Impostor syndrome is a real feeling and I get it at least twice a day with respect to what I do. Sure, I have a degree from a university saying I can do something and yes, I get paid to do it but all in all I feel like a fraud or a cheat. I’m not a statistician or a data scientist but someone pretending to be one and despite all the work I’ve done, my mind is riddled with a crippling doubt that I don’t really know my subject.
Even now if I see a probability brain teaser designed for some high school class, I have to labour with it for quite some time before I can come up with an answer and sometimes, I’m not even close – what’s happening here? Is my degree worthless? Am I a pretender? Am I not in the right field? Why is everything so complicated or is it that I’m not smart enough?
The best piece of advice I ever received comes from a work colleague who sat me down one day and was explaining some elementary computer science theory to me. He went through the material and could probably see from my face that I didn’t comprehend a word of what he was saying. My ego was bruised, and I remained silent and nodding as if I was right there with him all the while knowing that if he asked me even one question that I would be undone. It was at this point he looked at me, paused, put down the whiteboard pen and said to me “it’s not special”.
“What do you mean?” I replied, now genuinely worried I had missed an important part of his explanation – I was still concerned about how I would look in front of him. My colleague went on to give a full explanation of his words and they have stuck with me ever since:
“These ideas and concepts, they’re not special. The people who invented them, they were no different to you or me. They were not born more intelligent or with some ability that is outside your grasp. The difference between you and them is that they started from complete ignorance and went step by step building on their knowledge of the subject. They admitted when they didn’t know and did not rest until they found out. They repeated the formula so much that they eventually made their own contribution to the field. They were brilliant but not special, none of this is special. If you ask questions, apply yourself to the material and stick with it you will know this too – it’s not special”.
It was hard to recall the full exchange but one thing I never forgot was the “it’s not special” part of the advice. There are two ways to read it for me, one is in the apparent meaning – knowledge is from humans and just as they grasped it, I can grasp it too. It did not take the great thinkers a day to learn the material so why do I expect it from myself?
The second meaning is about me – I’m not special. I’m not special in the sense that I am not incompetent or inadequate because I haven’t got my head around something. I’m not special in the sense that just because I don’t understand something now – it does not follow that I will never understand it. Every human being I’ve met has eventually got their head around a concept they were struggling with and to which they were applying themselves. It seems to be a general rule that after much head banging and engagement that a breakthrough occurs, and the idea clicks into place.
However, I was not willing to extend this rule to myself; this rule applies for everyone else except me because if I didn’t understand something then I guess I never would, and I should give up. This stems from a destructive belief that I’m special. I’m especially incompetent or incapable compared to everyone else I know. Although this isn’t a classic manifestation of the “I’m special” belief it is a noticeable cousin.
Like many people, Richard Feynman is one of my heroes. There is a great deal of what he said which is remarkable and insightful, but I’d like to bring attention to one statement he made which has a profound impact on me when it comes to struggling with mathematical ideas. This statement can be found at the 12:52 mark in this video and it’s a statement that relates to the best piece of advice I have ever received.
Feynman responds to the interviewer who despondently speaks about the complexity of modern physics:
“But it is not complicated, there’s just a lot of it and if you start at the beginning; which nobody wants to do…”
The transcription really doesn’t do it justice, so I implore you to watch the video clip. Feynman is irritated at the suggestion that these ideas are complicated or rather, are special.
There is a very subtle and deep truth in his words about starting at the beginning (which nobody wants to do) – namely that if you want to understand the complex ideas you must start from the beginning. If you don’t understand an idea, then go one level down to see what other ideas your proposed idea rests on and very often you will find that your foundations need brushing up. Sometimes they need to be reconstructed all over.
Whenever I have been stuck with a mathematical topic, 9 times out of 10 it has been because there was something in the underlying foundations that I didn’t grasp clearly enough so I go back and review my fundamentals. This has led me to opening up topics that I haven’t touched since my school days and starting again from there – but eventually I get back to the original idea and achieve that “Eureka” moment of seeing all the pieces fit together.
Being successful at any type of mathematical work is about the attitude – it’s not a special ability gained from mystical experience or conveyed from a great teacher. Kevin Houston writes in the final chapter of his brilliant book How to think like a mathematician
“The one big secret that separates out the mathematicians from the non-mathematicians. It is attitude. It takes time to explore mathematics…. If you have the attitude that understanding is crucial – not superficial understanding but the understanding that comes from a deep attack on a problem – and if you are always looking beyond what you have been given, then magically you will understand what you have been given.”
I’ve found these words to ring true in my experience. I’m not there yet and I always have a voice in my head that I’m an impostor or exceptionally incompetent but whenever I hear it or feel overwhelmed, I always come back to this advice mentioned in this post. I’m doing the best I can, and I have the blessing of loving what I do. All those I look up to use this basic formula and since I’m too lazy to be original I will copy them in this regard. Mathematics is challenging and it is hard – but it’s not special.