Top new questions this week:
|
|
In Stallings's paper
Stallings, John, Groups with infinite products, Bull. Amer. Math. Soc. 68 (1962), 388–389.
he briefly discusses how to prove "several generalizations" of Brown's ...
|
|
Define the Erdős polynomial to be $f_n(x):= \sum \limits_{0 \leq i,j \leq n}^{}{x^{ij}}$ (the name is motivated by http://oeis.org/A027424).
For example for $n=5$, the polynomial is given by $x^{25}+...
|
|
I am a beginner, so this question may be naive.
Suppose we have a (sufficiently strong) consistent first order logic system. Gödel's first incompleteness theorem says there exists a Gödel sentence $g$ ...
|
|
One can show (see below for a sketch of a proof) that every odd prime number $p$
can be written in exactly $(p+1)/2$ different ways as
$$p=a\cdot b+c\cdot d$$
with $a,b,c,d\in\mathbb N$ satisfying $\...
|
|
Belyi's theorem establishes a correspondence between smooth projective curves defined over number fields and the so called dessins d'enfants which are bipartite graphs embedded on an oriented surface ...
|
|
I have a very naïve question: can one find anywhere a combinatorial description of the Mandelbrot set?
Let me try to be a bit more precise: is it possible to encode each of its "bulbs" by ...
|
|
In a comment at the recent question What is the standard 2-generating set of the symmetric group good for?, it was remarked that the symmetric groups $S_n$ for $n\gt 2$, $n\neq 5,6,8$, can be ...
|
Greatest hits from previous weeks:
|
|
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 ...
|
|
The purpose of this question is to collect the most outrageous (or ridiculous) conjectures in mathematics.
An outrageous conjecture is qualified ONLY if:
1) It is most likely false
(Being hopeless is ...
|
|
This talk is about a theory of "perfectoid spaces", which "compares objects in characteristic p with objects in characteristic 0". What are those spaces, where can one read about them?
Edit: A bit ...
|
|
This seems to be a favorite question everywhere, including Princeton quals. How many ways are there?
Please give a new way in each answer, and if possible give reference. I start by giving two:
...
|
|
I suppose this question can be interpreted in two ways. It is often the case that two or more equivalent (but not necessarily semantically equivalent) definitions of the same idea/object are used in ...
|
|
I would like to ask if anyone could share any specific experiences of
discovering nonequivalent definitions in their field of mathematical research.
By that I mean discovering that in different ...
|
|
Christmas is just around the corner and I haven't bought all the gifts for my family yet ( yeah, 😢)
My Dad has a PhD in Mathematics, he works in Graph theory and his thesis was about Quasiperiodic ...
|
Can you answer these questions?
|
|
Consider a two-state Markov process in continuous time, with states labelled $A$ and $B$. The transition rates for going from state $A$ to $B$, and state $B$ to $A$ are $\alpha$ and $\beta$ ...
|
|
It is well known that the category $\mathbf{HI}_{\rm Nis}^{\rm tr}(k)$ of $\mathbb{A}^1$-local Nisnevich sheaves with transfers is closed under subobjects and quotients, from the highly nontrivial ...
|
|
I have a program $P$ taking an integer as input and outputting a Boolean value. It runs in polynomial time in the length of the input.
There necessarily exists a Diophantine equation that has a ...
|
