Joshua O’Callaghan
The University of Queensland
I am an honours student in mathematics at the University of Queensland, interested in number theory of both the analytic and algebraic flavour.
Give me a quick overview of the type of mathematics you are studying, and/or the aims of your research and its potential applications/outcomes
I am studying the spacing statistics of the sequence of prime numbers. This is
interesting in itself: questions of this kind date back to (at least) Euclid. It also relates to other sequences of numbers occurring in nature and mathematics such as the energy levels of large nuclei and the fractional parts of the square roots of large numbers. It’s natural to ask if the spacings of the prime numbers and these other sequences behave like the gaps between randomly chosen numbers or if they follow strange and mysterious laws.
How did you get into the mathematical sciences? Was there someone or something that inspired you to this field?
I was drawn to mathematics for the patience it seemed to demand. My peers and lecturers inspire me.
You received a grant to attend AMSI Summer School. How important was this in terms of your ability to attend, fully participate in the program and meet others studying in similar fields?
Without the travel grant I would have struggled to come to AMSI Summer School 2026 in person, which I believe was absolutely necessary to get the best out of the event. Meeting new people, discussing mathematics, attending lectures in person – these were essential to the experience.
What was the most valuable part of the program for you?
Meeting peers from around Australia.
In the long-term, what do you think are the benefits of having attended Summer School?
The content I learnt in lectures and the connections I made.
Summer School included a special Careers Day program which aims to help give students an idea of the kinds of career paths available to maths graduates in industry and private sector research areas. Do you feel better equipped to explore career options in the mathematical sciences after attending AMSI Summer School?
I feel more informed with respect to the options for career paths.
What advice would you give to someone who is considering applying for Summer School in 2027? Should they apply and why?
If you’re interested at all in mathematics, definitely apply. It will prepare you for future study and give you the opportunity to meet wonderful people.
What are your current career ambitions in the mathematical sciences sector?
I would like to continue in research mathematics. Namely, I wish to pursue a PHD.
How did connecting with the community at AMSI Summer School support your experience?
Immensely. It helped me do more and better mathematics.
Any other feedback/comments you would like to provide on the AMSI Travel Grant or AMSI Summer School 2026?
Thank you for the grant and the wonderful 2026 Summer School Experience.