The **MEGA Grant** for 2023/4 has been awarded to **Number City**.

Every whole number can be written uniquely as a product of its prime factors - 4 is 2 × 2, 12 is 2 × 2 × 3 and 1790 is 2 × 5 × 179. Splitting numbers and writing them in this way is useful for mathematicians to understand the properties of a number - for example, any number which has a factor of 2 is an even number, and numbers which only have factors of 2 are powers of two. The Number City project will make these prime factorisations visible, by building a tower of blocks for each prime.

Imagine the City as a grid of rows and columns, with a column for each number, and a row for each potential prime factor. For a number *p* that is itself prime, the corresponding column of Number City will contain only one block, in the *p*^{th} row. But for numbers with more complicated factorisations, each factor will be represented by a separate cube: 12 will have a stack of 2 boxes in row 2, and one box in row 3. The number 120 will need 5 boxes - 3 in row 2, one in row 3 and one in row 5.

We plan to represent all numbers up to 128, and will use 50cm cube-shaped cardboard boxes for each prime factor, arranged in a large outdoor space. Participants will be invited to create and personalise a box for a particular factor, then place it in the city to form part of the installation. The patterns visible in the arrangement of boxes will reflect the patterns present in numbers and their relationships with their prime factors, and looking at the city from different directions will allow participants and visitors to visualise mathematical ideas. Activity resources for schools and families will be available, and you can use this Geogebra applet to explore a 3D model of the City.

The original idea for Number City was conceived by Paul Stephenson, who will be around on the day to talk to participants.

**Matt Parker says:**

*“We liked Paul Stephenson's Number City because it had the potential to work on a large scale in a way that would emphasise the maths, and wasn't just for the sake of being big. Being able to walk around the towers of factors will help to show the structure in them.*

*Even with no additional guidance, Number City will make people think mathematical thoughts. Even if someone knew it was a number line, walking through (or helping build) Number City will organically make them wonder and ask the same sorts of questions about the positions of the towers that mathematicians ask about numbers.”*

Number City will take place at the Orkney International Science Festival on **Saturday 7 ^{th} September 2024**, and the project will be managed by Hana Ayoob. To find out more about the project, visit the Number City website.

The **MEGA Grant** is a bursary scheme for mathematical public engagement activities, with funding organised by Stand-up Mathematician Matt Parker and coordinated by TMiP (Talking Maths in Public), the UK’s network for maths communicators. The grant will be awarded roughly every two years to a mathematician or maths communicator, to fund a maths activity taking place in the UK.

Matt has been involved in a variety of large-scale public engagement activities in the past, and would like to offer others the chance to bring in their own ideas and perspectives.

The concept is based on three revolutionary principles, summarised as RPM (Ridiculous Public Maths):

**Ridiculous**: the activity needs to be somehow spectacular, impressive or otherwise unusual. It should not be a maths activity that already takes place elsewhere, or that people could see or interact with normally; it should ideally take place on a large scale, take ideas to their extremes or be traditionally unfundable.**Public**: the activity must include some aspect of hands-on public involvement - ideally, members of the public can contribute something towards a larger whole, or produce something themselves to take away. At minimum, even if the activity itself is being undertaken by a project team, there should be other things alongside which people can interact with accompanying the project. Activities should be accessible and inclusive, and have a clear audience.**Maths**: the activity should aim to communicate or illuminate some piece of mathematics; maths should be the drive behind the activity, and not an auxiliary aspect. The mathematical content should be clearly explained and communicated to visitors so they can go away understanding or appreciating mathematics more (or differently) than they did before.

The activities will normally run as part of a science festival or other large-scale event, and be aimed at a science festival audience - consisting of adults, children and family groups, usually with a pre-engaged disposition to maths and science. Activities may be targeted at specific sub-audiences or age ranges within this - for example, some activities may be more suitable for older children as they require a higher level of mathematical understanding or development - although activities which incorporate ways for a variety of audiences to engage are encouraged. Applicants can, if needed, be connected with a maths/science festival or event by Matt or the MEGA admin, depending on preference, timing and suitability of the activity.

The grant application process will be administered by TMiP, and an application form will be added below when applications open for MEGA 2025.

Applications for the grant will be via an online form, and a panel including Matt, members of the TMiP committee and other maths communication experts will decide on which projects receive funding. Members of the TMiP committee who anticipate they may be involved in one or more of the applicants’ projects may be recused from the panel. TMiP committee members are not themselves allowed to be the lead applicant on any grant.

Discussions of the applications will be initially conducted anonymously, followed by a later round of discussion of deanonymised applications, with the goal of balancing the diversity of applications and ensuring applications from early-career communicators are given sufficient consideration. The winner will be announced at the Talking Maths in Public conference, which takes place every two years at the end of August - although the winner may be notified sooner.

The grant will cover costs of between £2,000 - £10,000 depending on the requirements of the activity. This funding should be used to cover material and equipment costs for the activity and any expenses, as well as a fee for the time of the applicant organising the activity to cover their work on delivery and preparation. The project should aim to strike a balance between producing a high-quality event without cutting corners, and keeping costs reasonable - ‘ridiculous’ should apply to the activity, not the budget. Funding will be coordinated via TMiP, with money being provided upfront where needed to cover costs, and receipts needed to claim any expenses.

The application may be a complete well-formed idea, or something more preliminary, and the awardee will have the chance to meet with Matt and other experienced providers of large-scale maths activities for advice and to help plan the final activity. They will receive advice on sourcing materials and equipment, activity design, and contacts for outsourcing graphic/web design work or fabrication. Matt’s network of mathematical activity volunteers may be deployed in support of the activity, or the awardee can organise their own team of volunteers.

Details of Matt’s previous large-scale ridiculous public maths projects (see above) will be available for applicants to get a sense of what’s possible - including information about budgets, organisation and production. These events should not be taken as a blueprint for what type of activity to do - these kinds of activities have proven to be successful in the past, but ideas with a completely different approach will also be considered and are encouraged.

Matt reserves the right to come along and join in with the activity if availability permits, and may also make a video for the Stand-up Maths YouTube channel if appropriate.

Funding for the grant may also involve sponsorship from external bodies or organisations, and all supporting organisations (Stand-up Maths Limited, Talking Maths in Public and any others) will need to be given credit in promotion for the event - this will likely involve including their logos on printed materials and web content as appropriate.

Applications can bend or ignore any of the MEGA Grant rules and requirements as long as they explain why.