In this interview, Dr Mary Hanley tells us about her fascinating and varied career, from studying chemistry in the sixties and becoming a science teacher before returning to university to become a mathematician. She gives us an insight into working as a mathematician.

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**Could you tell us a bit about your career?**

Officially I am now retired. But if you’ve done maths as a career, you’re never really retired, it’s a hobby as well.

I had a very varied career. The first two years after graduating I worked in industry. Then I taught in secondary school for a long time. The first time I went to college I had chemistry as my major subject, maths in my degree was my second subject, in those days it was called a subsidiary. I always wanted to go back and do maths, and twenty five years ago I did go back and did maths all over again, right through, until I’d got a PhD, eight years of it, and loved every minute of it.

So, then I did some lecturing in UCD. I loved teaching, be it at second level or third, and I also enjoy maths very much as a subject. I went back teaching in Wexford as well, for quite a while. I applied for a one year job in UCD, and took leave of absence for a year. Then I took early retirement and worked in UCD again. My research area, which you are probably more interested in, was potential theory, which is a branch of analysis.

It’s very difficult to describe a particular area of maths, really. Maths is divided into different areas – algebra, geometry, and analysis . I think what you call algebra in the maths olympiad has a lot of analysis in it actually. Algebra is a slightly different subject when you go to university. Analysis is the one where you deal with functions and sequences and series. Potential theory is a branch of that, and if you’ve done physics and heard of a potential it is related to that, except it is extrapolated into totally abstract terms in the complex plane and in n real dimensions.

**Why did you choose to study chemistry and maths?**

Well the question really could be why did I not choose maths the first time. There were a lot of subjects I enjoyed, I think an awful lot of mathematicians tend to be all-rounders. I wanted to pick something in maths or science where things weren’t a matter of opinion. I felt I’d do better if it wasn’t just going to be my opinion about literature, which somebody mightn’t like and might give me low marks. Now, I don’t think that universities work like that.

It was more sort of an idealism and total ignorance, I couldn’t see what use I could be in the world with maths. I thought with chemistry I was going to be so much use, I was going to really do good things, and then of course feeling guilty for not going off to do medicine. This was, remember, the late sixties, a very idealistic time in the world.

So I did physical chemistry, I kind of cheated, I was one of the last years when you had the opportunity of actually specialising in physical chemistry and my favourite topic in fourth year chemistry was statistical mechanics. Now,I think in any kind of teaching you can do some good. Anyway, 25 years ago I decided I’d be totally selfish and not even think about that. The subject I enjoy the most, way the most, is maths. So that was it. I treated myself by going back to university.

**What does working as a pure mathematician involve?**

I worked as a pure mathematician quite briefly toward the latter half of my career. Basically you work in university. You’re a lecturer and you do research usually, in areas like analysis, algebra or geometry. Basically, mathematicians, apart from giving lectures and preparing them, find problems that have never been solved, and try to solve them. In pure maths it’s not unusual to work entirely alone; sometimes two or three mathematicians collaborate on a problem.

Half the thing is finding the problem. The difference between that and maths olympiad problems is in maths olympiad problems you know there is a solution, you’re looking for a solution, you know there is one. When you’re a pure mathematician you don’t know there’s a solution. It would be lovely if you could prove that this is not true, that sometimes is even worth publishing. This thing that I thought I was going to prove actually cannot be proved, because it’s not true. And that can be useful.

I think the training you get in math olympiad is great for it, in that you do go in with the attitude ‘I can do this’. You have to go in with the attitude ‘I can do this’. I know people who’ve worked on problems for five, six years, on and off, and then suddenly light dawns and they’re thrilled, they finally got it. It’s great fun, huge fun, and I haven’t done anything like enough of it.

There are more problems that I’ve tried and failed to solve than I’ve ever solved. I am saying that, that’s me, not necessarily a typical mathematician. I’ve definitely tried a lot of things that I’ve got more limited results out of than I was trying to get. I can prove something is true in a particular case, but my aim would be to try and produce a general result.

There’s a big important difference between research and maths olympiad, in that in maths olympiad you are going to use various tricks. In research sometimes you have to invent the tricks. There’s a whole wonderful world, a structured world, out there, that you just have a deeper and deeper understanding of. You could study it forever and that would be extraordinarily enjoyable.

