Not mentioned so far is Bill Thurston's On proof and progress in mathematics (1994). With more than three hundred citations, it surely qualifies as a classic ... it is a permanent left-column link on Terry Tao's weblog, for example.
Thurston's essay is unique, relative to other such essays, in that it describes (in Section 6, "Some Personal Experiences") not one path, but two distinct paths relating to thought processes in mathematical research:
- a solitary path associated to Thurston's early work on foliations
- a social path associated to Thurston's later work on the Geometrization Conjecture
Thurston's latter approach is the topic of much research today, under various rubrics that include "social media", "social networks", and "roadmapping".
The foresighted points -- by 17 years -- of Thurston's essay include:
- social elements of research can be consciously chosen by individuals
- fundamental mathematics can provide uniquely strong foundations for social enterprises
- healthy mathematical communities make faster progress, and also, a better environment for nurturing the next generation of young mathematicians.
A recent well-respected essay that amounts to a consensus abstraction of Thurston's ideas is the International Roadmap Committee (IRC) More-than-Moore White Paper. For modern-day systems engineers especially, it is very instructive to read-out the main themes of Thurston's 1994 essay from the IRC's 2010 white paper, and thus to appreciate that Thurston's ideas were far ahead of their time.
In particular, the IRC's five consensus preconditions for successful roadmapping are anticipated with near-perfection by Thurston's essay ... and this is why Thurston's essay no doubt will continue to gather new citations through decades to come.