Suppose someone came up with an algorithm that could take any snark and perform edge contraction to result in the Peterson graph. If an inspection of the algorithm reveals that it works as claimed, would the algorithm be sufficient to prove the 4CT?

I've been trying to prove (maybe even disprove) the following inequality: $$ \sum_{n=1}^{N} \frac{a_n}{\sqrt{\sum_{i=1}^{n}a_i}} \leq C \sqrt{\sum_{n=1}^{N}a_n} $$ Where $ a_1,...,a_N\geq 0 $ are some positive numbers, and $C$ is an absolute constant. Help will be much appreciated.

I would like to ask about (old* and new) reliable mathematical literature relevant to various mathematical aspects of the recent coronavirus outbreak: In particular, standard statistical/mathematical models that are used to predict the spread, mathematical studies of effectiveness of various stra...

Let $(E,\mathcal E,\lambda)$ be a $\sigma$-finite measure space; $N\in\mathbb N$; $p_i$ be a probability density on $(E,\mathcal E,\lambda)$ for $i\in\{1,\ldots,N\}$; $w_i:E\to\mathbb R$ be $\mathcal E$-measurable for $i\in\{1,\ldots,N\}$ with $$\sum_{i=1}^Nw_i=1;\tag1$$ $n_1,\ldots,n_N\in\math...

Let $(E,\mathcal E,\lambda)$ be a $\sigma$-finite measure space and $$\lambda f:=\int f\:{\rm d}\lambda$$ for $\lambda$-integrable $f:E\to\mathbb R$; $p:E\to[0,\infty)$ be $\mathcal E$-measurable with $c:=\lambda p\in(0,\infty)$ and $$\mu:=\frac{p\lambda}c;$$ $I$ be a finite nonempty set and $$...

The background of this question is the talk given by Kevin Buzzard. The slides of the talk are available here. One of the points in the talk is that, people accept some results but whose proofs are not publicly available. (He says this leads to wrong conclusions, but, I am not interested in wro...

Let $$C^{\ast}:\mathbf{sSet}\rightarrow E_{\infty}\text-\mathbf{dgAlg}$$ be the cochain contravariant functor from the category of simplicial sets to the category of $E_{\infty}$-dg-algebras (over $\mathbb{Z}$). Theorem (Mandell): Suppose that $X$ is of finite type and $Y$ is nilpotent space ...