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Carnival of Mathematics 151

The next issue of the Carnival of Mathematics, rounding up blog posts from the month of October, and compiled by Frederick, is now online at White Group Mathematics.

The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

HLF Blogs: Is mathematics idealistic or realistic?

In September, Katie and Paul spent a week blogging from the Heidelberg Laureate Forum – a week-long maths conference where current young researchers in maths and computer science can meet and hear talks by top-level prize-winning researchers. For more information about the HLF, visit the Heidelberg Laureate Forum website.

Stephen Smale

5th Heidelberg Laureate Forum 2017, Heidelberg, Germany, Picture/Credit: Christian Flemming/HLF

The closing talk of the HLF’s main lecture programme (before the young researchers and laureates head off to participate in scientific interaction with SAP representatives to discuss maths and computer science in industry) was given by Fields Medalist Steve Smale.

“Pariah Moonshine” Part I: The Happy Family and the Pariah Groups

Being a mathematician, I often get asked if I’m good at calculating tips. I’m not. In fact, mathematicians study lots of other things besides numbers. As most people know, if they stop to think about it, one of the other things mathematicians study is shapes. Some of us are especially interested in the symmetries of those shapes, and a few of us are interested in both numbers and symmetries.

Footballs on road signs: an international overview

I’m an old fashioned manager, I write the team down on the back of a fag packet and I play a simple 4-4-2.

  • Mike Bassett, England Manager

I’m very much like Mike Bassett: I like standing on the terraces, I like full-backs whose main skill is kicking wingers into the ad hoardings, and – most of all – I like geometrically correct footballs.

Stirling’s numbers in a nutshell

This is a guest post by researcher Audace Dossou-Olory of Stellenbosch University, South Africa.

In assignment problems, one wants to find an optimal and efficient way to assign objects of a given set to objects of another given set. An assignment can be regarded as a bijective map $\pi$ between two finite sets $E$ and $F$ of $n\geq 1$ elements. By identifying the sets $E$ and $F$ with $\{1,2,\ldots, n\}$, we can represent an assignment by a permutation.

A new aspect of mathematics

This is a guest post written by David Nkansah, a mathematics student at the University of Glasgow.

Around the fourth century BC, the term ‘Mathematics’ was defined by Aristotle as the “science of quantity”. It’s my own experience as a young mathematician to say this definition, although correct in its own right, poses a problem for those who do not truly know what mathematics is. It fails to highlight the true creativity of the subject.

Human inspiration and imagination are essential ingredients in mathematics. Regarding creativity, one could say, with merit, that in a sense mathematics is an art. Before proceeding to outline similarities between sketching mathematical proofs and painting on a canvas, it is important to know what fundamental premises mathematical proofs are built on.