In comparison to doing mathematics, writing about the process is a poor thing. Discussing how it’s done is akin to writing a critique, and critics are, compared to actual doers, “second-rate.”

The author confronted scholar and poet A. E. Housman on his admiration for critics. Housman reluctantly agreed with Hardy that perhaps critics don’t have top-notch minds. Hardy thus feels somewhat chagrined that he has now been reduced to analyzing his own work because, having passed the age of 60, he has “no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job” (63).

Despite Einstein’s great achievements, philosophers continue to insist that nothing substantial can ever be known about the nature of reality. Whether that is true (and depending on how one defines those terms), the same certainly can’t be said about the discoveries of mathematics. Evidence of its power is obvious in the many advancements of technology.

For mathematicians, however, these side results don’t fully explain the value of their field. The book is thus an attempt to justify the pursuit of mathematics from the viewpoint of a practitioner, one who may be somewhat “egotistical” but whose successes in the field qualify him to make arguments in favor of doing math.