To celebrate this year's International Women's Day on March 8, 2022, we revisit some of the articles and podcasts we have produced with female mathematicians over the last year. We've really enjoyed learning about these women's fascinating work and we hope that you will too!

### From logic to cosmology

Maths is beautiful in its own right but it also has applications in all of the sciences and beyond. Here's a collection of topics we have explored over the last year with a range of contributors from different fields.

**The hardest logic puzzle ever ** — It might seem cruel, but we're gong to start off with a very hard puzzle indeed. It was introduced to us by Antonella Perucca who usually researches number theory and also likes to invent mathematical exhibits. Get ready to stretch your brain!

**The mathematical shapes in your brain ** — Talking about brains, it turns out that ours contain mathematical structures that can help us understand how they work. We learnt this in a fascinating lecture by Kathryn Hess at the European Congress of Mathematics 2021. (Photo Epfl-Mediacom.)

**Maths in a minute: Category theory ** — We've always been curious about category theory, and at this years *Black heroes of mathematics* conference we finally found out what it is. As PhD student Maurine Atieno Songa explained, it's something you can use when you want to know how different systems are connected.

**Black heroes of mathematics 2021 ** — The *black heroes of mathematics* conference was an inspiring event, which featured a number of female speakers, including Maurine Atieno Songa (see above) and maths teacher Susan Okereke (shown in the photo on the left). Find out more in our write-up of the event.

**Opening the black box ** — Many aspects of our lives today are possible thanks to something called *machine learning*. But what is it and why do even mathematicians need to understand it better? Carola Bibiane Schönlieb (pictured) and Gitta Kutyniok explain.

**Maths in a minute: Maths and music ** — When people say that maths and music are connected, what do they mean? Find out in this quick introduction by Kate Stansfield, a maths graduate who is training to be a secondary school teacher.

**Solving crimes with maths: Bloodstain pattern analysis
** — Do you like crime dramas and do you like maths? Then this article is for you! It's by maths and economics graduate Marcia Gomez, who now applies her mathematics in finance.

**On the road to dark energy (with chameleons) ** — Anne Christine Davis is a pioneering theoretical physicist who recently published some ground-breaking work on a mysterious substance called *dark energy*. Find out more here.

### Maths, our environment, and our climate

The climate crisis has loomed large over the last year, and maths has a crucial role to play in tackling it. Here's a collection of content that explains how.

**
How to predict our changing climate ** — Emily Shuckburgh is a renowned mathematician and climate scientist. In this podcast she tells us about the climate models that help us tackle the climate crisis.

**
Understanding the diversity of forests using AI ** — Debmita Bandyopadhyay is a member of the INTEGRAL project, which develops cutting edge machine learning techniques to help us understand the diversity of our forests. This article explains how.

**
Seeing traffic through new eyes ** — The INTEGRAL project also uses machine learning to understand the traffic that chokes our cities, in order to create a healthier environment for people and the planet. Find out more in this article featuring INTEGRAL member Kelly Kokka.

**
Maths in a minute: Semi-supervised machine learning ** — The algorithms developed by the INTEGRAL team involve something called *semi-supervised machine learning*. Here's a quick introduction, put together with the help of INTEGRAL member Angelica Aviles-Rivero

**
New ways of seeing with the INTEGRAL project ** — To hear Debmita, Kelly, Angelica, and the rest of team INTEGRAL describe their work in their own words, listen to this podcast.

### The maths of COVID-19

Over the last year we have also continued our coverage of the COVID-19 pandemic, often working with epidemiologists from the JUNIPER modelling consortium and covering relevant workshops hosted by the Isaac Newton Institute for Mathematical Sciences and the Newton Gateway to Mathematics. Here's a collection of articles, and a podcast, exploring the mathematics that has been so vital in fighting the pandemic.

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Why the generation time of COVID-19 is important ** — To really understand the spread of COVID-19 you need to understand the time between infections. This article, written with the help of JUNIPER co-head Julia Gog, explains how and why.

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Going with the flow: are lateral flow tests useful? ** — Here's a look at our most loyal companion over the second half of the pandemic: the lateral flow test. The article is based on an interview with epidemiologist Liz Fearon (pictured) with the help of JUNIPER member Deirdre Hollingsworth.

**
Will the virus escape the vaccines? ** — The thought that the virus may become completely immune to the vaccines is terrifying. This article explores how some basic mathematics can help us understand vaccine escape. It is partly based on a talk given by Jessica Metcalf at a Newton Gateway event guided by the JUNIPER consortium.

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Understanding waning immunity ** — What can we expect from a disease for which natural or vaccine induced immunity wanes? JUNIPER member Francesca Scarabel explains.

**
On the mathematical frontline: Ellen Brooks Pollock and Leon Danon ** — In this podcast JUNIPER member Ellen Brooks-Pollock talks about her research on COVID-19, the impact it has had on her personally (including receiving an OBE) and what it's like working with her partner Leon Danon.

**A breath of fresh air** — Will the COVID-19 pandemic raise our expectations for clean air indoors? We found out what this might take from Lidia Morawska, an aerosol physicist, and Catherine Noakes (pictured), a fluid dynamicist, at a Newton Gateway event.

### About this content

*Many of these articles were produced as part of our collaborations with JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium, and the Isaac Newton Institute for Mathematical Sciences (INI).*

* JUNIPER comprises academics from the universities of Cambridge, Warwick, Bristol, Exeter, Oxford, Manchester, and Lancaster, who are using a range of mathematical and statistical techniques to address pressing question about the control of COVID-19. You can see more content produced with JUNIPER
here.*

*The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more. *