Progress is a corollary of evolution. Progress is a prerequisite for survival. Progress is a consequence of human nature. Progress is synonymous with the virtue that in the best instances distinguishes humanity. Physical intuition and an understanding of the important problems that challenge scientists can greatly help a mathematician.
All worthwhile mathematics has direct and obvious practical application.
The best mathematics is the fruit of pure curiosity that originates in the playfulness of an individual mind and not in attempts to satisfy the pragmatic needs of others. While there are several equally valuable flavors of mathematics, students must choose and only the most exceptional students can hope to do good work in both pure and applied areas. By his pioneering example, he showed a younger generation skills that have become key for scientific productivity. He reached a wide audience through his books and articles. Through letters and numerous collaborations, he achieved great influence among his professional peers.