MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

Randall Munroe's Lost Immortals

In Randall Munroe's book What If?, the "Lost Immortals" question asks: If two immortal people were placed on opposite sides of an uninhabited Earthlike planet, how long would it take them to find ...

mg.metric-geometry spherical-geometry  
asked by Timothy Chow 39 votes
answered by Steven Gubkin 14 votes

What did Rolle prove when he proved Rolle's theorem?

Rolle published what we today call Rolle's theorem about 150 years before the arithmetization of the reals. Unfortunately this proof seems to have been buried in a long book [Rolle 1691] that I can't ...

real-analysis ho.history-overview ordered-fields  
asked by Ben Crowell 27 votes
answered by Gerry Myerson 21 votes

Is the regularity of finitely generated rings decidable?

Q: Is there an algorithm to decide whether a given finitely generated (over $\mathbb{Z}$) commutative ring is regular? I mean by regular that the localization at every prime ideal is a regular local ...

ag.algebraic-geometry ac.commutative-algebra lo.logic  
asked by Takehiko Yasuda 13 votes
answered by Count Dracula 2 votes

Is it possible to formulate the axiom of choice as the existence of a survival strategy?

Consider the following situation: There is an infinite set $G$ of giraffes. A lion comes and announces a set $C$ of all possible colours and an infinite cardinal $\kappa$. The hungry lion ...

lo.logic set-theory axiom-of-choice recreational-mathematics  
asked by Joonas Ilmavirta 11 votes
answered by Nate Eldredge 11 votes

Is there any relationship between the Euler class and the Vandermonde determinant?

Several Wikipedia articles claim that the relationship between the Euler class $e(V)$ and the top Pontryagin class $p_k(V)$ of an oriented $2k$-dimensional real vector bundle $V$ corresponds, via the ...

at.algebraic-topology vector-bundles characteristic-classes  
asked by Qiaochu Yuan 10 votes
answered by Qiaochu Yuan 2 votes

Take contraction wrt a vector field twice and define kernel mod image. Does that give anything interesting?

I apologize in advance if this question is too vague for mathoverflow. My main aim is to get some references for a concept. First, we make the following observation: let $X: M \rightarrow TM $ be a ...

dg.differential-geometry differential-topology cohomology homology  
asked by Ritwik 10 votes
answered by Joonas Ilmavirta 6 votes

Is every order type of a PA model the \omega of some ZFC model?

Let $N$ be a model of first-order Peano arithmetic, and let $\sigma$ be its order-type. Does it follow that there is a (non-transitive, expect when $M$ is the standard model) $ZFC$-model $M$ such that ...

lo.logic model-theory  
asked by M Carl 10 votes
answered by Joel David Hamkins 11 votes

Greatest hits from previous weeks:

Examples of great mathematical writing

This question is basically from Ravi Vakil's web page, but modified for Math Overflow. How do I write mathematics well? Learning by example is more helpful than being told what to do, so let's try to ...

mathematical-writing soft-question big-list  
asked by Anton Geraschenko 83 votes
answered by Ilya Grigoriev 74 votes

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 411 votes
answered by Tilman 330 votes

Can you answer these?

On a problem of Berkovich

What is the real history of the following problem proposed by Berkovich [Y. Berkovich, Z.Janko, Groups of prime power order. Volume 2, Expositions in Mathematics, 56, Walter de Gruyter, New York, ...

reference-request gr.group-theory p-groups outer-automorphisms  
asked by S. Mohsen Ghoraishi 3 votes

A good book on adeles and ideles

Many results in number theory are stated either in a classical language or in an adelic one. I am often impressed of the efficiency and the satisfactory computational properties of the adelic setting, ...

nt.number-theory gn.general-topology algebraic-number-theory local-fields adeles  
asked by Dydo 3 votes

Moduli interpretation of Eisenstein series

Let $N \geq 11$ be an integer and consider the basis of Eisenstein series for $M_2(\Gamma_0(N))$ described in Theorem $4.6.2$ of Diamond--Shurman's book. Pick and Eisenstein series $F$ in this basis. ...

nt.number-theory modular-forms moduli-spaces eisenstein-series  
asked by Emmanuel Lecouturier 3 votes
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