There are two main responses that I would offer as to why a graduate physicist might be found loitering about at the AMSI Summer School 2022.

The first such response stems from ancient roots. Mathematics and physics have found themselves hopelessly entangled in a great mass of vines arguably winding themselves back to the earliest studies of nature. The mathematics cultivated by many civilisations throughout history, like that of ancient Mesopotamia as discussed by Dr Daniel Mansfield in an entertaining summer school lunchtime lecture, often emerged out of the fervent desire to nourish ordered and systematic descriptions of the world.

How best to articulate this decidedly complicated relationship? I found myself contemplating this question once more during a discussion with AMSI Summer School Event Director Professor Tony Dooley over tea and coffee at the University of Technology, Sydney. This occasion was to mark the first of three in-person events, with the rest of the school being conducted online, where hubs where organised in each state for students to watch the lectures together and generally engage in social activities more akin to those of pre-pandemic times.

While I unceremoniously burnt my lips in too-eager anticipation of my tea (admittedly, I was a little giddy at the prospect of live interactions with fresh faces), Professor Dooley struck upon a familiar chord. The conversation typically goes something of the sort:

‘You know, physicists use a lot of intense and interesting maths,’ they begin, ‘but the reasons why it works never manages to be satisfying enough; I want to *actually understand* the maths properly before I do all these crazy things with it!’ rounded with a sigh and a wild gesture or two.

‘Hand-waving,’ they say, ‘endless hand-waving! It seems that physicists feast upon maths worked out long ago and cram the leftovers into tight spaces for possible snacks down the line because “physical intuition”.’

‘But,’ a young mathematician protested to me once, ‘physicists have also provided a lot for mathematicians to work with, particularly in the case of modern developments!’ She was right; it is most definitely not a case of single-direction traffic as history has demonstrated.

This is not to say that all students of physics lament the mathematical shortcomings of their initiation into the world of physics. Among those more mathematically inclined however, in my experience, it is rather common. Sometimes to the point that they find themselves eventually relocating to the mathematics building in the aftermath of an academic crisis.

In fact, I wonder at times how I found physics. Mathematics was my first love at school despite not being particularly adept at it. The flow of logic, the transition from question to answer, conjecture to proof, appeals strongly to my nature. I worked hard at it, because I enjoyed it, and thoroughly surprised myself.

Eventually I would go on to study mathematics at Sydney University, with physics, a subject I had also enjoyed at school, as a second major. By second year, I gradually became entrapped by the allure of a subject whose principal aim is to throw off the cloak of mystery that appears to engulf the Universe while simultaneously rejoicing in the virtues of mathematics as a faithful assistant. Whether it is fair to paint mathematics as just an assistant in relation to physics is certainly debatable; moreover, mathematics by no means lacks its own sense of grandeur and aesthetic allure, as illustrated by Professor Kate Smith-Miles in her public lecture ‘When Mathematics Becomes Art…The Unexpected Beauty of Self-Evolving Mathematical Functions’ held in the third week of summer school.

I am now pursuing a PhD in theoretical particle physics, having completed an honours year in physics and a one-year coursework master’s in theoretical physics at Cambridge University (incidentally enough, this was officially a mathematics master’s, more famously known as ‘Part III of the Mathematical Tripos’, with the theoretical physics and mathematics departments being considered one and the same at Cambridge).

My current research certainly involves interesting mathematics; I study gauge theories, theories for which there are certain redundancies present in the mathematical descriptions of physical systems. The Standard Model of particle physics, currently the most accurate theory describing the nature of elementary particles and their interactions, is a theory of this type. The trouble is that it is not generally the *modus operandi* of the physicist to spend time agonising over the smallest of details or carefully examine the correctness of a statement or proof – an extremely attractive pastime for myself and others in similar position. I suppose that when all is said and done, physics is an experimental science. There is much more to say here of course; perhaps for another time.

The second response as to why a physicist might be lurking around AMSI Summer School requires an uncomfortable plummet back to Earth. To put it frankly, how does one land a job? For those considering careers outside academia, it is imperative to arm ourselves with transferable skills and most likely brace for a change of pace. As MathsFeed’s own Dr Adrian Dudek remarked in one of two careers related sessions at summer school, while being trained in mathematics certainly represents an advantage in relation to jobs in industry, just a little more work reaps considerable rewards.

The range of industries at the careers event day, from finance to meteorology and defence, spoke to the opportunities open to the emerging mathematician. There is a typically a serious interjection at this point: one had better iron out those cold, limp creases in their knowledge of statistics, mathematical modelling, and programming, in addition to having the fundamentals packed down tight. When the mouth of industry opens and available jobs (hopefully) pour forth, the flavours ‘machine learning’, ‘data science’ and ‘programming’ become all too familiar. The beast is temperamental though; it may just spit out something unexpected or change its tastes completely.

I was on a quest to wet my feet at the edge of the beast’s swamp water and took Machine Learning in Financial Mathematics as well as Computational Complexity at summer school. The former illustrated the central role of stochastic calculus behind the scenes of the oft talked about glitz and glamour of financial markets, while the later showcased interesting and thought-provoking mathematics in a relatively young and growing field studying the required resources (for example, amount of computation time) to solve algorithmic problems. They were both excellent courses and most enjoyable, though also very intense – a four-week ‘summer intensive’ would be an apt description.

As the school approached its conclusion, I found myself breathing a considerable sigh of relief that my usefulness may not be limited to questioning whether the Universe is described by this or that complicated gauge theory. With the usual caveats applied when offering advice, for those considering participating in the AMSI Summer School in the future: if you take the maxim ‘you get out what you put in’ seriously to heart, expect a demanding and thought-provoking four-weeks of mathematics where the rewards will be rich, sometimes a little surprising, and almost certainly play a nontrivial role your personal and professional development.

Best of luck!