Joseph Edwards, a University of St Andrews Laidlaw Scholar, on overcoming hurdles in research, becoming a conscientious leader and selfless leadership.
Research title: Topological Origami: Material Properties from Geometry and Combinatorics
In 1766, Leonhard Euler claimed that a polyhedron made of solid faces and flexible joints could not be deformed whilst maintaining face shape and connectivity. In the following 200 years, many steps were taken to prove or disprove Euler’s conjecture, yielding results pertaining to the rigidity of almost all polyhedra (Gluck, 1975), ultimately concluding with the discovery of a counter-example (Connelly, 1977).
During the process of exploring Euler’s claim, the study of rigidity theory was born. By introducing mathematical rigour and purity into a field that was historically rooted in the manufacturing industry, we have unlocked new techniques and algorithms for generating large rigid frameworks that may influence modern engineering (Tay, Whiteley, 1985).
The goal of my research was to contribute to the field of rigidity theory, specifically trying to categorise the infinitesimal rigidity or flexibility of infinite screw periodic frameworks modelled on a triangulation of the torus. This consisted of proving a series of intermediate results and developing a Python package to help rigidity theorists visualise, manipulate, and enumerate such frameworks.
As a pure mathematician, the role of my research is not to explicitly produce real-world impact but rather to try and enhance our understanding of the abstract world of maths. By doing so, it is possible that someone else can use the results I prove to inform their work to have a real-world impact, such as answering questions in engineering(as illustrated by Tay and Whitley above).
Where did your passion for this research originate?
I have always been curious about a career in academia. When I first heard about the Laidlaw Scholarship, an experience that would allow me to explore my interest in academia whilst developing as a leader, I was adamant that I wanted to participate. Therefore, I began searching for a topic to research.
Since beginning university, I have found myself drawn towards pure maths more than applied maths and statistics. As much as I love the rigour and logic associated with pure maths, I often get bogged down in how abstract it can be. It’s not uncommon for me to ask myself questions like, “what is the point of doing this?” After all, you can’t see or feel pure maths directly. However, you can use pure maths to try and make sense of the things you can see and feel.
Therefore, when looking through the research interests of my pure maths lecturers, I was hoping to find something that I could relate to real-world objects. Rigidity theory sits at the intersection of recent trends in mathematics and theoretical physics and isn’t all that removed from tangible objects, so this offered me the ‘pure but not completely abstracted’ topic I was hoping for.
What is the most memorable moment from your Laidlaw experience?
The most memorable moment from my scholarship experience was the farewell the people of Toga village – the Fijian village that hosted me during my Leadership in Action project – gave the volunteers. After spending six weeks living, working, and learning together, the volunteers had been truly welcomed and accepted into the families within Toga. Therefore, we were fortunate to receive a traditional send-off to release us from the village. Needless to say, emotions were running very high throughout.
Our farewell celebrations and ceremonies spanned several days and consisted of family meals, meals with the whole village, kava ceremonies, traditional songs, heartfelt messages of thanks, and lots and lots of dancing. After all the celebrations and reminiscing, we ultimately had to leave the village. Many tears were shed as we said our final goodbyes to our friends and families, and we climbed aboard the carrier that would take us away. As we drove off, the entire village sang and waved us off, and that is an experience I will never forget.
What is the biggest challenge you came across, and what did you learn from it?
Undoubtedly, the most challenging experience of my scholarship came towards the end of my research project. My supervisor and I had outlined a proposition for me to prove that was closely related to an existing theorem in rigidity theory, so we expected our proof to follow similarly.
I spent several weeks on this problem, making no progress. Every time I thought I had a breakthrough, I would spot a mistake. This was the first piece of work where I had been given complete independence, and I was failing. I seriously doubted my ability as a mathematician and a researcher and just felt generally defeated.
As the end of my project loomed, I asked my supervisor if he would try and prove the proposition with me. I explained everything I had tried and highlighted the places I was getting stuck. After doing so, he seemed quite stumped too. He spent a day on it and concluded that this proposition was tough and might not even be true. Hearing this was extremely validating and massively boosted my morale.
We later refined our statement, which allowed me to attack the problem from a different direction, and I finally produced a proof!
What does it mean for you to be a Laidlaw Scholar?
To me, a Laidlaw Scholar is someone that is committed to better understanding themselves; someone that is willing to try new things and put themselves in unfamiliar environments and, in return, learn more about the world around them and how they interact with it.
Through my research and leadership projects, the Laidlaw Scholarship has allowed me to explore potential careers, immerse myself in new cultures, and interrogate my core ethical and moral values. These experiences will lay the foundation for my future development as I become a conscientious leader and global citizen.
Being surrounded by like-minded scholars – seeing their success and growth in myriad different fields – has fuelled my desire to better myself. It is inspiring to be within a group of such intelligent, bright, creative thinkers; I extend my thanks to the Laidlaw Scholarship for bringing us together.
Which leaders inspire you and why?
One of my favourite and most inspirational leaders is Demis Hassabis – the co-founder and CEO of the AI research laboratory DeepMind. Not only is he an incredibly talented scientist, but he also has the leadership skills necessary to allow his company to develop ground-breaking programs faster than would be possible in a classical academic environment.
One of Hassabis’ most admirable qualities is that he is committed to developing the field of AI for the betterment of society, not for his financial gain. In an interview with Hannah Fry on Deep Mind: The Podcast, Hassabis describes himself as “an entrepreneur second, a scientist first” with an “insatiable thirst for knowledge”. I think this selflessness is quite uncommon, particularly in the technology sector, so I love that such an influential figure has this attitude.
Another characteristic I wish to mirror from Hassabis is his optimistic attitude, always planning for success. As he believes so firmly that AI will shape the future, he futureproofs his technologies by addressing potential issues that will arise to ensure the most ethical integration of his technology into society.
Briefly describe a scene from the future you are striving to create.
Half of the working-age population in the UK have the numeracy skills of primary school children (National Numeracy, 2017). Furthermore, there seems to be a social norm that some people can do maths, and others just can’t.
I think this idea stems from a perceived disconnect between the current maths curriculum and the ‘real-world’, hearing students often ask, “when am I ever going to need to know this?” Whilst it might not be clear immediately clear how simultaneous equations will help you outside the classroom, it has been shown that people that improve their numeracy are more likely to be in employment, have higher wages, and have better well-being.
In the future, I would like to be in a position where I can share my passion for maths and demonstrate the utility of maths, particularly to young people, instilling confidence in them that they have the ability to be numerate.
🌈 Something that made me feel joy recently: I went to watch a cricket match with my parents recently. I haven’t been at home much over the summer, and it was really enjoyable spending the day with them.
Joseph is a Laidlaw Undergraduate Leadership and Research Scholar at the University of St Andrews. Become a Laidlaw Scholar to conduct a research project of your choice, develop your leadership skills, and join a global community of changemakers from world-leading universities.
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