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I love getting the chance to communicate some of math's most surprising results to different kinds of audience - not just math undergrads! In this section, you can find slides to a few of the outreach talks which I have designed and given to school-level students over the past several years. Some of the topics I have tackled are social media math (The #Math of Social Media), Gödel's incompleteness theorems (Proof), and transfinite numbers (Numbers: Big, Small, and Weird). I am currently developing new outreach material on machine learning and artificial neural networks (like ChatGPT).
I have also given a general pedagogical talk on using YouTube and Twitch streamers as inspiration to design digital content: check it out here!
In 2018, I won a Principal's Pioneer Prize at Heriot-Watt University for my work on mathematics outreach.
1. Numbers: Big, Small, and Weird
In this talk, I give high-school-level students an insight into numbers that they may never have seen before, such as imaginary numbers, and transfinite cardinal numbers - the most common of which is aleph naught, the cardinality of the natural numbers.
We encounter topics like Hilbert's hotel, Cantor's diagonalisation argument, and surreal numbers. This talk involves a lot of audience participation, which makes it much more fun for me to deliver! I especially like trying to fill up Hilbert's hotel with members of the audience.
2. Let's pwn some n00bs!
This talk is an informal introduction to Game Theory. It was an invited talk for the Scottish Mathematics Council (SMC) which was delivered to all those High School students who had won awards, having solved the SMC's Mathematical Challenges over the academic year.
It's a light-hearted talk on the applications of Game Theory. My favorite parts of the talk are telling the audience about my love of the game Magic: the Gathering, as well as playing a game of Nim with the audience!
3. Proof
In this non-technical talk, I introduce prospective University students and their parents to the strangeness of proof in mathematics. Many students in science say that they prefer math over the humanities as "there is always a right answer". Whilst this is true in day-to-day arithmetic, as well as when solving quadratic polynomials for their zeros, this is not quite the case in research-level math!
The talk focusses on the mathematical and logical achievements of Kurt Gödel, a contemporary of Einstein, with particular attention on his two famous Incompleteness Theorems. It is always kind of cool to tell an audience that there are mathematical statements which are true but unprovable!
4. Shift a Sand Dune to Predict a Typhoon
In this talk, which was delivered to a Festival of Science audience, I introduce the audience to some techniques meteorologists use to model the weather. This is a research-based talk, being centered on (at that time) the recent research work I had published with Mike Cullen, a meteorologist who worked at the UK Met Office (the UK's version of the National Weather Service, or the National Oceanic and Atmospheric Administration).
I focus on the use of the theory of Optimal Transport that is used to model the transport of air parcels around the Earth's atmosphere. The talk even features math related to a 2018 Fields medal!
5. How to Count
In this talk, delivered to high school students and their parents, I teach the audience how to count. I know this sounds a tad insulting, but what I really do is introduce the audience to the mathematician's view of counting (namely constructing bijections between sets of objects and subsets of the natural numbers).
By viewing counting in this way, it allows me to introduce the audience to transfinite cardinal numbers - like the famous aleph naught of Georg Cantor. Aleph naught is the smallest transfinite cardinal number and it models the size of the (infinite) set of all natural numbers.
I find this to be quite a fun talk to give, as it takes a mathematical topic which is rather mundane (basic arithmetic, which most people don't enjoy!) and puts a new spin on it. I find that people typically find it strange (and interesting) that there exists a rigorous mathematical theory of "infinite numbers"!
6. The #Maths of Social Media
This material was developed for a Masterclass which was delivered during "Maths Week 2017" in Scotland. The audience comprised over 100 High School students.
The material focusses on the issue of misinformation and how it spreads in a social network. It was a 4-hour-long event, made up of an extended talk, as well as a collection of exercises taken from a specially-designed activity book which I produced myself.
The main math content is reasonably elementary, being made up of some elementary combinatorics and graph theory, and so is reasonable non-technical.
7. Origami and Algebraic Equations
In this talk, I introduce students to the beauty of axiomatic mathematics - but without taking them through the (perhaps at the pre-college level, deemed to be slightly dry) formality of the "definition, axiom, proposition" approach to geometry.
Rather than using a straight edge and pair of compasses, I introduce students to constructions in plane Euclidean geometry using origami! It's a really cool, hands-on way to do axiomatic math without knowing you are!
This talk came with live demonstrations and paper-folding activities for students to participate in.
8. Using YouTubers and Twitch Streamers for Inspiration
In this pedagogical talk (aimed at a general academic audience, rather than a school student audience), I talk about my experience using "streamer tech", as well as streamer practices, to enhance my own teaching (both online and in person).
This talk was delivered during the pandemic, and is one of the more highly-viewed talks on the official TALMO (teaching and learning mathematics online) YouTube page.
9. Journeys and Triangles
In this short school talk for 13-year-old school children, I introduce students to the concept of mathematical proof (without using the word "proof"!). The vehicle for doing this is plane Euclidean geometry.
This is delivered as a 'physical' session, in the sense it involves students getting on their feet, marking out triangles on the floor with tape, and then walking around the boundary of their triangle while keeping track of how much they are turning on the spot. At the end of the session, they see a physical 'proof' that the sum of all interior angles in a plane triangle is 180 degrees.
At the end of the talk, I mention some of the other cool geometries that they may see in the future, such as spherical geometry, projective geometry, or even hyperbolic geometry!
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