# Linked Questions

39 questions linked to/from Examples of common false beliefs in mathematics

**95**

votes

**24**answers

26k views

### Examples of math hoaxes/interesting jokes published on April Fool's day?

What are examples of math hoaxes/interesting jokes published on April Fool's day?
For a start P=NP.
Added 2020-04-01 Anything new in 2020?

**168**

votes

**13**answers

48k views

### Why doesn't mathematics collapse even though humans quite often make mistakes in their proofs?

To begin with, I am aware of these questions, which seems to be related:
How do I fix someone's published error?, Examples of common false beliefs in mathematics, When have we lost a body of ...

**92**

votes

**4**answers

24k views

### Is the analysis as taught in universities in fact the analysis of definable numbers?

Ten years ago, when I studied in university, I had no idea about definable numbers, but I came to this concept myself. My thoughts were as follows:
All numbers are divided into two classes: those ...

**64**

votes

**3**answers

7k views

### Cohomology and fundamental classes

Let X be a real orientable compact differentiable manifold. Is the (co)homology of X generated by the fundamental classes of oriented subvarieties? And if not, what is known about the subgroup ...

**66**

votes

**4**answers

5k views

### When is a singular point of a variety ($\mathcal{C}^\infty$-) smooth?

If $X$ is a nonsingular algebraic (or analytic) variety over $\mathbb C$ or $\mathbb R$ then it is certainly $C^\infty$ over the reals.
The converse is false for a silly reason : in the real or ...

**38**

votes

**4**answers

14k views

### When is $L^2(X)$ separable?

I have never studied any measure theory, so apologise in advance, if my question is easy:
Let $X$ be a measure space. How can I decide whether $L^2(X)$ is separable?
In reality, I am interested in ...

**25**

votes

**5**answers

7k views

### Is there a version of inclusion/exclusion for vector spaces?

I am asking for a way to compute the rank of the 'join' of a bunch of subspaces whose pairwise intersections might be non-zero. So in the case n=2 this is just $\dim(A_1+A_2) = \dim(A_1) + \dim(A_2) - ...

**13**

votes

**5**answers

7k views

### Projection of Borel set from $R^2$ to $R^1$

Hello
This should be easy to prove but i have no idea how to do it:
If $X \subseteq \mathbb{R}^2$ is borel then $f(X)$ is borel where $f(x,y) = x$
Thanks
Tobias

**33**

votes

**3**answers

3k views

### Arithmetic geometry examples

(This is inspired by Algebraic geometry examples.)
I want to collect here (counter)examples in arithmetic geometry.
Curves violating the Hasse principle: The Selmer curve $3X^3 + 4Y^3 + 5Z^3 = 0$. ...

**56**

votes

**2**answers

5k views

### What is the current status of the Kaplansky zero-divisor conjecture for group rings?

Let $K$ be a field and $G$ a group. The so called zero-divisor conjecture for group rings asserts that the group ring $K[G]$ is a domain if and only if $G$ is a torsion-free group.
A couple of good ...

**39**

votes

**4**answers

4k views

### Cocomplete but not complete abelian category

This is a duplicate of the following question to which I did not receive any answer: https://math.stackexchange.com/questions/238247/complete-but-not-cocomplete-category
Let $\mathfrak C$ be an ...

**12**

votes

**2**answers

2k views

### When is sin(r \pi) expressible in radicals for r rational?

Perhaps this question will not be considered appropriate for MO - so be it. But hear me out before you dismiss it as completely elementary.
As the question suggests, I would like to know when $\sin(...

**23**

votes

**3**answers

790 views

### Does every convex polyhedron have a combinatorially isomorphic counterpart whose faces all have rational areas?

Does every convex polyhedron have a combinatorially isomorphic counterpart whose faces all have rational areas?
Does every convex polyhedron have a combinatorially isomorphic counterpart whose edges ...

**17**

votes

**2**answers

6k views

### Geometric vs Arithmetic Frobenius

If an algebraic variety $X$ over a field characteristic p is given by equations $f_i(x_1,...,x_k) = 0$, we can consider the variety $X^{(p)}$ obtained by applying p-th powers to all the coefficients ...

**25**

votes

**3**answers

5k views

### Is “compact implies sequentially compact” consistent with ZF?

Over at the nForum, we've been discussing sequential compactness. The discussion led me to realise that I naively assumed that nets were simply Big Sequences, and that I could make a reasonable guess ...