarks on the $abc$-conjecture", Math. Comp. 62 (1994), no. 206, 931–939, state the following generalization of the $abc$ conjecture to more than three variables: …

nt.number-theory abc-conjecture  
asked by Greg Martin 13 votes
answered by Felipe Voloch 4 votes

Artin L-function and Zeta function of twisted Dirac operator

If one thinks of a Frobenius as an element in the fundamental group of an arithmetic curve and of a Galois representation $\sigma$ as a flat connection on the curve, then the definition of the Artin …

nt.number-theory dg.differential-geometry arithmetic-geometry  
asked by Urs Schreiber 12 votes

Three old questions on the Sacks forcing

I came across the two following Qs in 1970. Find reals $a,b$ such that $a$ is Sacks over $L[b]$ and vice versa $b$ is Sacks over $L[a]$. Note that a Sacks $\times$ Sacks generic pair definitely does …

lo.logic set-theory forcing descriptive-set-theory  
asked by Vladimir Kanovei 11 votes

Are the quaternions not uncountably categorical?

Boris Zilber has argued that the field of the complex numbers is "logically perfect". For one thing, the theory of an algebraically closed field of characteristic zero is uncountably categorical: it …

asked by John Baez 11 votes
answered by Will Sawin 10 votes

Greatest hits from previous weeks:

How can an extremely mathematically talented young person be helped to fulfill his/her potential?

Obviously, this question is not a research level mathematics question at all. But, I've just met an extremely mathematically talented 11 years old student and I don't know how I can help him. For …

soft-question mathematics-education advice  
asked by Amir Asghari 39 votes
answered by user44032 67 votes

Good programs for drawing graphs ( directed weighted graphs )

Hi, does anyone know of a good program for drawing directed weighted graphs? Thanks

asked by dan 12 votes
answered by William Stein 16 votes

Can you answer these?

Invariant definition of the space of symbols on a vector bundle (pseudo-differential operators)

Normally, in the context of pseudo-differential operators, a symbol on a vector bundle $E$ is defined as a smooth function on $E$ which in each trivializing chart fulfills the usual symbol estimates …

dg.differential-geometry fa.functional-analysis ap.analysis-of-pdes  
asked by Tobias Diez 9 votes

Probability of matching under cyclic permutations

In A conjecture about the entropy of matrix vector products I asked a conjecture relating to the entropy of a matrix-vector product. This conjecture is as yet unproven. domotorp then made another …

asked by Anush 6 votes

If $B\subseteq A$ are free & finite rank $R$-algebras, is $R\to A \otimes_B R$ injective?

(In this question, all rings and algebras are commutative with identity.) I have a situation that boils down to the following data: a ring $R$, an $R$-algebra $A$ with a subalgebra $B$ such that $A$ …

ac.commutative-algebra ra.rings-and-algebras  
asked by Owen Biesel 5 votes
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