In this podcast we hope to give you some interesting information. This information is encoded in terms of 0s and 1s – the classical bits in your computer or phone. But what if instead we were using a quantum computer? Then we'd be dealing with quantum bits, or qubits, opening up exciting new possibilities. And quantum information theory is the area of mathematics that explores how we can do that.

Adina Goldberg was one of the participants at a recent research programme in this area at the Isaac Newton Institute for Mathematical Sciences (INI). In this episode of Living proof, our podcast produced in collaboration with the INI, we speak to Adina about her work and how her intriguing motto – "the meaning is in the arrows" – applies to her research, her career path, and the way she looks at life.

You can find out more about quantum information in this short introduction and delve into the details of information theory in this collection of content.

Make sure you visit Adina's website to find out more about her work and her fascinating career. Since we recorded this podcast Adina has finished her PhD – congratulations Dr Goldberg!

This podcast forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration 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.

From sunny parks to banquets in castles – come with us on an exciting adventure in Oslo as we join the celebrations for the 2025 Abel Prize! We meet Masaki Kashiwara, winner of this year's prize, who tells us about the importance of collaborations and creating new things. Ragni Piene, previous chair of the Abel Prize Committee, gives us a look behind the scenes. And Andrea D'Agnolo, one of Masaki Kashiwara's most recent collaborators, celebrates his friend and fellow bridge-builder between mathematical worlds.

You can read more about Masaki Kashiwara's work in our article, and you can listen to a recent podcast where we spoke to Helge Holden, Chair of the Abel Prize committee, about the Abel Prize and about Masaki Kashiwara's work. And can you see all our reporting on every Abel Prize since it was first awarded in 2003 here.

Thanks to the musicians Peter Baden, Astrid Garmo and Liv Lande for playing such wonderful music in the Abel Prize ceremony which you'll hear a little taste of in this podcast. And thank you to all the Abel Prize team, including Unni Irmelin Kvam, Pål Petterson, Marina Tofting and Anne Lise Stranden for inviting us to Abel Week and for such a fantastic celebration!

Photo of Masaki Kashiwara is copyright Thomas B. Eckhoff/DNVA and used with permission

Sarah Hart is a mathematician who is interested, not just in the maths itself, but also its connections to other areas of culture and art. She's done an amazing number of things throughout her career — from research in pure mathematics and heading up a maths department, to being the first woman Gresham Professor of Geometry and President of the British Society for the History of Mathematics.

Sarah has also written a fascinating book, called Once upon a time: The wondrous connections between mathematics and literature, and she gave a talk at this year's Cambridge Festival, with the intriguing title Life in Lilliput – The Mathematics of Fictional Realms. The talk was the contribution to the Festival of the Isaac Newton Institute for Mathematical Sciences (INI). Sarah also participates in the Modern History of Mathematics research programme that is currently taking place at the INI.

In this episode of Living proof, produced in collaboration with the INI, Sarah tells us about the many things she has done and how they all fit together, and gives some advice for budding mathematicians of all ages: keep pursuing all the things you love doing, and one day it may turn out that they all fit together.

To find out more about some of the things mentioned in this podcast see the fllowing links:

• Sarah Hart: Once upon a prime — In this episode of our Maths on the Move podcast Sarah talks about her book and the connections between maths and literature.
• Maths in three minutes: Groups — This article gives a brief introduction to Sarah's research area.
• Life in Lilliput – The Mathematics of Fictional Realms — Click this link to watch a recording of Sarah's Cambridge Festival talk at the INI.
• Sarah Hart at Gresham College — Click this link to watch Sarah's Gresham College public lectures.

This podcast forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration 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.