The Gatsby Computational Neuroscience Unit is a research centre at UCL with the broad focus of the "mathematical foundations of adaptive intelligent behaviour", approaching this topic from multiple lenses (theoretical neuroscience, machine learning, statistics and many more). I jumped at the chance to attend their 7-week bridging programme, designed for students requiring mathematical knowledge for entering postgraduate research. With a rigorous curriculum spanning calculus, linear algebra, probability, ordinary differential equations and Fourier analysis, I was envisioning all the interesting papers I'd be able to understand and abstract conversations this newfound knowledge would unlock.
Sitting in lab meetings or presentations, I often felt myself following the threads linking concepts together but feeling like the lights had been turned off when the conversation veered anywhere mathematical. Similarly, it is difficult for me to communicate my ideas about quantitative findings or motivations behind choices with data analysis. Through the course I set out to find the missing pieces and set the foundations for further exploration of ideas in my research.
We started with a exploration of proofs, including terminology and approaches for proving theorems and solutions. They were introduced as formalisation of ideas into standard premises that could be employed, no matter what the context was. It is simple to say that A equals B, but formalising what this actually means requires some unravelling. If you can show that A is a subset of B and B is a subset of A, then this is only possible if A and B are the same set. This set up the language with which we would be communicating our ideas, and as things became more complex and abstract, having these tools helped tremendously in simplifying problems. (Interestingly, this dialect began to bleed into the day to day speech between my coursemates).
Whilst the content will ultimately be incredibly important for future study, learning how to solve differential equations and multivariate calculus problems was not the only takeaway. If you can split a problem up into its constituent parts in this way, the process of problem solving starts to look more standardised. The complexity comes from knowing how to break it up and we tackled this with many practice questions, some of which we completed as groups. I enjoyed hearing different perspectives and our discussions gave me a glimpse of what collaboration in a lab environment might feel like.
The Gatsby programme gave me a new lens for approaching complex problems and the confidence to engage with research. Most importantly, it transformed my relationship with mathematical thinking from something that felt exclusionary to a powerful tool for understanding and communicating ideas. Of course, this is the start of a longer journey. I am filled with uncertainty about what research in computational neuroscience and machine learning will look like for me. But definitely better off than when I started and excited to ask real questions.
I would also like to emphasise the rigour and passion from all of our lecturers. It was incredibly interesting to see the creative ways in which they expanded our appreciation for proofs as well as hearing about their lines of research.