Nicola Harif
Monash University
I’m Nicola Harif and I was born and raised in Melbourne. I’ve always had a passion for mathematics but only began pursuing it in the last couple years. I’m currently midway through my Honours year at Monash, with my project being a side-adventure to a paper my supervisor, Dan Mathews, wrote on spinors and their explicit correspondence to horospheres
1. Can you give me a quick rundown about the type of mathematics you are studying and its potential impacts for the broader community (think how you would explain your work and studies to others who don’t study maths)
My studies lie in an intersection of Geometry, Topology and Abstract Algebra. Broadly what I’m trying to do is give a visual representation of what certain collections of spinors can correspond to in hyperbolic space. Spinors are complicated to say the least, but we’ll just say they’re vectors, or arrows, which need to rotate not once but twice to go back to how they were originally. Hyperbolic space is kind of like the reality we live in but there tends to be “more” space available – for instance in 2-dimensions hyperbolic space looks like a curly kale leaf, you can’t lie it down flat on a table without folding it over somehow. The kinds of things I want to know are along the lines of what collections of spinors correspond to “nice” or interesting looking collections of horospheres and why. Due to the type of mathematics I study being so theoretical, as with a lot of pure mathematics, the potential impacts are unclear but I believe visual representations of mathematics helps develop intuition and connections that may have been difficult to attain otherwise. An impact on my immediate community is that I’ve acutely developed the skill of explaining difficult concepts in laymen’s terms.
2. How did you get into mathematics/statistics/data science? Was there someone or something that inspired you to this field?
I’ve been told my journey into maths has been an odd one. I always enjoyed maths as a kid, the kind of kid that enjoyed their maths homework. Straight out of high school I wanted to be an artist, specifically a painter but a year into Art school I realised it wasn’t for me so I took a gap year and ended up transferring into an Engineering/Computer Science degree – because “I was good at maths”. By the first time I saw a mathematical proof I was 20 and completely in awe so I started taking more math units, changed majors, had a taste of Group Theory and something just clicked. Now I’m in the realm of pure maths. In a way I ended up back in a creative field with a lot of abstraction just in a completely different context.
3. You received a Travel Grant to attend AMSI Summer School 2024. How important was this in terms of your ability to attend, fully participate in the program and meet others studying in similar fields? Do you think it was an advantage to attend the program in-person?
The travel grant was integral to me being able to attend and completely dependent on being able to full participate and meet people. I would say it’s extremely advantageous to attend in-person, I mean you can’t really play table tennis online but you can in person against an entire group of people that have the same extremely niche interests as you do. It’s also extremely beneficial to be able to study with people in the same course as you in person, at this level of mathematics it’s so important to discuss the concepts and work with other people. Not only that, you can just sit in on lectures from other courses to learn more about what you like and don’t like, plus you don’t have to deal with the technical problems online-learning can have.
4. What was the most valuable part of the program for you?
Aside from being able to take my course for credit – definitely meeting new people and forming new friendships. There’s a huge range of people that attend the summer school of all demographics and backgrounds. You get to learn more about what the maths community is like around the rest of Australia as well as different career paths and how to transition into them.
5. In the long-term, what do you think are the benefits of having attended Summer School?
It definitely broadens your perspective on your potential as a mathematics student. This is in regards to not only what can come next in the future in terms of study or a career but what you’re capable of doing. I think I also met a lot of people that I’ll have lasting friendships with both personally and professionally.
6. 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 better equipped to explore my career options after attending. The presentations from the Careers Day give you a wide range of places to look for future opportunities but being able to pick the speakers brains for the time afterwards over lunch was even more valuable.
7. What advice would you give to someone who is considering applying for Summer School in 2025? Should they apply and why?
If you have a passion for maths and are considering study beyond a bachelor’s degree then definitely apply, it gives you a great taster for how further study kind of works but as a crash course. Don’t worry about being overwhelmed with your first assignment, it’s usually a shock at how hard it can be and you’ll find that you’ll need to talk to your peers and the lecturer about it as well as a bit of faith in yourself. It should be noted that you will need to study quite a lot while you’re there so manage your time wisely. Generally I wouldn’t recommend the program while you’re working full-time – see if you can take some time off or lighten your duties.
8. What are your current career ambitions in the mathematical sciences sector?
A lot of people tend to have this visceral reaction to me telling them I study maths – it’s one of the few fields where people are very willing to tell you that they absolutely “hate” the thing you find beautiful. For that reason (and obviously others) I’m leaning towards doing something to do with the education sector but not necessarily teaching. The demand for higher capabilities in maths is growing but quite a lot of people will say “Oh, I hated maths when I was in school” or that they’re “bad” at it so I’d like to do something to change that or at least reduce the anxiety and subsequent trauma that they seem to experience in primary/high school. More specifically, I’d like to find my way into a career path that allows me to create and work with other people to find methods of teaching and communicating mathematical ideas with higher engagement than the standard model.
9. How did connecting with the community at AMSI Summer School support your experience?
Connecting with the community at AMSI Summer School made the experience a lot more fun and engaging. Talking to students and lecturers after-hours in a more relaxed environment livened the culture in mathematical fields. I can definitely say to people not in the field that no – we absolutely do not sit around on calculators and solve equations all day. A lot of connecting with people in the community is throwing around out-of-the-box questions, realising how difficult they are to answer, going on wild tangents and then finding more people in the community to help find an answer.