David Abrahams, Professor of Applied Mathematics at DAMTP, has been awarded a prestigious Gold Medal from the Institute of Mathematics and its Applications (IMA).
The IMA Gold Medal is awarded every two years in recognition of outstanding contributions to mathematics and its applications over a period of years. Abrahams received the award for providing "three decades of enthusiastic, inclusive and energetic leadership to the UK applied mathematics community."
Abrahams received the medal from IMA President Hannah Fry at the Royal Society in June 2025. In her glowing introduction Fry described Abrahams as a "human whirlwind" who has been "the most generous champion of our community we have ever had." He is, she said, "applied mathematics' answer to David Attenborough".
The world is waves
Abrahams contests Fry's claim, but he has roamed the applications of maths almost as widely as Attenborough has explored our planet. "That's one of the great things you can do as an applied mathematician," he says. "You have a bag of tools, mathematical skills, that you can move around from one area to another. It's important for an applied mathematician not to work in just one specific field, but to look how you can adapt. We know that innovation in science mostly comes from taking something that has been well developed in one area and moving it across to another. Very rarely is something new invented."
Science is built on scepticism, not accepting anything without being convinced by evidence. Now more than ever do we need to question what's going on in the world. Professor David Abrahams
Abrahams’ main research area, wave mechanics, finds a huge range of applications, from optics and acoustics to seismology, crystallography and even mathematical finance.
"We know that the Universe is wavy," he says. "Every time you oscillate anything on any scale it sends information that travels at the speed of some wave. There's a uniformity about it — I focus on certain types of physical problems that can be expressed as mathematical equations of Wiener-Hopf functional form. The methodology has produced a universal tool we all can use inside wave mechanics but also outside. Myself and many other people around the world are trying to extend the method. The biggest achievement in my career is making an advancement in this area."
Alongside working on theoretical aspects of wave mechanics, Abrahams has also been collaborating with industrial partners ever since the time of his PhD, implementing the mathematics in real-world applications. In the last few years his main industrial interest has been metamaterials, human-made materials that don't appear in the natural world. Being smart about their design you can create sound-absorbing walls, build stealthy submarines, and reduce the damage caused by the vibrational energy of earthquakes — all using the same mathematical and physical insights.
Glaciers and meteorites
Apart from waves, Abrahams has also developed an interest in geophysical problems, inspired by a workshop on glaciers which took place in the Alps around ten years ago. "I had a fantastic week talking to glaciologists and other mathematicians who work on problems related to glaciers. I realised how fascinating the area is."
The result of the workshop was a new understanding of how the melt rate of glaciers, important because it acts as a proxy for the advance of climate change, depends on the amount and type of debris cover (stones, rocks, etc) on a glacier. This first foray into geophysics then led Abrahams to look at other evolutionary questions concerning glaciers, and also sea ice, and even to a highly ambitious project hunting meteorites in Antarctica!
Regarding climate change, Abrahams believes that mathematics has an important role to play, not just in understanding its effects, but also in tackling them. "Mathematicians should be at the pointy end of helping to come up with practical solutions," says Abrahams. "Broadly the skill of applied mathematicians is seeing if we can look at a problem in a different way than, say, engineers would do, and using this to create a paradigm shift in the way we approach a problem and solve it."
Community and exchange
Abrahams' research activities have been highly collaborative, but his sense of community reaches beyond the confines of his own area. From 2014 to 2016 he was Scientific Director of the International Centre for Mathematical Sciences (ICMS) in Edinburgh and from 2016 to 2021 he was Director of the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge. Both these institutions are international research centres which allow mathematicians to connect and work together beyond the boundaries of their fields and institutions.
Abrahams guided the INI safely through the first part of the COVID-19 pandemic and, in 2020, was instrumental in forming the Virtual Forum for Knowledge Exchange in the Mathematical Sciences (V-KEMS), which has mathematicians address challenges from outside mathematics in high-intensity virtual workshops. Further connecting mathematicians to business, industry and government Abrahams played a vital role in setting up the UK Knowledge Exchange Hub for Mathematical Sciences. To support the communication of mathematical research to much broader audiences, he also initiated a collaboration between the INI and Plus, a free online platform that publishes content about mathematics for a range of non-expert audiences. Plus is part of maths.org, the award winning education and outreach initiative based here at DAMTP.
Abrahams' motivation for all these activities is to effect change. "When I started my career all I wanted to do was write papers," he says. "But as you progress you realise that you can make bigger change through organisational structures. I took the jobs at ICMS and INI because you can influence the research of many, many people. I am piggy-backing on the work of huge characters like Michael Atiyah to make some changes I think are important. It is critical now that mathematics recognises its responsibility to society and is informed by the problems that are out there — to inform the pure mathematics of the future by the applications we presently pursue."
Taking part in the debate
Overall, Abrahams thinks that the UK mathematics community is not taking its place in current debates that affect everyone. "Mathematics has changed society, it's the power behind science, but not many people understand that story. For example, artificial intelligence is set to bring enormous change, so why are we not at the heart of the community debating the ethical implications and defining the mathematical tools we will need to resolve problems arising in the rush to implement AI? Somehow, politicians have forgotten that mathematicians are fundamentally involved and in some sense have a broader perspective on this problem than computer scientists or pressure groups from other areas."
A body that is designed to change this is the budding Academy for the Mathematical Sciences which Abrahams has been instrumental in setting up. "When the idea of an Academy was mooted by Phillip Bond back in 2016, I got it within 30 seconds! An academy will put all the mathematical sciences learned societies together, all the teaching associations, and people and organisations from industry, and then speak with a really effective and powerful voice."
While the Academy is being set up and seeking funding, Abrahams keeps busy with activities aimed to broaden and nurture the mathematical community from the ground up. At the time of this interview he had just spent a Sunday talking to teachers from the North East of England, discussing how to widen participation in mathematics education, and was involved in a modelling camp for Martingale Scholars — PhD and Masters students from lower socioeconomic backgrounds supported by Martingale fellowships (you can see profiles of two Martingale scholars here).
Broadening access to mathematics is one of Abrahams' passions and he is well aware of his responsibility towards those who want to participate — which doesn't just consist of teaching them mathematics. "Our role is to give students and early career mathematicians a bigger vision. To open their eyes to be more confident, to push the boundaries, to experiment, and to question. Science is built on scepticism, not accepting anything without being convinced by evidence. Now more than ever do we need to question what's going on in the world. So let's encourage young mathematicians to be sceptical."
Punching above weight
Abrahams came to Cambridge in 2016 from the University of Manchester, where he was Beyer Professor of Applied Mathematics. He enjoys the "formidable level of activity" that goes on in DAMTP: the number of talks, the number of visitors passing through, and the number of opportunities for collaboration, which has been a mainstay throughout his mathematical life.
"I've really appreciated working with other people, throughout my career, who have been passionate about things," he says. "The maths community is amazing. We're much smaller than people think we are, but we are small and perfectly formed! We're also very honourable. We want to do good work and advance the subject. We punch above our weight." The Mathematics Faculty at Cambridge sits at the heart of this community and has, Abrahams thinks, the means and the clout to deepen its impact — not only by producing brilliant research mathematics but also by hosting projects, such as Plus, that reach beyond the field itself.
Abrahams is planning to make full use of the opportunities that Cambridge offers him. Despite the IMA Gold Medal, which might be viewed as a lifetime achievement award, he stresses that he is not done yet. "I feel that I'm just starting out on my career and I think that I still have a few things left to give." David Attenborough would surely approve.