Miscellaneous Mathematics

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

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

Reports on Impact of Mathematics

A week ago the EMS posted links to reports on the impact of mathematical research on society and economy. You can access these reports here: link. Though probably for many too long to read in detail, reading just the introductions is already interesting.

Ten Years of Polymath

Ten years ago the first Polymath project was launched (link to the original proposal of Timothy Gowers). Polymath can be described as massively collaborative mathematics, i.e., a large groups of mathematicians works on a predefined problem and each member posts his or her (partial) ideas, so that the collective makes progress from each small step … Continue reading

Mathematik in der Blütezeit des Islam

Die Wikipedia veranstaltet jährlich einen Schreibwettbewerb (link). Es gibt jeweils einen Jurypreis und einen Publikumspreis, und dieses Jahr ging der Publikumspreis an einen mathematischen Artikel: Mathematik in der Blütezeit des Islam. Ein paar mehr Infos gibt es auch in diesem ScienceBlog: link.