# Linked Questions

42answers
74k views

### Most interesting mathematics mistake?

Some mistakes in mathematics made by extremely smart and famous people can eventually lead to interesting developments and theorems, e.g. Poincaré's 3d sphere characterization or the search to prove ...
32answers
16k views

### Interesting examples of vacuous / void entities

I included this footnote in a paper in which I mentioned that the number of partitions of the empty set is 1 (every member of any partition is a non-empty set, and of course every member of the empty ...
25answers
28k 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 2021-04-01 Anything new in 2021?
12answers
51k 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 ...
41answers
8k views

### What are some mathematical sculptures?

Either intentionally or unintentionally. Include location and sculptor, if known.
4answers
26k 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 ...
3answers
25k views

### Slick proof?: A vector space has the same dimension as its dual if and only if it is finite dimensional

A very important theorem in linear algebra that is rarely taught is: A vector space has the same dimension as its dual if and only if it is finite dimensional. I have seen a total of one proof of ...
7answers
5k views

### In “splendid isolation”

While browsing the Net for some articles related to the history of the Whittaker-Shannon sampling theorem, so important to our digital world today, I came across this passage by H. D. Luke in The ...
3answers
8k 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 ...
4answers
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 ...
6answers
10k views

### What does Mellin inversion “really mean”?

Given a function $f: \mathbb{R}^+ \rightarrow \mathbb{C}$ satisfying suitable conditions (exponential decay at infinity, continuous, and bounded variation) is good enough, its Mellin transform is ...
4answers
16k 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 ...
6answers
8k views

### Limits in category theory and analysis

Is it possible to regard limits in analysis (say, of real sequences or more generally nets in topological spaces) as limits in category theory? Is there some formal connection? Edit ('13): Perhaps it ...
5answers
8k views

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 $\dim(A_1+A_2) = \dim(A_1) + \dim(A_2) - ... 3answers 6k views ### What is the current status of the Kaplansky zero-divisor conjecture for group rings? Let$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 ...

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