# Dr Lynne Walling

"As mathematicians we look at things differently, which means that we can produce things that other people aren’t going to, and that’s exciting."

A familial connection with mathematics, coupled with a disenchanting educational experience, had initially deterred Lynne Walling from the scientific path.

But she was ultimately drawn back to her fascination with mathematics and after years spent working in senior positions at notable US institutions – from the University of Colorado to the National Science Foundation – took up post in Bristol’s School of Mathematics in 2007.

As Head of Pure Maths, Lynne is passionate about the inherent beauty in numbers, and firmly believes in the importance of challenging students and researchers to work harder and go further.

She splits her time between working with quadratic forms and various types of automorphic forms in number theory, and lecturing and supervising both undergraduates and postgraduates, for whom she regularly sets additional assignments such as maths quizzes that bring the beauty and the rigour of the discipline alive.

"I always liked math. I went to university for a year but they weren’t really trying to teach us so I quit, disenchanted by it all.

After two years working low-end jobs I went back to get a degree in accounting; I ended up at a small university, where they really cared about teaching. So I picked up math again for fun, realised it was just getting better and then decided to go to graduate school in math.

I did my PhD in Dartmouth and the professor I wanted to work with was in number theory, he was amazing, a really great guy, and a career in math followed.

Results in number theory are very pretty. When you look at problem and have some idea of a structure that exists, trying to uncover that structure can become addictive.

It’s the same when you try to take the right point of view and explain to others what that structure is and then prove that it’s true, and get them to share that insight and vision.

I want to see the structure and the beauty, and once you see that – through whatever question led you to that – it makes you realise you can understand other things in a similar way too.

I remember being a kid in the back of my father’s car being driven around the country a lot, staring out of the window driving past orchards and thinking, ‘how do they arrange these things, it just looks completely random?’.

I remember that one moment where you’re at precisely the right point that all the trees are perfectly lined up and it all comes together. To me, that’s what uncovering a mathematical structure is like – at first you’re looking at it, and it looks a mess.

But if you have confidence and faith that this is pure math, it should be pretty, then getting to the right position, looking at it the right way, is just beautiful.

Pure math is very different to lab science. In lab science, it’s your basic assumptions that are questioned, or the conclusions you draw from your empirical evidence.

Whereas in math we write proofs so you know you’re right – what gets debated is how interesting it is, and that’s just down to point of view, just as different people will have different opinions if you take them to an art museum.

Math is a mixture of hard graft, logic, and creativity – you have an idea that you think might work and then you have to find a way to make it happen. Maths contributes to culture, to society and teaching – you’re training people to organise their thoughts, and articulate clearly, it’s about problem solving and tenacity.

I think there is probably some predisposition [to math], something about how your brain works perhaps, and then training certainly helps.

Some people, however, are just amazing – you can see them sit in a seminar that’s not even related to their own area but they absorb all these ideas and it makes sense to them completely.

Others have to study hard to get to the same point, it takes a long time but it’s interesting.

All of us get excited in pure math because we have a certain way of seeing things that’s a little bit different, which means that we can produce things that other people aren’t going to. That makes it a really rich experience – different ideas, processes, perspectives on the same topic. And it’s neat to see how they all come together.

If you’re passionate about math, if you find it intriguing and wonderful, continuing to study it to go further is a great thing. The further you go into math the more questions there are and the more directions you can go in, it doesn’t stop, which is great – imagine how depressing it’d be if all of a sudden somebody said they had gotten to the end, because then what?”

## Related links

- Hecke eigenvalues and relations for degree 2 Siegel Eisenstein series (PDF, 319kB)
*Journal of Number Theory*, 2012 - Restricting Hecke-Siegel operators to Jacobi modular forms (PDF, 293kB)
*Journal of Number Theory*, 2009 - Women in Mathematics: Participating, Surviving, and Succeeding (PDF, 66kB)
*A talk in honor of Audrey Terras*