# Jordan Barrett

Jordan was not originally a mathematician; he came to Te Herenga Waka—Victoria University of Wellington to study Physics and Computer Science.

“The MATH161 paper really opened my eyes to a whole new side of mathematics you don’t see at school—namely discrete mathematics, logic and graph theory. It was the first time mathematics was presented to me as an exploration of structures and patterns, rather than a sequence of computations and rules to memorise.”

After switching to a mathematics major, Jordan found his mathematical curiosity was still not satiated so he began an Honours degree. “This has allowed me to delve much deeper into topics of interest as well as round out my mathematics knowledge. At Honours level the classes are much smaller and you have much better chances to interact one-on-one with your lecturers and soak up some of their genius.”

In his coursework, Jordan is exploring mathematical logic, delving into questions such as, “What does it mean for a statement to be true/false?”, “What is a mathematical proof?” and “What does it mean to calculate something?”. Currently, Jordan is working with Professor Rod Downey and Professor Noam Greenberg on reverse mathematics—looking at a mathematical statement and then establishing which axioms are needed to prove the statement. For his project, Jordan is currently exploring Cousin’s Lemma using reverse mathematics.

In addition to Honours, Jordan has been involved in mathematical research through the Summer Research Scholars programme in both 2018/19 and 2019/20. The programme has enabled Jordan to dive deep on some big questions in mathematics. “Mathematical research is the polar opposite of a maths exam—instead of solving problems under time pressure, you have significantly harder problems to solve, but unlimited time in which to do it. Some of these problems require hundreds of years and many, many great minds to solve.”

These summer research opportunities have enabled Jordan to have some co-authored publications under his belt before moving on to further postgraduate research projects, including an exploration of partition regularity of Diophantine equations. “Dr Martino Lupini and I used some tools from nonstandard analysis to prove certain equations were not partition regular. Then along with Joel Moreira, we used tools from topological dynamics and ergodic theory to prove certain equations were partition regular.”

The second research project was also with Dr Lupini and focused on different problems in Ramsey theory, still using the tools of nonstandard analysis. Together they have been able to extract a common generalisation—forthcoming in their write up of the project.

“You have to love math, and you have to learn to manage your brain time. I plan to begin a PhD in 2021. After completing my PhD, I aim to get a research or lecturing position in mathematics, and hopefully start a long and illustrious career as a logician.”