“Mathematics is a tool that all of the sciences rely upon”

Exclusive interview with Mathematics Teacher Daniel Knowles, taken from the NSMC student magazine πnation:

Dan Knowles, Teacher of Mathematics

AS: Could you please tell me about your background, studies and teaching experiences?
DK: I completed A-levels in Mathematics, Further Mathematics and Physics, and my AS level was in PE. Then I went to Warwick university, studied straight Mathematics for 3 years and I then stayed at Warwick university for my Post Graduate Certificate in Education (PGCE).


AS: What were your early Mathematics influences and did anybody, prior to your university studies, inspire you to do Mathematics?
DK: My sixth form teacher believed in all the students and that’s what inspired me to be a teacher, specifically a Mathematics teacher but I had a lot of experience in youth work as well. I loved Mathematics and working with young people, so I put two and two together and went into teaching Mathematics.

AS: The role of Mathematics in sciences is central and obvious but what importance does it have in arts and music, other fields that might not be associated with Mathematics?
DK: I think there’s a strong link between music and Mathematics. Even the intervals and the ratios things make up, it’s very mathematical in its structure and relationships between certain things. That’s what Mathematics is all about – it’s abstracting relationships between two concrete things and making them more generalised.

AS: What do you think is the role of social media for young mathematicians in the 21st century?
DK: I think Youtube is playing a major part in the development of young mathematicians nowadays, because there are Youtube channels such as Numberphile3Blue1BrownVeritasium. There’s lots of channels that are seeking to increase young people’s knowledge on the world around them and, specifically with Mathematics in mind, are really grabbing people’s attention.

Mr Knowles talks to students

AS: Do you see Mathematics as a competition?
DK: No, I don’t see it as a competition but I can see how students who are competitive enjoy Mathematics because sometimes there is an element of who can get to the answer first and a bit of a race. If people have qualities that are competitive, they might enjoy the nature of Mathematics being a race to the answer. Mathematics shouldn’t always be competitive, it doesn’t matter how long it takes to get to the solution, as long as you are learning more in the process.

AS: What is the better way of working on Mathematics problems – alone or in collaboration?
DK: I definitely think collaboration is the better way forward, but you have to be working with the right people. If you are collaborating with someone who is too dominant or too passive, that is not good, you may as well work on your own. I have experienced that collaboration has been fantastic for myself, particularly in university where I had three particular friends where we would struggle on problems together, and we would come out having learnt massively more than we would have done on our own. There’s something called a zone of proximal development – that is worth looking into.

AS: What fields of Mathematics do you see growing in importance and what fields might be fading away?
DK: In terms of encryption, it’s been at the forefront for a while now because of internet security, especially as the rate of processing power increases, we can crack codes quicker. Similarly, the use of Mathematics in software development is obviously on the rise. A major thing for the future is going to be the environment, solutions for sustainability, linked more with biology, chemistry and physics than with Mathematics but Mathematics is a tool that they will rely upon.

AS: What does the future of Mathematics look like to you? Is it in any danger from automation?
DK: There will always need to be human input at some point, I don’t think we will get to the point where the machines will be creating their own theorems without initial input from humans to tell them to look for certain proofs. There’s always going to be space for humans in Mathematics.

AS: Are there any mathematicians that you particularly admire?
DK: Galois was one of my favorite mathematicians when I was at university. His field was in the number theory, algebraic theory field, he created lots of mathematics that no one could really understand at the time. They were still struggling to understand what he was talking about way after he died, and he died at the age of 20. He was political and he got into a duel at the age of 20 and got shot and killed in this duel. The night before, he stayed up all night writing theorems that were in his head, that were in this letter. This letter that he sent is what people were struggling to understand for decades after he died, trying to understand the mathematics that he had written down before going to this duel.

AS: If you were not to have been a Mathematics teacher, what career would you have chosen?
DK: When I was nine or ten years old I wrote in a book at school that my ambition was to become a Maths teacher, a cricketer or in the army. Preferably I would have been a football player, my career has been  plagued with injuries, so that wouldn’t have worked out so well either. I am pretty pleased I’m a Mathematics teacher.  If I could retrain, I would probably retrain in programming because I enjoy it; I’m not very good at it but I love the little I can actually do.

AS: Any advice for young mathematicians who aspire to study Mathematics at university or choose it as their main career discipline?
DK: I’d recommend finding out what Mathematics is actually about before applying for it because undergraduate Mathematics is very different from A-level Mathematics. You are sitting in a lecture, frantically taking notes, not really understanding what is going on and then trying to figure out everything that happened before the next lecture. Whereas at A-level you have lessons, you are spoon-fed with everything. If you struggle with something, you just ask whoever is there and you feel free to talk about it, whereas that’s not always the case at university. So, it’s good what we do here in terms of Mathematics lessons having one lecture a week, that it really gets you used to the whole system of you sitting and trying to listen to someone, trying to understand what they’re saying from the board. Also, the topics themselves, there’s a lot of ‘proof’ at university and a lot of work with functions, understanding notation. There’s a topic called analysis which you would probably want to look into before going off to do degree in Mathematics because that is major element of your first year. Don’t go into a degree without knowing what Mathematics is like, do your research first, otherwise you might prefer Physics. Physics may be a lot more appropriate, use a lot more A-level Mathematics than degree level Mathematics does. Pick a good university that is going to support you well, speak to your Mathematics teachers about the content because they love speaking about Mathematics.