What takes a mathematician to the Arctic? In short, context. The ice of the Arctic Ocean has been a rich source of mathematical problems since the late 19$^{th}$ century, when Josef Stefan, aided by data from expeditions that went in search of the Northwest Passage, developed the classical Stefan problem. This describes the evolution of a moving boundary at which a material undergoes a phase change. In recent years, interest in the Arctic has only increased, due to the rapid changes occurring there due to climate change.

Oxford Mathematicians Samuel N. Cohen, Christoph Reisinger and Sheng Wang have developed new methods to help machine learning build economically reasonable models for options markets. By embedding no-arbitrage restrictions within a neural network, more trustworthy and realistic models can be built, allowing for better risk management in the banking system.

In the 1680s there was a coffee house in London by the name of "Lloyd's". This place, catering to early maritime insurers, lent its name to the nascent English insurance market place, the now famous Lloyd's of London.

As we have seen over the past year, the ability to accurately predict the course of an epidemic is imperative when making decisions about how to control the spread of a virus.

Tissue oxygenation plays a crucial role in the growth of cancerous tumours and their response to treatments. While it may seem intuitive that reducing oxygen delivery to a tumour would be a treatment therapy, low oxygen levels (hypoxia) can significantly reduce the effectiveness of treatments such as radiotherapy and some chemotherapies. Therefore, understanding the dynamics of a tumour's red blood cells - which carry oxygen through the vasculature - is of vital importance.

One of the great puzzles of the current COVID-19 crisis is the observation that older people have a much higher risk of becoming seriously ill. While it is usually commonly accepted that the immune system fails progressively with age, the actual mechanism leading to this effect was not fully understood. In a recent work, Sam Palmer from Oxford Mathematics and his colleagues in Cambridge have proposed a simple and elegant solution to this puzzle.

How do we design face masks that efficiently remove contaminants while ensuring that we can still breathe easily? One complicating factor with this question is the fact that the properties of the material that we start off with for our face mask can be very different when in use. A key example is seen when you stretch the mask around your face to put it on. In doing so, you also stretch the pores, i.e., the holes in the material that allow the air to pass through.

The International Congress of Mathematicians (ICM) that was held in Oslo in July 1936 was a unique event that took place in turbulent times, research by Oxford Mathematician Christopher Hollings has revealed.

Oxford Mathematician Ben Green on a tale of conjectures, mistaken assumptions and eventual solutions: a tale of mathematics.

Take a piece of rope and knot it as you wish. When you are done, glue the two extremities together and you will obtain a physical realisation of what mathematicians also call a knot: a simple closed curve in 3-dimensional space. Now, put the knotted rope on a table and take a picture of it from above. It is now a planar projection of your knot. The mathematical equivalent of it is a knot diagram with multiple crossings as shown in the figure.

Oxford Mathematician Dawid Kielak talks about his joint work with Marek Kaluba and Piotr Nowak in which they used a computer* to prove a theorem about the behaviour of other computers.

Oxford Mathematician Vidit Nanda discusses his recent work with colleagues Bernadette Stolz, Jared Tanner and Heather Harrington on detecting singularities in data.

Oxford Mathematician Christopher Hollings and Oxford Egyptologist Richard Bruce Parkinson explain how our interpretation of Egyptian Mathematics has changed over the past two centuries and what that says about how historians of mathematics approach their subject.

Oxford Mathematicians Dmitry Belyaev and Michael McAuley explain the ubiquitous role of Gaussian Fields in modelling spatial phenomena across science, and especially in cosmology. This case-study is based on work with Stephen Muirhead at Queen Mary University of London (QMUL). 

Oxford Mathematician Sam Palmer tackles a crucial issue in our understanding of the risks of serious diseases such as cancer.