"Before coming to Canberra, I considered research in mathematics as somewhat of an exalted pursuit that only a few chosen people could aspire to.”

“Now that I have done it, it seems like anyone can, and that is exactly how I wish mathematics was viewed at large."

These are the first words you’ll see if you read Shehzad Hathi’s PhD thesis in mathematics.

When most people think of high-level mathematics, mind-numbing equations probably come to mind, and you’d be forgiven for immediately thinking of something else.

But not Shehzad, who graduates this week from UNSW Canberra having completed his PhD. He can appreciate the beauty and value in mathematics as a discipline and hopes others will too.

Growing up in Rajkot, in western India, Shehzad wanted to be a lot of things before deciding he wanted to be a mathematician. After a visit to Lothal, the site of a prehistoric civilisation close to his home, he wanted to be an archaeologist. Later, science-fiction books made him want to pursue a career in astrophysics.

But when a retired schoolteacher began to teach local students ‘non-routine mathematics’, Shehzad was hooked.

“It was maths for the sake of maths,” Shehzad recalls.

“He would teach me and many others like me for free, his only expectation being that we were infinitely curious.

“My perception of mathematics transformed from being that of a soulless machine in the service of science to an end in itself, capable of not only holding its own as an intellectual pursuit but also a vantage point from where to look at other scientific disciplines.”

Studying mathematics took Shehzad on a journey across the globe, first completing an undergraduate degree in Kanpur in northern India, before completing a master’s degree in Padova, Italy and Bordeaux, France.

Shehzad then chose to complete his PhD at UNSW Canberra for the opportunity to work with his supervisor, Tim Trudgian, and because the university offered him the chance to pursue the kind of research he was interested in.

Shehzad’s thesis examined a collection of results on different, but related, equations. His favourite result focused on the well-known Goldbach conjecture, an unsolved mathematical problem dating back to 1742. It states that every even number greater than 2 is the sum of two prime numbers, and has stumped mathematicians for centuries.

“While it doesn't seem like the mathematical community is anywhere close to solving the problem, we have some really good partial results,” Shehzad says.

“I was able to prove a partial result in a problem very similar to the Goldbach problem.

"It was really exciting to be able to contribute to the accumulated knowledge about this problem that dates back centuries.”

While the equations proved difficult, Shehzad’s PhD experience wasn’t without other challenges. But these taught him valuable lessons about resilience and when to lean on your support networks.

During his PhD studies, Shehzad was diagnosed with vestibular migraines. These are a type of migraine that, along with a recurring headache, can cause balance problems.

“In my case, these issues were quite persistent, and I was unable to do even the most basic stuff like cooking, reading and running,” Shehzad says.

“What was even more frightening was the prospect that this condition was permanent, as there is no way to know when it will abate.”

Shehzad contemplated taking a break from his PhD while he recovered, but with persistence he learned to manage the things that were likely to trigger the migraines so that he could continue his studies.

“Meditation and running played a crucial role in being able to overcome the condition,” he says.

“Along the way, I set small goals for myself, such as conducting a tutorial class for an hour, being able to read a full paper, or walking around Lake Burley Griffin.

“Tim [Trudgian] and everyone else in my research group were extremely supportive during this difficult period.

“I couldn’t have done it without them.”