Enjoy your work

No profit grows where is no pleasure ta’en;
In brief, sir, study what you most affect.

— William Shakespeare, The Taming of the Shrew

To really get anywhere in mathematics requires hard work. If you don’t enjoy what you are doing, and do not derive satisfaction from your contributions, it will be difficult to put in the sustained amounts of energy required to succeed in the long term.

In general, it is much better to work in an area of mathematics which you enjoy, than one which you are working in simply because it is fashionable. For similar reasons, one should base one’s work satisfaction on realistic achievements, such as:

• Advancing the state of knowledge in one’s specialty
• Improving one’s understanding of a field
• Communicating this understanding successfully to others

Rather than basing it on exceptionally rare events, such as:

• Spectacularly solving a major open problem
• Achieving major recognition from one’s peers

(Daydreams of glory may be pleasant to indulge in for a few moments, but they are poor sustenance for the patient, long-term effort required to actually make mathematical progress, and overly unrealistic expectations in this regard can lead to frustration.)

Enthusiasm can be infectious; one reason why you should attend talks and conferences is to find out what other exciting things are happening in your field (or in nearby fields), and to be reminded of the higher goals in your area (or in mathematics in general). A good talk can recharge your own interest in mathematics, and inspire your creativity.