### Quasi-local operators

In the first post of this series we asked at the end two questions – in this post we start working towards the answers in the general setup of the third post of this series. Our setup from the third post is the following: We have a metric space $$(X,d)$$ and we consider a bounded, … Continue reading "Quasi-local operators"

### The unplanned impact of mathematics

In 2011 Nature published a short article about The unplanned impact of mathematics which I stumbled upon just now. Since it is just 4 pages long, I can recommend reading it just for fun – or for one’s ease of mind. 😉

### Computer assistance and pure mathematics

Today I want to tell you a story of a preprint in pure mathematics that came into existence only by crucial help of precise computer computations. To explain the results, let us first define for a set $$A \subset \mathbb{N}_{>1}$$ of natural numbers $f(A) := \sum_{n \in A} \frac{1}{n \log(n)}\,.$ For $$k \ge 1$$ let … Continue reading "Computer assistance and pure mathematics"

### Validity of results

Can you vouch for the validity of the results in papers that you cite and use in your own articles? In April this year Blagojević, Cohen, Crabb, Lück and Ziegler posted a preprint on the arXiv (arXiv:2004.12350) writing in the abstract “This invalidates a paper by three of the present authors […] who used a … Continue reading "Validity of results"