If somebody’s proved something, and it’s useful, it might take you two weeks to try and understand why this result they have is true. It’s useful to you in your theorem, in what you’re trying to prove. In one case I spent three months trying to see how this particular statement by someone was justified, and it was. I kept working using this, saying I’m pretty sure this is correct, but I’m not certain. It’s all very well to say he’s an important person, he said this, but I can’t see where he got it from. And that can be important, because sometimes people discover ten years later that somebody made a mistake, and everybody was working with a result which actually had a flaw in it.

**Did you encounter any discrimination due to your gender?**

For my generation gender discrimination was there and still is to some extent in certain areas of life. One of the beautiful things though about mathematicians – I’m totally prejudiced in favour of them – is that people who are very good at their subject recognise when other people are, and they don’t even notice whether they’re men, women, children, what they are. So they don’t discriminate. I never came across any discrimination in the maths field. Ever. They’re not interested. In the same way you could go in with your jumper back to front and nobody would notice.

But when I was in school I had to fight very hard to do honours maths at Leaving Cert level. It just wasn’t done, girls didn’t do it. Very few girls did it. I loved maths, so I wanted to do it. Now, in those days the standard in most subjects was far higher than it is nowadays, so you’re not really comparing like with like. It was challenging. So was chemistry, challenging, so was physics. The most difficult concepts have been taken out long ago. They take more out every few years. These subjects are more descriptive now; they weren’t in those days.

But I had to fight very hard to do honours maths. Girls weren’t encouraged to. And we also wanted to do Latin. We had a teacher who offered us pass Latin because she didn’t see why girls would do honours Latin. Well, she gave in! We persuaded her to do it. I had to basically do maths on my own outside school. I got a load of books – many went way beyond the course – from a friend whose father was a maths professor. He lent me books and that was great.

**What maths books would you recommend?**

I like popular maths books. I give a list to the enrichment class. If you’re interested in maths at all, everybody expects you to have heard about the Riemann Hypothesis. You get all these people who know nothing about maths asking you about it. There’s the Marcus du Sautoy book on that, *Music of the Primes*. There’s another one, it’s called *Prime Obsession*. It’s by a guy called John Derbyshire. It’s got a little bit more to it than *The Music of the Primes*, which I thought was a very good book as well. But there’s more to that one and it’s still an accessible book.

**What’s the biggest difference between student life and life while working?**

In my case, it’s so long since I’ve been a full time student. I’m thinking about it, you know. I mean, I did go back as a mature student. Twenty five years ago. It was Heaven. It’s just a different experience. I think when you’re doing a job, you try to do it well, it’s not always interesting. Some of it will be. Most, if you’re fortunate enough and I have always been, apart from my two years in industry. I got very bored towards the end of those two years. It was interesting for a year when I was learning new things and then it began to get quite tedious.

And I could also see the other things that can happen in industry and probably won’t happen to you. You start in the technical field, but you can find that the only way there’s promotion is you’re sort of expected to head into some sort of administrative management type stuff, which didn’t even remotely interest me.

Even the best of jobs isn’t always interesting. There are always things you just have to do and get on with. As a student it is much the same. Though, if you don’t care about grades, you can leave out the boring bits – you can’t in a job.

**Do you have any advice for young people interested in STEM subjects?**

My advice very much in terms of careers is pick a subject you really enjoy, that you find really interesting itself. I think too many people feel you must pick a STEM subject. I know because I’ve asked them, ‘why did they pick maths? You had enough points to get into university. They didn’t come from maths, obviously. Why have you picked maths?’. And they said ‘because the career guidance teacher in school advised that maths was a good subject to have’.

I won’t give you that advice. Pick the subjects you really find interesting and look for the career that you will enjoy doing. Don’t worry too much about the money – well it depends on what you want. I don’t give advice to people whose aim is to make money because my advice would be no good for that. I give advice to people only on the assumption that they want a job they really enjoy – and earn at least enough to live on.

Use the time when you’re studying to educate yourself in a broader sense. I think if you have the luxury of being able to afford not to go and get training for a job at university initially, then choose subjects in arts or science and try to go into some depth in one or two of them. Okay, maybe at the end of it you might like to be an actuary, but please study a subject you might like first, and don’t go in and say ‘right, I’m going to be trained for a job in university and become an actuary’. If you have the luxury of being able to spend a few years actually educating yourself in one or two subjects you find interesting, take advantage of it. Be really glad you’ve got it. So many people don’t have that opportunity.

*Thank you very much to Mary for sharing her experiences as a teacher and mathematician, as well as her helpful advice! *

*This article is transcribed from a spoken interview.*

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