# Holo-Math sounds pretty wild

Any project which manages to make Cédric Villani look even more like a time traveller gets my immediate attention. Look!

HOLO-MATH’s website is short on firm details, but it seems to be something to do with using Microsoft’s HoloLens VR goggle thingies to make interactive VR maths “experiences”. Here’s the blurb:

HOLO-MATH is an international project to produce immersive live experiences in mathematical sciences using the latest mixed reality technology.

It’s the first project to use state of the art technology for scientific knowledge transfer in a museum environment and on a large scale.

The experiences are presented in science museums/centers and at special events. They are targeted at groups of 20 participants led by human guides and virtual avatars. New forms of augmented visualization and interaction are core features. The audio-visual experience is of the highest quality.

In different HOLO-MATH experiences, participants will be able to play, discover, experiment and learn about science history and current research.

There’s more information on holo-math.org, and some pictures of be-goggled guests at the project’s launch on the hashtag #holomath.

# Mathematical modelling of Facebook use (video)

Watch mathematician and data scientist Jonny explain mathematical modelling of networks.

# Circular reasoning on Catalan numbers

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

Consider the following question: How many ways are there to connect $2n$ points on a circle so that each point is connected to exactly one other point?

# Save the Further Maths Support Programme

The Further Maths Support Programme is an organisation in the UK that supports students wishing to take an A-level in Further Maths. Since this isn’t offered in all schools and colleges, the Programme helps organise tuition for people who can’t do it through their school, but also encourages students at younger ages to consider taking the A-level through workshops and university visit days. They also run excellent training courses for teachers, and have a number of resources on their website for students and teachers, including problem solving materials, videos, podcasts and maths competitions.

According to a recent blog post by maths teacher Jo Morgan, a government review has made the FMSP’s future precarious. Their funding through the Department for Education will be removed next April, and they’ll be replaced by the “Level 3 Maths Support Programme”. The L3MSP will support Core Maths as well as A level mathematics and further mathematics, but will focus on only certain geographical areas, meaning many will lose access to the resources currently provided.

Two of the programmes previously supported by the same funding have already had their funding stopped – the Core Maths Support Programme, and Underground Maths – but the FMSP hasn’t finished yet, and Jo hopes that by contacting the DfE we could convince the government to continue funding it. As they point out in the blog post, the FMSP has made a huge difference to the numbers of students taking maths and has had a direct impact in classrooms supporting teachers all over the UK.

So what do we do? Start a petition? Tweet the DfE to tell them? Over to you, readers.

Save the FMSP! on Resourceaholic

# Measuring π with a pendulum

Friends of the Aperiodical, nerd-comedy troupe Festival of the Spoken Nerd, are currently on tour around the UK. As part of their show, questionably titled You Can’t Polish a Nerd, Matt Parker attempts to calculate the value of $\pi$ using only a length of string and some meat encased in pastry. He’s previously done this on YouTube, and the idea was inspired by the Aperiodical’s 2015 Pi Approximation Challenge, and in particular my own attempt to approximate $\pi$ with a (more conventional) pendulum.

# HLF Blogs: Efim Zelmanov’s Desert Island Maths

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.

At the start of his HLF lecture on Asymptotic Group Theory on Thursday morning, Fields medalist Efim Zelmanov described the ‘group’ as: “the great unifying concept in mathematics,” remarking “if you go for a trip, and you are allowed to take only two or three mathematical concepts with you, give serious consideration to this one.” Very loosely defined, a group is a set of things (its ‘elements’) that you can ‘multiply’ together, with this multiplication behaving in certain helpful ways. Think of numbers being added, functions composed together or rotations and reflections of a shape being carried out one after the other. I doubt any mathematician would accuse Zelmanov of overstating their importance in mathematics.

In his talk he discussed residually finite groups. These are groups which are infinite in size but still just a little bit finite-y. In technical terms, the group has a set of homomorphisms with finite kernels having trivial intersection. Although the group is too large to see all at once, as Zelmanov put it, we have “photos from all sides of the group”. He contrasted this to “hopelessly infinite groups”, for which no such photo album is possible.

A common way to look at a group is to find a set of ‘generators’: these are elements of the group which you can multiply together to create any element of a group (the elements ‘generate’ the entire group). Some infinite groups can’t be generated from a finite set — consider trying to find a set of rational numbers that you can multiply together to create any rational number. Those that can be generated from a finite set are unexcitingly called ‘finitely generated’. Of course, finite groups are also finitely generated.

Zelmanov considered under what circumstances finitely generated groups can be proved to be finite. One immediate way this won’t happen is if one of the generators is not periodic: if you keep multiplying it by itself you keep getting new elements forever, never ‘looping back’ to the original generator. (Imagine starting with 1 and continually adding 1…) The Burnside problem asks whether there are any other ways to make a finitely-generated, yet infinite, group. In 1991, Zelmanov proved that for residually finite groups, there aren’t. However, this isn’t the case for the ‘hopelessly infinite’ groups.

In his lecture Zelmanov, accompanied by his excellent hand-drawn slides, discussed this before moving on to related topics such as the growth of groups (if you start with a generating set, and create new elements by multiplying them together, how quickly does the set grow?) and ‘approximate groups’ (which, as the name suggests, are things that are like, but not quite, groups).

# Stupid-looking maths question does the rounds, isn’t stupid

You may by now have seen the image below knocking around on Twitter and other social medias, in which a maths question appears to be almost a parody of itself: