Vishal Gupta studied Mathematics as an undergraduate at Cambridge and has just completed Part III. He is one of the Mathematics Faculty’s student ambassadors, and most recently one of the inaugural cohort of Martingale Scholars. We caught up with Vishal before he starts studying for his PhD to talk about what most appeals to him about maths, the opportunities the Martingale scholarship has opened up, and why he hopes to inspire others to apply to Cambridge too.
I've had an amazing time studying maths at Cambridge. One of the great things about Tripos is the wide range of courses you can study. I took courses as diverse as Quantum Field Theory, Lie Algebras, Asymptotic Methods and Logic & Set Theory.
The area of maths I'm most interested in is analytic number theory, which is about using methods of analysis to study prime numbers and their distribution. A great example is the prime number theorem which tells us asymptotically how many primes there are up to n - the answer is n/log(n) - which is really interesting!
Several factors attracted me to this area. The most appealing mathematics to me is learning deep things about familiar objects - prime numbers are inherently interesting and appear when we first start learning mathematics. Secondly, analytic number theory involves lots of the types of mathematics I've enjoyed through my time at university such as complex analysis and integration. It also helps that I can explain what I'm working on to my parents!
I'm going to Oxford to do my PhD under the supervision of [Fields Medallist and Cambridge alumnus] Professor James Maynard. The topic of the PhD isn't decided beyond it being analytic number theory yet, but the direction will evolve once I start as there's a few different areas which seem interesting.
I've been involved with widening participation since my first year, including working on the STEP Support Programme, the Sutton Trust Summer School and open days. I help out because it's a lot of fun talking about maths to interested students but also because I came from a widening participation background and took part in the Sutton Trust Summer School in 2019. I really enjoyed the event - it was what convinced me to apply to Cambridge so I hope to help others and convince them to apply to Cambridge too!
Something I've worked on outside of Tripos at university is a national maths competition, the UK University Integration Bee, which is hosted at 9 universities across the UK. A common integral in competitions is the log sine integral, that is, the integral of log(sin(x)) from 0 to $\pi$/2. While writing resources, I challenged myself to come up with as many methods to solve this integral as possible. I remember being stuck at 9 for at least a month - one day, the 10th method appeared to me as I was working on something else, which I was really happy with! Since then, I've gotten to 12.
Being a Martingale Scholar has given me great opportunities. It made the PhD application process a lot smoother and I now belong to an amazing community of scholars across the UK. Martingale organises lots of events for us too, both social and to help progress our careers. And being in the inaugural cohort means I have the opportunity to shape the future of Martingale!
The Martingale Foundation provides fully-funded Scholarships to enable talented students to pursue Masters and PhDs in STEM subjects at some of the leading research universities in the UK, including Cambridge. You can find out more about the Martingale Foundation scholarships here.
