# Tony Carbery

Elinor Flavell has written the following article as part of our series of Academic Interviews; featuring Tony Carbery!

The most fitting way to start an article about Professor Tony Carbery is to pose a question which is simple to explain but may be hard to solve. So, imagine a square box with sides N by N, and you are throwing balls into this box. The question is how many balls can you throw into the box such that if you draw a line connecting two balls no other balls will lie on this line. Carbery is not so much interested in an actual answer as seeing how this answer changes as N becomes larger. This a variant of a problem that he has been working on for the last fifteen years or so and he welcomes you to have a go at it; he isn’t sure if it is hard or easy, but for him that is part of the fun. For Carbery maths is a collaborative and social subject; it involves being curious about the topic and willing to have a go.

**Early life**

One of his first examples of him being willing to have a go was in school. He really enjoyed Chemistry and thought that it was what he wanted to do as a career, so he did an extra experiment on the rate of reactions. He wrote up the results and presented his teacher with a graph (which we might recognise as an exponential curve). However, the teacher said it was incorrect – “it should have been a straight line” – and that he must have made lots of mistakes in his experiment; this understandably, deflated his enthusiasm somewhat. As such, he began to become more interested in mathematics and, several months later, came across differential equations. He observed that some can have exponentially decreasing solutions, which helped him to make the connection over what he had actually plotted on the graph during his extra experiment. It was at this point that he became more interested in pursuing maths.

**Time studying at University**

This led to him studying mathematics for his undergraduate degree. However, attending Oxford University, during the 1970’s, he found it a very elitist environment which did not suit his collaborative nature. With regards to mathematical themes, he preferred pure, even though he often performed better within applied. He particularly liked functional analysis (which is the study of vector spaces confined by a certain topology) and algebraic topology (which uses the tools of abstract algebra to study topological spaces); both subjects he was interested in focusing on in his PhD. For this he applied to several places, and eventually settled on UCLA. Carbery loved his time there as, although California was a bit of a culture shock, the intellectual environment was much more free and open. It was this open and friendly atmosphere at UCLA which led him to approach one of the faculty members whose interests lay in complex analysis, with a view to becoming his PhD student; however he ended up with a thesis in harmonic analysis (which begins with the study of Fourier series and their generalisations). It was this collaboration which opened the door for him.

From there he went to Chicago and then Caltech for postdocs with both, again, having a culture of mathematical collaboration.

**Life as an Academic**

2022 marks twenty-eight years since Carbery started at Edinburgh University. For him, spending time teaching is just as important as his time researching, and he spends about an equal amount of time on both. He loves the idea that students are being taught by people at the cutting edge of intellectual endeavour, while spending time teaching students influences his scholarship and research – it is rare that teaching something doesn’t increase one’s own understanding and appreciation of it, even after so many years!

Being able to do maths as a job and career is a joy for Carbery and as such is his ultimate hobby. However, he does also enjoy travelling, learning about, and experiencing other cultures. This can be seen by his time spent in America and more recently Spain. This love of travel is still linked back to maths though, as it is often through the connections, he has made at other institutions, that see him travelling abroad to learn more about maths.

Since moving back to the UK in 1985 Carbery’s infectious curiosity about harmonic analysis and his constant willingness to share and work with others is partly responsible for the UK now being a leading nation in this field.

For Carbery, maths is social, collaborative and for those who are willing to give it a go and see what happens.