Packing spheres — In 2016 Maryna Viazovska stunned the mathematical community with a breakthrough in the theory of sphere packings: how to arrange balls in space so they fill up as much volume as possible. In this article she tells us what she did and how she did it.

How to tame uncertainty — You may not know it, but you rely on mathematical models many times every day. But models come with uncertainties — how to we get to grips with them? Catherine Powell and Masoumeh Dashti explain.

Combining traditional approaches with machine learning — Carola-Bibiane Schönlieb received a 2017 Philip Leverhulme Prize for her work on the foundations of image analysis. This article, which we wrore for the Mathematics Faculty of the University of Cambridge, explores her work.

Emmy Noether and the power of symmetry — Obviously we did not work with Emmy Noether - she passed away over 80 years ago. But 2018 marked the centenary of some of her mathematical work which forever changed the character of theoretical physics. Find out more in this article.

The cosmic microwave background — Few things have given as profound an insight into the Universe as the cosmic microwave background. This faint glow, which originated in the Big Bang, tells us what the Universe is made of, what shape it is, and even what its future is likely to be. Hiranya Peiris helped us find a way through the science.

Arithmetic billiards — Need to find the least common multiple or greatest common divisor of two numbers? A billiard table of the right proportions holds the answers, as Antonella Perucca explains. She also inspired us with her mathematical clock faces, which you can see here.

Ailsa Keating — Ailsa Keating is a new maths lecturer at Cambridge. In this video, produced for the website of the maths faculty in Cambridge, she talks about her work in symplectic geometry and her experience of doing research. The video is accompanied by an article.

June Barrow-Green — June Barrow-Green is a professor at the Open University, UK. We caught up with her at the International Congress of Mathematics 2018 to find out about the history of women in mathematics.

Cheryl Praeger — We talk to Cheryl Praeger, former executive member of the International Mathematics Union and Foreign Secretary of the Australian Academy of Science, about her mathematics, her work encouraging the next generations of mathematicians, and her role in the early career of Fields Medallist Akshay Venkatesh.

Nalini Joshi — Nalini Joshi is Vice President of the International Mathematical Union (IMU), which organises the International Congress of Mathematicians and awards important prizes. We talk to her about the work of the IMU, her own work in mathematics, and her work improving gender equity in STEM subjects.

Maria Esteban — We talk to Maria Esteban, mathematician and President of the International Council for Industrial and Applied Mathematics, about her work and last year's talk at the World Meeting for Women in Mathematics.

Nadia Bahjat-Abbas — Nadia Bahjat-Abbas is a mature student in theoretical physics who has previously worked in finance and teaching refugees in Malaysia. We talk to her about her career path and her work on one of the biggest problems of modern physics.