Tom takes part in a Q&A with the Robinson College communications team about his career to date and what the future of mathematics might hold. You can find the original article on page 12 of the College Magazine – download at the link below.

Who has been the greatest influence on your teaching style and why?

I’m not sure I can narrow down to one individual – I think I have taken lots of tips and ideas from a range of different people over the years. In terms of formal teaching, I think my approach here follows that of my tutors from my undergraduate days at Oxford. There were two professors, Charles Batty and Paul Tod, who would ensure that before leaving you would know how to answer every question on a problem set. It sometimes meant that the tutorials felt a little rushed – particularly when it came to proofs in first year pure courses for me – but I found that I could always write up full solutions after each tutorial using my notes. I try to use this approach myself now when holding supervisions at Robinson.

Regarding my online teaching style, I think this is a mix of other communicators that I’ve interacted with over the years, plus some lessons from my PhD supervisor, Paul Linden. Working with Paul not only helped to refine my abilities as an academic, but it also helped to shape myself as a person. His laid back and relaxed attitude, whilst also caring deeply about his students and their work, really showed me the type of mentor I wanted to be. Someone that is friendly, open and approachable, but also passionate about their work. Combining this with traits of other YouTubers that I enjoy watching – for example the comedy of Matt Parker, the enthusiasm of James Grime, and the deep knowledge of Grant Sanderson, has evolved into the teaching style I use online today.

You regularly reach millions through your Tom Rocks Maths website, via social media including your YouTube channel, as well as via Maths Corner on Channel 4’s Countdown. Has this experience of bringing maths to the masses informed/enhanced your in-person teaching methods and vice-versa?

Without a doubt. When crafting content for social media, I try to think about the best way to explain the topic to a random person I might meet at the pub. This often means distilling the concept down into its simplest form and using analogies that people can relate to. Plus, trying to make it as entertaining and memorable as possible!

I think all of these techniques translate perfectly to teaching. I want to be able to help my students understand the topic, which usually means starting at the core concepts and building up. If they are struggling to grasp the meaning or significance of a result, then being able to reframe it through an analogy can often help. And I want them to remember the key ideas of a course when it comes to exams so telling stories or referencing pop culture when discussing a subject helps it to stay in their head.

Are there any Maths topics that you struggled with at school/College? If so, how did you overcome these difficulties?

I really did not get on well with Linear Algebra as an undergraduate. It was my least favourite topic and ended up being the lowest mark in any of my university exams. As a student, I think I just accepted it as something that I didn’t enjoy, but needed to do, and so just got through it – much like marking hundreds of exam scripts now!

But this all changed once I started teaching. As the old saying goes, “you don’t really understand something until you can teach it” and having to relearn first year Linear Algebra ahead of teaching it to cover for a colleague, was when it all began to click. It’s now one of my favourite subjects to teach because of the universality of the concepts – I regularly reference how a certain result or theorem is used in Quantum Theory, or Statistics, or even Mathematical Biology, and I think knowing this has really helped me to overcome my initial dislike for the subject.

If you could give your younger self any advice about academic/social life at University, what would it be?

In all honesty, I’d probably start by congratulating myself on the motivation and self-determination that I showed, and thank my younger self for helping to develop the work ethic that has stuck with me through my adult life. That’s not to say there aren’t any aspects that I could have improved on, but I think it’s important to acknowledge where good behaviours developed, and for me that was my time as an undergrad.

On the social aspect, I think it would have been a lot of fun to have tried out more activities. I spent a lot of time playing football, which I loved, and I did try out rowing for a few terms, but looking back now it feels like university is the perfect time to try something outside of your comfort zone. As an example, I’m currently writing a stand-up comedy show – based around maths of course – which is mildly terrifying, and I can’t help but feel my younger self would be far less self-conscious about the whole endeavour!

Are there any emerging trends or tools in maths education – whether tech-based, interdisciplinary, or otherwise – that you are you most excited about and why?

I’m purposefully avoiding AI here as I’ll happily go on the record to say that I think it’s a really bad idea for education. I don’t want to focus too much on the negatives so I’ll simply direct the reader to a video I made titled “ChatGPT Can’t Do Maths”.

On a more positive note, I’m involved in a lot of exciting initiatives about awarding university level credits to students around the world taking online courses. I think the future of education is in partnerships between traditional educational institutions, such as universities, and online platforms creating high quality courses that can be taken anywhere in the world. The role of the university is to ensure the quality of the course content and that assessment procedures remain robust, whilst the online platforms provide access to the material globally. A great example of this is the CS50 Introductory Computer Science course from Harvard which has now been taken by over 6 million students. I’ve been working with the team for the past 18 months to create a UK-focussed version which will be endorsed by universities in the UK. It’s currently available at Oxford and hopefully will be coming to Cambridge in the not-so-distant future – watch this space!

What do you anticipate will be the hottest topics/discoveries in maths in the near future and how could they help us with in real life?

It’s hard to look past the 6 unsolved Millennium Problems – announced in the year 2000 as the greatest unsolved problems in mathematics, each with a $1-mllion prize. (Originally there were 7, but one – the Poincare Conjecture – has since been solved.)

The problems were selected not because their solutions would have any impact on real-life, but because they were notoriously difficult. However, given the fundamental nature of many of them in terms of how they relate to our understanding of the universe, I think a solution to almost any of them would have far-reaching consequences in both the mathematical, and real, world.

To give you a concrete example, the P versus NP problem asks about the time taken for computer algorithms to solve different types of problems. We currently divide the problems up into P and NP, but there is evidence to suggest that these two categories could in fact be the same. If we are able to show this is indeed the case, it would mean a whole host of techniques used to encrypt your data online (such as credit card numbers, passwords etc.) would suddenly be a lot less secure than first thought. It wouldn’t necessarily mean that the encryption could immediately be broken, but it would lead to a redesign of the entire ecosystem.

Would you like to share a Maths-based joke? (If you have one up your sleeve)

The only joke I have requires knowledge of second year Complex Analysis, so instead I’ll share a chat-up line. “You’re sine-squared, I’m cos-squared, but together we could be 1”.

Disclaimer: I have never used this personally so take no responsibility for its success (or more likely complete failure).