Top new questions this week:

Is there a generally available (commercial or not) complete implementation of the Risch algorithm for determining whether an elementary function has an elementary antiderivative?
The Wikipedia article ...

Suppose we have a function $f(x_1 ,x_2 ,x_3 ,x_4).$ We know that we can factor it in two ways as $f(x_1 ,x_2 ,x_3 ,x_4)=\phi_1 (x_1 ,x_2 )\phi_2(x_3 ,x_4 )=\psi_1 (x_1,x_3)\psi_2(x_2,x_4)$
Show that ...

The question in brackets in the title is my main mathematical question, but does not reflect my initial motivation for writing this post. It is in fact above all for personal reasons that I'm ...

Essentially, my question is how strong a restriction it is to be simply connected.
Here is a way of making this precise: Let's say we want to count simplicial complexes (of dimension 2, though that ...

Given a compact smooth manifold $M$ denote by $b_i(M)$ the $i$th Betti number and denote by $q_i(M)$ the minimal number of generators for $H_i(M)$. Let $f$ be a Morse function on $M$. The Morse ...

The Alexander horned sphere is a closed embedding of $S^2$ into $S^3$ which is not flat because otherwise the Schoenflies Theorem would be true for it. However, not being flat is not the same as not ...

Is there a framed bordism model for the units of the sphere spectrum, $gl_1(S)$?
At the level of individual homotopy groups, the PontrjaginThom construction identifies the group of bordism classes of ...

Greatest hits from previous weeks:

I am very interested in proofs that become shorter and simpler by going to higher dimension in $\mathbb R^n$, or higher cardinality. By "higher" I mean that the proof is using higher dimension or ...

The history of proving numbers irrational is full of interesting stories, from the ancient proofs for $\sqrt{2}$, to Lambert's irrationality proof for $\pi$, to Roger ApĂ©ry's surprise demonstration ...

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, ...

Can you give examples of proofs without words? In particular, can you give examples of proofs without words for nontrivial results?
(One could ask if this is of interest to mathematicians, and I ...

While doing laundry at my local laundromat, I saw a coin pusher game. Below is a picture, and here is a video depicting how it works (disregard noncoins).
Essentially, one has a distribution of ...

It would seem that John Nash and his wife Alicia died tragically in a car accident on May 23, 2015 (reference). My condolences to his family and friends.
Maybe this is an appropriate time to ask a ...

Some mistakes in mathematics made by extremely smart and famous people can eventually lead to interesting developments and theorems, e.g. PoincarĂ©'s 3d sphere characterization or the search to prove ...

Can you answer these questions?

Upon looking at the graphs of various Fourier sine and cosine transforms (ones without Dirac deltas in their domain) I've noticed a pattern that is probably already known, but that I thought would be ...

Let $C$ be smooth projective curve, $\mathcal{M}$ be the moduli space of semistable Higgs bundles, $H:\mathcal{M}\rightarrow W= \bigoplus H^0(C,K_{C}^{\otimes i})$ be the Hitchin map, and $\pi :C_s\...

Given $q>1$, consider the critical Sobolev space $W^{n/q,q}(\mathbb{R}^n)$, which fails to embed in $L^{\infty}(\mathbb{R}^n)$. I'm wondering if we can recover some critical estimate by considering ...
