From Churchie to Columbia University and now the rapidly evolving world of artificial intelligence, Old Boy Ivan Zelich (2015) has followed a path driven by curiosity, ambition and a passion for mathematics. Having recently completed a PhD in Pure Mathematics at Columbia University in New York City, he shares his reflections on life in America, his research journey and what’s next.

New York

New York is an unstoppable force. It’s an engine pumping unrelentingly forward but never backward.

For someone growing up in Brisbane, living in New York required some getting used to. Having peace and quiet, clean streets or shops, politeness or generosity, doesn’t come freely. You want to be heard? Speak louder. You want peace? Go upstate. You want healthy food? Find it. New York really teaches you the lesson that it’s your job to find your place in a city that has everything. Once you find that place, welcome aboard the time-tested unstoppable train with your ticket to success.

More prosaically, I loved my time in New York. Everyone I met there was highly driven and motivated, always up to talk turkey and expand their web of connections. The sheer amount of skyscrapers seen when driving into NYC, representing generations of hard work, never ceases to amaze me. There is no shortage of things to do: music concerts, comedy and Broadway shows, jazz festivals, sport games, you name it. The soul of the city, especially during the Fall months leading up to Christmas, is truly unique, and I look back on my time in NYC fondly.

Columbia University

While I always wanted to attend an Ivy League university, I didn’t quite understand what that truly meant. My primary motivation for attendance was to do good research, and Columbia’s pure mathematics department is world-class. But Columbia provided much more than an education. Obtaining a PhD at Columbia was opening doors left, right and centre. There was no shortage of recruiting events by elite companies, and it certainly felt that the name of the university carried weight.

In terms of my research work, I achieved what I set out to do. While I attended Churchie, I was inspired by the works of Alexander Grothendieck to one day pursue algebraic geometry for a PhD. My area could be loosely described as studying the symmetries of numbers through a geometric lens.

My advisor was Aise Johan de Jong, one of the most prolific living algebraic geometers. Early on, he told me about a problem he had been trying to solve for years, originally proposed by Grothendieck in the 1960s. At the time, the problem seemed impossible and I did not feel I had the experience to tackle it. Instead, I solved a number of other problems that felt more achievable.

In the final six months of my PhD, I decided to give Grothendieck’s problem my full attention. After a long run in Central Park, I stumbled upon an idea. As I began to scribble down my thoughts, all of the ideas I had accumulated over those six months started to fit together until finally the puzzle revealed itself, and the problem was solved.

I then wrote the solution down, finished my thesis, successfully defended my work before a defence panel and obtained my doctorate.

What’s Next?

After the PhD, I wanted to start working in the AI industry. I had already begun taking courses at Columbia in my free time about a year before finishing my doctorate, which led to opportunities to undertake paid AI research within the Computer Science Department and apply machine learning to biological research.

This is another aspect of education in America that truly stood out to me: cross-disciplinary research is welcomed with open arms. In the end, I secured a position with an AI startup in Palo Alto and am extremely excited for the next steps.

All in all, my biggest recommendation for studying abroad in the USA is to take advantage of every opportunity you can. When there’s a will, there’s a way, and I think New York and Columbia University exemplify that.