Conway’s Recipe for Success

One fine day in January 2010, John H. Conway shared with me his recipe for success.

1. Work at several problems at a time. If you only work on one problem and get stuck, you might get depressed. It is nice to have an easier back-up problem. The back-up problem will work as an anti-depressant and will allow you to go back to your difficult problem in a better mood. John told me that for him the best approach is to juggle six problems at a time.

2. Pick your problems with specific goals in mind. The problems you work on shouldn’t be picked at random. They should balance each other. Here is the list of projects he suggests you have:

  • Big problem. One problem should be both difficult and important. It should be your personal equivalent to the Riemann hypothesis. It is not wise to put all your time into such a problem. It most probably will make you depressed without making you successful. But it is nice to get back to your big problem from time to time. What if you do stumble on a productive idea? That may lead you to become famous without having sacrificed everything.
  • Workable problem. You should have one problem where it’s clear what to do. It’s best if this problem requires a lot of tedious work. As soon as you get stuck on other problems, you can go back to this problem and move forward on the next steps. This will revive your sense of accomplishment. It is great to have a problem around that can be advanced when you do not feel creative or when you are tired.
  • Book problem. Consider the book you are working on as one of your problems. If you’re always writing a book, you’ll write many of them. If you’re not in the mood to be writing prose, then work on math problems that will be in your book.
  • Fun problem. Life is hardly worth living if you are not having fun. You should always have at least one problem that you do for fun.

3. Enjoy your life. Important problems should never interfere with having fun. When John Conway referred to having fun, I thought that he was only talking about mathematics. On second thought, I’m not so sure.

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2 Comments

  1. More on choosing problems to work on: advice from John H. Conway « Successful Researcher:

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  2. Cristi Stoica:

    Hi, this is my first comment on your nice blog.

    The first point in the recipe reminded me of Feynman’s advice (as presented here: http://www.math.osu.edu/~nevai/MYMATH/rota_ams_notices_01_97.html):

    “Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!””

    Of course, the two advices are different, and probably they can be combined, for example Conway’s six problem may be a subset of Feynman’s 12.