Top new questions this week:

This question is inspired by On moments of inertia of planar and 3D convex bodies.
Let $f:{\mathbb R}^3\setminus\{0\}\to{\mathbb R}$ be an even homogeneous ($f(kx)=f(x)$ for all real $k\neq 0$) ...

Typical courses on real integration spend a lot of time defining the Lebesgue measure and then spend another lot of time defining the integral with respect to a measure. This is sometimes criticized ...

The BanachMazur game on a poset $\mathbb P$ is the $\omega$length game where the players alternate choosing a descending sequence $a_0 \geq b_0 \geq a_1 \geq b_1 \geq \dots$. Player II wins when ...

Lately I have become interested in solid $F$modules where $F$ is some discrete field. Ideally, one would want a category that is as nicely behaved as solid abelian groups or solid $\mathbb{F_p}$...

Consider the game of infinite Hex, where two players Red and Blue alternately place their stones on the infinite hex grid, each aiming to create a winning configuration.
Red wins after infinite play, ...

Let $X$ be a smooth proper algebraic curve over $\mathbb{C}$. Say a complex local system $\mathbb{V}$ on $X$ is motivic if there exists a dense Zariskiopen subset $U\subset X$, and a smooth proper ...

In 2002, the discovery of the AKS algorithm proved that it is possible to determine whether an integer is prime in polynomial time deterministically. However, it is still not known whether there is an ...

Greatest hits from previous weeks:

There is a standard problem in elementary probability that goes as follows. Consider a stick of length 1. Pick two points uniformly at random on the stick, and break the stick at those points. What ...

In his talk, The Future of Mathematics, Dr. Kevin Buzzard states that Lean is the only existing proof assistant suitable for formalizing all of math. In the Q&A part of the talk (at 1:00:00) he ...

A. Is there natural numbers $a,b,c$ such that $\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b}$ is equal to an odd natural number ?
(I do not know any such numbers).
B. Suppose that $\frac{a}{b+c} + \...

In Michael Atiyah's paper purportedly proving the Riemann hypothesis, he relies heavily on the properties of a certain function $T(s)$, known as the Todd function. My question is, what is the ...

One of the most salient aspects of the discipline of number theory is that from a very small number of definitions, entities and axioms one is led to an extraordinary wealth and diversity of theorems, ...

I'd like to ask if people can point me towards good books or notes to learn some basic differential geometry. I work in representation theory mostly and have found that sometimes my background is ...

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 ...

Can you answer these questions?

Suppose $\Omega \subset R^N$ is a smooth bounded domain. Is there an explicit solution to the reaction diffusion equations (RDE) in the following special form?
\begin{equation}
\left\{\...

Let $E := \mathbb R^d$. Let $f:E \to \mathbb R_{>0}$ be continuous and integrable. For $r>0$, we define
$$
f_r (x) := \frac{f(x)}{ \frac{1}{B(x, r)} \int_{B(x, r)} f(y) \, \mathrm{d} y} \quad \...

Let $I =([0,1),\mathcal{B},\lambda)$ stand for the unit interval with a Lebesgue measure constrained on it. This is just a uniform probability distribution, an infinite power $I^{\infty}$ is a well ...
