I share some thoughts on my experience with the all too common mathematical imposter syndrome. It must be emphasised that imposter syndrome disguises as modesty, but is a destructive and often self-fulfilling force. I hope in sharing, another future VRS scholar may find some comfort and confidence such that they can achieve closer to their full mathematical potential.

In a workshop for a mathematics unit last year, some friends and I lamented our feeling of imposter syndrome. “No matter how well you do”, we conjectured, “there always seems to be this shadow-person lurking in the background, always doing better; always doing more”. A deep, German voice ominously warned: “that feeling doesn’t go away”. The voice belonged to our professor.

As mathematicians, we accept ideas only if we can prove them. Induction is insufficient. Perhaps this is why academic validation seems necessary but far from sufficient in giving us confidence to sit in the same room as people who always seem so much smarter than us. Genius is abundant in mathematics, and so it is very easy to feel inferior, rightly or wrongly, compared to your peers.

In the beginning of this research project, I genuinely felt as though my mathematical academic journey was approaching its limit. As I was increasingly surrounded by highly intelligent experts, what should have been inspiration was replaced by dread that I would be unable to keep up. It is tempting to assign your own imposter syndrome to being an act of modesty. I want to be very clear that it is not. It is a destructive force that is at the very least demotivating and can go as far to prevent you from achieving your potential. I found this point especially pertinent as I began to read and engage with highly technical papers as part of my research. When you don’t believe you are capable of grasping these papers, it can be extremely difficult to find the resilience to spend the time that is required to understand them. Maths is hard, after all, and perseverance is the only way to experience the reward it offers.

Sometime close to halfway through the research project, I managed to get over myself. Maybe I am an imposter…maybe I really am bad at maths…who cares? I had a presentation to make, and that leaves no room for wallowing in self-deprecation. Once you fix your resolve that you will attack a complicated task fearlessly, but ready to learn and ask questions, you will be amazed at how far you can go.

We must admit that we may never have the natural ability of Einstein or Tao. We must be comfortable with this, and realise that we shouldn’t place any expectation to do so. Don’t let your feeling of inadequacy get in the way of you doing fun and beautiful maths. If you’ve made it this far, there’s a good chance you can make the next step. Tao at age 5 couldn’t do what you’re doing (maybe he could at age 6…who knows?), and you probably couldn’t do what you’re doing now a few years ago. Stay humble, curious and confident in your mathematical journey, and whether or not you win a Fields medal, it will be time well spent.

Joshua Troy
University of Western Australia

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