There are many reasons why you might want to write for an audience that doesn't consist only of experts in your field.

Perhaps it's for a job or grant application that will be read by a panel of people with different areas of expertise. Or maybe it's a paper for a mathematical or scientific journal that covers a broad range of fields, not just yours. Or maybe you'd like to write a newspaper article, or even a book, aimed at an audience where little mathematical background can be assumed. This might be to inform about important research — for example to do with climate change or public health — or simply because you'd like to share the joy and beauty of your subject.

Whatever the reason and motivation, it always pays to write well. Even if you are just writing for your own peers, a clear and engaging style goes a long way to getting your message across and enthusing people for your work.

As Editors of plus.maths.org we have spent many years writing about the mathematical sciences for non-expert audiences, and training researchers to communicate their work. The most important lesson we have learnt is that writing is a skill, a craft, that you will get better at each time you sit down to write. Indeed we are still learning ourselves! And although there aren't any hard and fast rules, we hope our practical tips will help you when you need it most — when you are sitting at your keyboard, ready (or perhaps not so ready) to put your ideas on the page.

This guide is mostly based on personal experience, but we also include a section at the end containing useful tips on how to be worthy of your audience's trust. These are drawn from an event about communicating mathematics for the public which was organised by the Newton Gateway to Mathematics in Cambridge in January 2023.

The guide is divided into sections for each stage of the process – they each stand alone so you can dive in at any point. We hope this guide is useful!

Getting started — Two questions lie at the beginning of any writing process. Who you are speaking to and what you want to say?

Writing your first draft — Have you found a story you want to tell your audience? Here are some tips to help you on your way.

Writing clearly for any audience — Whether you're still getting your ideas together, writing your first draft, or revising and editing, here are some tips to keep in mind to help make your piece work for any audience.

Editing your work — You don't have to get it right the first time! And remember your ears are your best editor. Find out more about how to edit your work effectively.

Be clear, be trustworthy — When it comes to communicating maths or science that some people find hard to accept, you cannot take your audience's trust for granted. Instead you have to be trustworthy.

This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics. The INI is an international research centre in Cambridge which attracts leading mathematicians from all over the world. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.