In order to do great work with one’s life and career, it is essential to choose the right problems: that is, problems that are the most important for humanity to solve.

One American mathematician, Richard Hamming, published two particularly helpful discussions of this topic. 

A Stroke of Genius- Striving for Greatness in All You Do

In Hamming’s A Stroke of Genius- Striving for Greatness in All You Do, he discusses the qualities needed to work on important problems with one’s life.

Here are a few highlights:

• An important aspect of any problem is that you have a good attack, a good starting place, some reasonable idea of how to begin.
• Knowing when to persist is not easy – if you are wrong then you are stubborn, but if you turn out to be right, then you are strong willed.
• These traits are not all essential but tend to be present in most doers of great things in science.
  • First, successful people exhibit more activity, more energy, than most people do.
  • This trait must be coupled with emotional commitment. Deep emotional commitment seems to be necessary for success. The reason is obvious. The emotional commitment keeps you thinking about the problem morning, noon and night, and that tends to beat out mere ability.
  • Courage is another attribute of those who do great things. Without courage you are unlikely to attack important problems with any persistence, and hence not likely to do important things. Courage brings self-confidence, an essential feature of doing difficult things.
  • There is another trait that took me many years to notice, and that is the ability to tolerate ambiguity.
  • Another obvious trait of great people is that they do their work in such a fashion that others can build on top of it.
• You need a vision of who you are and where your field is going.
• While you are leaning things you need to think about them and examine them from many sides. By connecting them in many ways with what you already know, you can later retrieve them in unusual situations.
• Some of the greatest work was done under unfavourable conditions.
• The evidence is overwhelming that steps that transform a field often come from outsiders.
  • When someone’s flavor of brains does not match yours may be more reason for paying attention to them.
• It is in the struggle and not in the success that the real gain appears. In striving to do great things, you change yourself into a better person.

You and Your Research: my key lessons

Here are some great points from You and Your Research (not all are direct quotes, some are my interpretations of his points):

• First admit that you want to do first-class, important work.
• “Luck favours the prepared mind” – Louis Pasteur.
• Think original thoughts and have the courage to pursue them.
• Work on small problems that lead you to the big ones.
• Great scientists have tremendous drive and hard work.
• Knowledge and productivity are like compound interest.
• Be committed to the problem but have some tolerance of ambiguity.
  • This helps you to have a critical eye for the points about your theory that don’t add up.
• Identify what are the important problems in your field and then how you can attack them.
• Problems are only important if you have a reasonable attack on them.
• When you find the right problem, drop everything else and go after it until it is solved.
• Be open to collaboration and inspiration from your peers.
• Get good at selling.
• Educate your bosses.
• Know your value and also your weaknesses.