MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

Nelson's proof of Liouville's theorem

The paper "A proof of Liouville's theorem" by E. Nelson, published in 1961 in Proceedings of AMS, contains just one paragraph, giving a (now) standard proof that every bounded harmonic function in ...

ho.history-overview harmonic-functions  
asked by Kostya_I 21 votes
answered by Willie Wong 15 votes

Mathematicians with Aphantasia (Inability to Visualize Things in One's Mind)

Are there any mathematicians with aphantasia? If so, could they please elaborate upon what their experience with mathematics is like? I realize that this question probably falls outside of the scope ...

asked by Trent 19 votes
answered by MurphyKate Montee 25 votes

Adapting arguments and plagiarism

I'm currently working on my PhD thesis. I have several suggested problems to work on, some of them are very similar to some problems that my advisor have worked before and published already, either in ...

asked by Gustavo Marra 19 votes
answered by Joel David Hamkins 66 votes

Does $E_8$ know $Spin(7)$?

One way to define the compact group $Spin(7)$ is as the stabilizer of a certain 4-form on Euclidean $\mathbb R^8$ (see e.g. this MO question). This 4-form can be defined in various ways. For ...

dg.differential-geometry rt.representation-theory lie-groups euclidean-lattices  
asked by Theo Johnson-Freyd 17 votes

Checking Mertens and the like in less than linear time or less than $\sqrt{x}$ space

Say you want to check that $|\sum_{n\leq x} \mu(n)|\leq \sqrt{x}$ for all $x\leq X$. (I am actually interested in checking that $\sum_{n\leq x} \mu(n)/n|\leq c/\sqrt{x}$, where $c$ is a constant, and ...

nt.number-theory analytic-number-theory computational-complexity computation  
asked by H A Helfgott 14 votes

Table of (integral) cohomology groups of K(Z,n)

Can I find somewhere a table of the (first few) cohomology groups of $K(\mathbb{Z},n)$ with integer coefficients? It seems like a natural counterpart to the table of the homotopy groups of spheres, ...

homotopy-theory cohomology  
asked by Guillaume Brunerie 14 votes
answered by Benjamin Antieau 5 votes

Is there a $C_c^{\infty}( \mathbb{R}^d)$ function whose Fourier transform we can explicitly write down?

I noticed that although $C_c^{\infty}$-functions are dense in some quite large spaces and well understood (especially their Fourier transform) I have never encountered an explicit example of a ...

real-analysis fourier-analysis fourier-transform  
asked by Jonathan 13 votes
answered by Terry Tao 23 votes

Greatest hits from previous weeks:

Examples of common false beliefs in mathematics

The first thing to say is that this is not the same as the question about interesting mathematical mistakes. I am interested about the type of false beliefs that many intelligent people have while ...

big-list mathematics-education  
asked by gowers 551 votes
answered by Tilman 453 votes

What are some important but still unsolved problems in mathematical logic?

In the past, First order logic and its completeness and whether arithmetic is complete was a major unsolved issues in logic . All of these problems were solved by Godel. Later on, independence of ...

lo.logic soft-question big-list open-problem open-problems-list  
asked by Maths Lover 30 votes
answered by Noah Schweber 38 votes

Can you answer these?

Computing the ordinal of a rational language well-partially-ordered by the subword relation

Let $\Sigma$ be a finite set or "alphabet", $\Sigma^*$ the free monoid on $\Sigma$ or set of "words". If $w,w'\in \Sigma^*$, write $w\leq w'$ when $w$ is a "subword" of $w'$, i.e., can be obtained by ...

co.combinatorics order-theory formal-languages ordinal-numbers  
asked by Gro-Tsen 8 votes

The axiom $I_0$ in the absence of $AC$

It is well-known that if $AC$ holds and if $j: L(V_{\lambda+1}) \to L(V_{\lambda+1})$ is a non-trivial elementary embedding with $crit(j) < \lambda,$ then $\lambda$ has countable cofinality (and in ...

lo.logic set-theory large-cardinals axiom-of-choice  
asked by Mohammad Golshani 9 votes

Morphisms for good reduction are maps respecting filtration

Please see edit below. So, let $A,A'/K$ be abelian varieties where $K$ is a $p$-adic local field with residue field $k$. Suppose further that they have good reduction with models ...

ag.algebraic-geometry arithmetic-geometry abelian-varieties p-adic-hodge-theory crystalline-cohomology  
asked by Alex Youcis 7 votes
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