MathOverflow

My question is :Can you please let me know some books in English or in French how research in mathematics is done? ( more specifically: about the culture and environment of mathematics graduate departments, about the process of research and discovery...

Let $X$ be a topological space, and consider its Moore path category $MX$, which is an object in the category $\mathsf{CAT}$ of small categories. This question asks whether the classifying space of the path category of a space is homotopy equivalent...

I did not find this question on this site when I had a look, but it may have been asked before by someone else.
Let for simplicity $K$ be a fixed algebraically closed field and let $X$ be an algebraic variety of finite type over $K$ of dimension $d$ (this means $X$ is an integral scheme of finite type over $K$). Let $E$ be a rank $r$ geometric vector bundle on...

Many attempts to understand Collatz sequences focus on finding patterns. My view is that perhaps no meaningful global pattern exists, and that proving convergence may instead require showing that, along typical trajectories, decreasing steps occur more...