Finding My Own Niche

I enjoy doing research in recreational mathematics. The biggest problem is that the probability that something I’ve done has already been done before is very high. This is partially because of the nature of this area of research. Trying to find new questions that are not buried deep in the abstract means someone else could have stumbled upon the same question. In addition, I like going in different directions: geometry, number theory, probability, combinatorics, and so on. That means I am not an expert in any of the areas. This too increases my probability of doing something that has already been done before.

This is quite unpleasant: to discover that I reinvented the wheel. And I keep reinvented different wheels on a regular basis. When I complain, my mathematician friends give me the same advice over and over:

Find your own niche!

I’ve been trying to understand what they mean, and finally I got it:

Do something no one else is interested in using methods no one else can understand.

Finding a topic that is not interesting almost guarantees that other people didn’t do it before. Developing new complicated methods helps limit the number of followers and prevents the niche from becoming crowded.

Now I know why I see so many boring math papers I can’t understand.

To hell with my own niche!



  1. Felipe Pait:


  2. Mike:

    Well said and wisely considered! And you know what, it’s completely cool to re-invent the wheel. It means you got the same joy of discovery at discovering the wheel as the original discoverer did. It’s like time travel. And it makes you less of a passive consumer who merely receives each new wheel, and more of an engineer who fashions your own wheels. Maybe your discoveries aren’t completely novel, but they are new and original to you, which means you are just as clever as whoever came across it first. And, who knows, someday, if you keep following your muse rather than succumb to the desire to find the undiscovered country, said muse may lead you someplace wondrously pristine. If not, at least travelling with your muse is a much more enjoyable ride than being alone with hypothermia because you wanted to be the first at the North Pole.

  3. Charles G:

    I remember when I was 19 and I discovered that every odd number could be represented as the difference of two perfect squares. I was on top of the world, thought I’d be getting a PhD at 19. Then I found that a French guy named Fermat had discovered this same thing about 200 years prior. I let it ruin the moment for a while, but then I realize how much I enjoyed that feeling. So who cares if I’m the first or just the latest.

    Then when was applying for graduate school and later for jobs, I was asking the same questions, but a lot more practically. I did find that as well studied as algorithms are in computer science, there are still ample opportunities to be the first to apply some of these algorithms to problems that have real world value. One key thing is that some algorithms are still new so for each new algorithm that is discovered, there is a question of how broad we can apply it. But from the other angle, there are always emerging industries that pose problems similar to those of yesterday but have a small twist that means the the old algorithms won’t quite work.

    But I don’t focus on this. I’m like you in the sense that I’m much more interested in doing what I love than in discovering the “new thing”. There is so much mathematics that has already been written that I have fun just going to a series of different sites trying to understand a new (to me at least) idea, or trying to explain an old concept that I know others have struggled with.

  4. Misha:

    You finally got the right attitude 🙂

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