Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville: “The big experts in the field had already tried to make this approach w …

A couple hours, I'd posted a Diophantine equation question, but realized that I'd committed a rather preposterous blunder deriving it. This is the actual question which I'm trying …

This question is inspired by Joseph O'Rourke's beautiful answer to my previous question. Let $\mathbb{S}^{d\times n}$ denote the set of real $d\times n$ matrices whose columns hav …

For a research problem that I'm working on, I need to solve this Diophantine equation:- $a^3+b^3+c^3-3d=-83449$, where $a,b,c,d>0$ are all DISTINCT positive integers and$ a,b,c∉ $ …

M is an n-dimensional closed orientable manifold. I find in a book "Intuitively,the fundamental class can be thought of as the sum of the (top-dimension) simplices of a suitable tr …

It happens a lot of times that when one defines a new object (ring, module, space, group, algebra, morphism, whatever) out of given data one first chooses some additional structure …

Assume that $f$ is (Euclidean) $L-$biLipchitz mapping of the unit circle onto a triangle $\Delta(A,B,C)$. Can we find a $10000 L$ bi-lipchitz extension of $f$ onto the whole plane. …

Lagrange proved that every (positive) rational integer is a sum of 4 squares. Are there general results like this for ring of integers of a number field? Is this class field theo …

Let $\scr A$ be an abelian category with exact products and a cogenerator (e.g. $\scr A$ is a category of modules). Let ${\mathbf K}(\scr A)$ be the homotopy category of cochain c …

I have the following, probably very elementary question: Let $Cl^{p,q}$ be the Clifford algebra on generators $e_i$, $i=1, \ldots, p+q$ with $e_i e_j = -e_j e_i$ and $e_{i}^{2}=-1$ …

This is a question I asked at Math.SE but got no answers: http://math.stackexchange.com/q/396217/7110/ The tautological vector bundle $\gamma_k(\mathbb{K}^N)$ over the Grassmann m …

Suppose we are given a commutative ring R with unit-element. Now we have a composition of R as the direct product of two rings $R\cong R_1\times R_2$. It is now straight forward, …

Inspired by this question, I would like to determine the probability that a random knot of 6 unit sticks is a trefoil. This naturally leads to the following question: Is there a …

Given $N$ and $a$ positive integers, with $a\ge 2$ is it possible to prove the inequality: $$\sum_{k=1}^N\frac{k^a}{(k+1)^a+(k+2)^a}\le\frac{N}{2}$$

Let $K$ be a local field with mix char, $k$ residue field. We have an exact sequence $0 \longrightarrow I \longrightarrow G_{K} \longrightarrow G_{k} \longrightarrow 0$ Then we o …