This tag is used if a reference is needed in a paper or textbook on a specific result.

**21**

votes

**2**answers

1k views

### Similarities between Post's Problem and Cohen's Forcing

Remark: I have since learned that G.H. Moore addresses this question in the third reference listed at the end of this post, beginning on p. 157 in which he cites a letter from Kreisel to Gödel dated ...

**6**

votes

**1**answer

278 views

### coloring in lattice

This is a mathematical question raised from engineering and physics:
Is there some established mathematical approach in filling a physical lattice with some colored basis (black and white here)? For ...

**5**

votes

**0**answers

269 views

### Reference for Wang Tile

I am working on projects in solving ground state of generalized ising models. One recent work involves tiling with basic tiles that filled the whole lattice. For example, we could obtain results:
...

**17**

votes

**8**answers

2k views

### Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature

A curve in the plane is determined, up to orientation-preserving
Euclidean
motions, by its curvature function, $\kappa(s)$.
Here is one of my favorite examples, from
Alfred Gray's book,
Modern ...

**6**

votes

**2**answers

1k views

### Riemann zeta function at positive integers and an Appell sequence of polynomials related to fractional calculus

I was exploring some raising and lowering operators related to an infinitesimal generator for fractional integro-derivatives and found an Appell sequence of polynomials, i.e., an infinite sequence of ...

**78**

votes

**41**answers

23k views

### Ways to prove the fundamental theorem of algebra

This seems to be a favorite question everywhere, including Princeton quals. How many ways are there?
Please give a new way in each answer, and if possible give reference. I start by giving two:
...

**86**

votes

**10**answers

10k views

### Is there an introduction to probability theory from a structuralist/categorical perspective?

The title really is the question, but allow me to explain.
I am a pure mathematician working outside of probability theory, but the concepts and techniques of probability theory (in the sense of ...

**54**

votes

**14**answers

5k views

### Mathematical research published in the form of poems

The article
Friedrich Wille: Galerkins Lösungsnäherungen bei monotonen Abbildungen,
Math. Z. 127 (1972), no. 1, 10-16
is written in the form of a lengthy poem, in a style similar to that
of the ...

**10**

votes

**7**answers

3k views

### Roadmap to learning about Ricci Flow?

Hello,
I'm curious to what books etc. one could use to understand the basics of Ricci flow, what areas of math are needed and so? What areas should one specialize in? See it as a roadmap to ...

**20**

votes

**3**answers

4k views

### Are nontrivial integer solutions known for $x^3+y^3+z^3=3$?

The Diophantine equation
$$x^3+y^3+z^3=3$$
has four easy integer solutions: $(1,1,1)$ and the three permutations of $(4,4,-5)$. Elsenhans and Jahnel wrote in 2007 that these were all the solutions ...

**24**

votes

**12**answers

4k views

### Explicit computations using the Haar measure

This question is somewhat related to my previous one on Grassmanians. The few times I've encountered the Haar measure in the course of my mathematical education, it's always been used in a very ...

**15**

votes

**9**answers

3k views

### The free group $F_2$ has index 12 in SL(2,$\mathbb{Z}$)

Is there someone who can give me some hints/references to the proof of this fact?

**33**

votes

**1**answer

2k views

### Probability that a stick randomly broken in five places can form a tetrahedron

The following problem was brought to my attention by a doctoral dissertation on Mathematics Education, but - as far as I know - the solution remains unknown.
I have already asked this question on ...

**21**

votes

**5**answers

1k views

### Verlinde's formula

"Verlinde's formula" predicts the dimension of the space of conformal blocks of a chiral CFT.
Depending on...
• which chiral CFT one considers (does one restrict to WZW models, or not?)
...

**29**

votes

**6**answers

3k views

### Is the Mendeleev table explained in quantum mechanics?

Does anybody know if there exists a mathematical explanation of Mendeleev table in quantum mechanics? In some textbooks (for example in "F.A.Berezin, M.A.Shubin. The Schrödinger Equation") the authors ...

**2**

votes

**3**answers

955 views

### The Lagrangian formulation of mechanics without going through variational principles.

In some texts on classical mechanics and not only, the Euler--Lagrange equations of motion are directly obtained as solution of variational problems.
On the other side, sometimes reading about ...

**12**

votes

**3**answers

633 views

### Is there a midsphere theorem for 4-polytopes?

The (remarkable) midsphere theorem says that each combinatorial
type of convex polyhedron may be realized by one all of whose edges are
tangent to a sphere
(and the realization is unique if the center ...

