The Divine Proportion: A Study in Mathematical Beauty,
 by H. E. Huntley, Dover Publications (1970)

A CAREER IN MATHEMATICS

If you, the reader, contemplate a career in pure or applied
mathematics, whether in industry or research, or in the
teaching profession, you should be warned that although there
can be one infallible, enduring reward for you in this
pursuit-joy in creative activity-there stand certain
discouraging hazards, of which four may be noted briefly:

1. The burden of hard mental concentration is a sine qua non.
You may find that you have to live with a problem day and night
for weeks, giving all you have of mental resources in order to
solve it: no inspiration without perspiration.

2. Your best efforts may be fruitless. Despite extravagant
expenditure of time and skill, the result is nil.
Disappointment, frustration and near-despair are common
experiences of serious mathematicians.

3. You may be lonely. Scarcely anyone will appreciate your work
because few will be capable of understanding it.

4. The results you do obtain will always appear to be
disproportionately meager in comparison with the effort you
expended to produce them: "The mountain laboured and brought
forth a mouse."


The one sure path to satisfaction in a mathematics career is to
cultivate assiduously the aesthetic appreciation of the
discipline. That pleasure will not fade, it will grow with
exercise.