“Let’s chat any time, I’m fairly free.” Coming from Chris Budd, a professor of mathematics at both the University of Bath and the Royal Institution, as well as a board member of several of the most influential mathematics organisations in the UK, this is somewhat of a surprise. But he is true to his word, and one Friday afternoon we sat down for a conversation with one of the UK’s most experienced voices in mathematics communication.

A quick glance at Budd’s website reveals, through a CV that runs to 25 pages, the diversity of his interests and professional experiences. At various times, he has advised on setting A-level examinations, held high-ranking positions in professional societies like the Institute of Mathematics and its Applications, directed the Bath Taps into Science festival and been part of the Vorderman Committee, which produced a report in 2011 about recommendations for mathematics education.

All of this is in addition to a research career that has seen him tackle problems in nonlinear partial differential equations, high performance computing, weather forecasting and cancer treatment. Speaking to Budd, however, it is clear that all of these are underpinned by one thing: a love of mathematics, yes, but more importantly a passion for communicating it, and a willingness to engage with those in industry, politics and education who might not otherwise support mathematical research.

## Maths in the real world

Such a noble undertaking cannot, however, be faced alone. Since 2001, Budd has run an accredited course at Bath about maths communication, which trains up mathematics students and has them going into schools, running workshops and working at science festivals. Although the programme was initially designed to provide a formal structure and training for those who would be doing these things anyway, Budd quickly saw another advantage. “It turns out that some of the best ambassadors for maths are students. They’re closer in age to the audience, and they’re often better at communication than older generations.” The course now attracts around 25 students per year and he has just written a comprehensive guide about it. King’s College London and the University of Bristol, among others, have independently begun running similar courses. “I think all universities should run this course,” Budd says. “It leaves a lasting impact on the students, teaches them transferable skills and helps the wider community as well. I can see no downside to it really.”

It turns out that some of the best ambassadors for maths are students… they’re better at communication than older generations.

The idea of talking about mathematics outside of schools, allowing people to have fun with it and see it as the ‘hands-on’ science that it is rather than something bound to books, is surely an invaluable way to boost the profile of the subject. The fact that undergraduates are taught to do this—that it is seen as a valuable asset for a mathematician—is similarly revolutionary, and with Budd at the helm we have no doubt that the course produces talented communicators.

Building transferable skills, doing things during a maths degree that are not just mathematics, crops up again when we speak about Budd’s own research, which he describes as “industrial applied mathematics”. Again, even in his academic work it is clear that Budd enjoys breaking out of the university bubble and getting his hands dirty in the real world, working on problems that he hopes can “benefit society directly”.

He has had several students funded by CASE awards—industry-supported PhD positions that require the student to spend a portion of their time with the organisation that sponsors them. “It broadens your overall experience, and it’s a lot of fun. I had a student working with the food industry, looking at the design of microwave cookers. It’s just great!” Other students on similar awards have worked with the electricity board, and have worked on designing sensors for whale conservation. Today, however, the meaning of industrial mathematics is changing somewhat. The importance of cybersecurity in the modern economy has driven a boom in industrial number theory, and pure mathematics is also playing a big part in hot topics such as big data and machine learning. Hearing this is somewhat surprising, and perhaps comes from a slightly snobbish attitude towards industrial mathematics that Budd believes to be completely unjustified. “Industrial mathematics is not about dumbing things down. When you start working on a real problem, you very quickly find that you run out of mathematics that you know. Industrial problems are, and always have been, a marvellous way of generating new mathematics.”

Industrial problems are, and always have been, a marvellous way of generating new mathematics.

## Maths in the future

As well as training the next generation of research mathematicians, Budd has invested a lot of time in trying to broaden the appeal of elite mathematical events to new audiences, particularly those from state schools. He is chair of the UK Mathematics Trust, an educational organisation that reaches 600,000 pupils a year—providing many of them with the joy of problem solving that is, “on some level, why we all do mathematics”. In particular, Budd is keen that competitions like the International Mathematical Olympiad attract a more diverse team. “If you look at the make-up of the team, it’s been mostly male and mostly they come from independent schools… if I can achieve more diversity in my time as chair I’ll be rather pleased.” He points to the recent launch of the European Girls’ Mathematical Olympiad, as well as team challenges that include a poster round, as ways of making the competitions more approachable.

Charitable organisations like the UKMT could be even more vital in the near future, as the full effects of educational reform become apparent. Mathematics A-levels were changed from modular to linear in 2017, meaning that students have to sit exams on subjects ranging from calculus to statistics all in the same season at the end of a two year period. The fear is that this will scare people away from taking additional (further) mathematics courses: with little opportunity to test the water via modular exams, they could feel like it is too much of a gamble to take two A-levels in the same subject. “I fear that this will affect the state sector disproportionately… teachers at state schools are just as dedicated, but they don’t have the time or the resources.”

But why is mathematics getting a short shrift in schools? Budd has previously spent time in Singapore, a country which tends to do very well in mathematical league tables. One reason for this could be that Lee Hsien Loong, the prime minister, holds a mathematics degree from Cambridge. “Mathematics has support from the top down, and that goes right the way through the system. In the UK, I don’t know of a single mathematician in the House of Commons.” (In fact, since the 2017 general election, there are three members of parliament with mathematics degrees-Stephen Timms, Karen Bradley and Bill Esterson.) The point, however, is still that mathematics does not enjoy the same political profile as it might in other countries. As an anecdotal example, Budd recalls applying to a scheme organised by the Royal Society, where 30 research scientists each year are partnered with a politician in order to learn about how research findings can have an impact on policy. Budd’s application was successful on the Royal Society’s side, but was not chosen by any of the participating MPs. “That was rather disappointing, actually.”

## Maths on the television?

If politicians are not reliable conduits for mathematical knowledge, where else can we look? “My advice is to work with the media. TV is a hard nut to crack, but people have done it.” Throughout our conversation, Budd namedrops previous *Chalkdust* interviewees Hannah Fry, Marcus du Sautoy and Ian Stewart, as well as Eugenia Cheng, as exemplars of mathematics communication. “Hannah is excellent. She’s out there, prepared to take on the challenge of going public. It’s not easy being in that position.”

Although this route may not be for everyone, Budd is insistent that mathematicians should support their colleagues who spread mathematics outside of the classroom, whether that be through the media or industry. “Don’t give up. Remember that most journalists think of themselves as ‘English people’ rather than ‘maths people’ and be sensitive to that.”

From someone who has built a reputation through speaking about mathematics to those who aren’t necessarily ‘maths people’, we think this is advice worth listening to. “People really are fascinated by mathematics. They love the idea that there are problems that can take years to solve. Get out there. Be bold!”