**12**

votes

**3**answers

2k views

### Proof of the Reidemeister theorem

While preparing for my introduction to topology course, I've realized that I don't know where to find a detailed proof of the Reidemeister theorem (two link diagrams give isotopic links, iff they can ...

**10**

votes

**0**answers

730 views

### Complexes of representations with complementary central charges

This is another question asking for references. There is an important phenomenon of correspondence between (complexes of) representations of infinite-dimensional Lie algebras with the complementary ...

**8**

votes

**5**answers

2k views

### totally disconnected and zero-dimensional spaces

When do the notions of totally disconnected space and zero-dimensional space coincide? From what I gather, there are at least three common notions of topological dimension: covering dimension, small ...

**8**

votes

**3**answers

581 views

### Consistency of Analysis (second order arithmetic)

Is there a proof of the consistency of Analysis (second order arithmetic), which is similar to Gentzen's proof of the consistency of arithmetic?
Update:
Which (different) methods can be used to ...

**8**

votes

**5**answers

1k views

### Measure theory treatment geared toward the Riesz representation theorem

I'm looking for recommendations for books (or lecture notes) that develop measure theory in sufficient detail to state and prove the Riesz representation theorem (which is the characterization of the ...

**14**

votes

**1**answer

386 views

### Unpublished works of Woodin on SCH and Radin forcing

There are many unpublished results of Hugh Woodin on ''singular cardinals hypothesis'' and '' Radin forcing''. Some of his results are published later by others, but it seems that there are still many ...

**4**

votes

**4**answers

896 views

### Delaunay triangulations and convex hulls

This is a reference request.
I have the impression that those who work in computational geometry are accustomed to the following. You have some locally finite set of sites in $\mathbb{R}^n$ and you ...

**15**

votes

**1**answer

638 views

### Formality of classifying spaces

Let $G$ be a compact Lie group (or reductive algebraic group over $\mathbb{C}$), and let $BG$ be its classifying space. Fix a prime $p$. Let $\mathcal{A}$ denote the dg algebra of singular cochains on ...

**5**

votes

**1**answer

451 views

### List of open problems of formal languages [closed]

As we know, there are some open problems of formal languages. I am wondering if there is a somehow complete list of open problem of formal languages. If there isn't such a list, can we make it one as ...

**5**

votes

**2**answers

1k views

### Consequences of Legendre's conjecture

I am looking for a list/reference which explores the consequences of Legendre's conjecture, which states that one can always find a prime number between $n^2$ and $(n+1)^2$.

**4**

votes

**1**answer

571 views

### Uniform boundedness of an $L^2[0,1]$-ONB in $C[0,1]$

Assume that we have an orthonormal basis of smooth functions in $L^2[0,1]$. Are there useful practical criteria to determine whether the sup-norm of the basis functions has a uniform bound? I am sure ...

**3**

votes

**4**answers

1k views

### Measure on real Grassmannians

OK, so I'm reading about this nice measure you can define on a (real) Grassmannian on Wikipedia. Basically, and to save you the trip through the link, consider the Haar measure $\theta$ on $O(n)$, fix ...

**2**

votes

**2**answers

445 views

### $ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$ if and only if $f$ is linear

I know the following is a well-known result.
Let $D = B(0,1) \subset \mathbb{C} $ a disc, $f$ holomorphic on $D$. Show that $$ 2|f^{'}(0)| \le \sup_{z, w \in D} |f(z)-f(w)|$$
Furthermore, there is ...

**14**

votes

**1**answer

910 views

### Some unpublished notes of Hofstadter

I'm looking for some unpublished notes called "Eta Lore," which are apparently related to a talk Douglas Hofstadter first gave at the Stanford Math Club in 1963. I know these notes exist because ...

**7**

votes

**2**answers

398 views

### Equivariant Stratifications of a Variety

Let $X$ be a complex variety acted upon algebraically by a complex torus $T$. Suppose that $\{X_{\beta}\}_{\beta\in S}$ is a finite $T$-equivariant stratification of $X$, so that the $X_{\beta}$ are ...

**7**

votes

**1**answer

353 views

### On the irrationality measure of $\sum_{n=1}^\infty a^{-b^n}$

Pick integers $a, b \ge 2$ and let $\xi_{a,b}$ be the sum of the series $\sum_{n=1}^\infty a^{-b^n}$. It is known that $\xi_{2,2}$ is transcendental: I learned a proof of this from notes by M. ...

**6**

votes

**0**answers

166 views

### “Fraïssé limits” without amalgamation

All structures are countable with countable signature.
Given a structure $\mathcal{A}$, the age of $\mathcal{A}$, $Age(\mathcal{A})$, is the set of structures isomorphic to finitely-generated ...

**20**

votes

**6**answers

2k views

### Covering a unit ball with balls half the radius

This is a direct (and obvious) generalization of the recent MO question, "Covering disks with smaller disks":
How many balls of radius $\frac{1}{2}$ are needed to cover completely a ball of radius ...

**10**

votes

**2**answers

526 views

### What are Moschovakis cardinals?

The question is exactly that of the title: what are Moschovakis cardinals?
Background. In a recent answer to the question, "Are there examples of statements that have been proven whose consistency ...

**6**

votes

**1**answer

237 views

### Reference for embeddings of reflection groups (related to folding ADE Coxeter graphs?

There are a couple of indirect methods, using Lie theory or Springer's general theory of regular elements in (real, complex) reflection groups, to construct natural embeddings among certain Weyl ...

**3**

votes

**3**answers

452 views

### Estimate for products of integers that are relatively prime with $N$

Let $N$ be a positive integer. Are there known estimates for the product of all numbers that are smaller than $N$ and relatively prime with $N$? One can assume that $N$ is free of squares, if this ...

**2**

votes

**0**answers

113 views

### Rewrite sum of radicals equation as polynomial equation

My question is about a method described in Dr.Math forum for simplifying equations involving sums of radical functions.
(The following is a transcription of the example given by Dr. Vogler):
--- ...

**2**

votes

**1**answer

215 views

### Tools for Removing Radicals from Equations

I am currently doing some investigations on Sylvester's 4 Point Problem Probability of 4 Points being in Convex Configuration
and repeatedly face the problem of solving equations between sums of ...

**2**

votes

**1**answer

149 views

### reference request: Riesz/Newton potential and HLS inequality in L1.logL1

Let's consider in dimension $d\geq 3$ the Newton/riesz potential $f=I_2[g]$
$$
f(x)=\int_{R^d}\frac{1}{|x-y|^{d-2}}g(y)dy,
$$
which solves $-\Delta f=g$ (up to positive normalizing constants, which I ...

**2**

votes

**1**answer

99 views

### Hilbert's Finiteness Theorem for connected semisimple Lie groups in Weyl's “Classical Groups”

First of all, sorry for using this account. Somehow I can't login to my previous one anymore and am thus using the account associated to my MSE one. Also, I already asked the question on MSE, but ...

**38**

votes

**13**answers

9k views

### A reading list for topological quantum field theory?

Can you suggest a reading list, or at least a few papers that you think would be useful, for a beginner in topological quantum field theory? I know what the curvature of a connection is, know basic ...

**63**

votes

**6**answers

8k views

### How to find ICM talks?

I am very interested in reading some and skimming through the list of invited talks at the International Congress of Mathematicians. Since the proceedings contain talks supposedly by top experts in ...

**18**

votes

**6**answers

4k views

### Why are local systems and representations of the fundamental group equivalent

My question: Let X be a sufficiently 'nice' topological space. Then there is an equivalence between representations of the fundamental group of X and local systems on X, i.e. sheaves on X locally ...

**29**

votes

**5**answers

3k views

### Which nonlinear PDEs are of interest to algebraic geometers and why?

Motivation
I have recently started thinking about the interrelations among algebraic geometry and nonlinear PDEs. It is well known that the methods and ideas of algebraic geometry have lead to a ...

**40**

votes

**10**answers

6k views

### The functional equation $f(f(x))=x+f(x)^2$

I'd like to gather information and references on the following functional equation for power series $$f(f(x))=x+f(x)^2,$$$$f(x)=\sum_{k=1}^\infty c_k x^k$$
(so $c_0=0$ is imposed).
First things that ...

**27**

votes

**6**answers

4k views

### Triangulating surfaces

I've had a few undergraduate students ask me for references for the classical fact (due to Rado) that closed topological surfaces can be triangulated. I know two sources for this, namely Ahlfors's ...

**29**

votes

**9**answers

3k views

### Dimensional Analysis in Mathematics

Is there a sensible and useful definition of units in mathematics? In other words, is there a theory of dimensional analysis for mathematics?
In physics, an extremely useful tool is the Buckingham Pi ...

**47**

votes

**3**answers

6k views

### Nelson's program to show inconsistency of ZF

At the end of the paper Division by three by Peter G. Doyle and John H. Conway, the authors say:
Not that we believe there really are any such things as infinite sets, or that the Zermelo-Fraenkel ...