Here are additional mathematicians' thoughts.

S. Ulam, [Adventures of a mathematician][1].A recollection of his life, from Lwow to Los Alamos. I am linking to excerpts. The book is still available for purchase. 

[Advices to a Young mathematician][2], a collection of advice and anecdotes by M. Atiyah, B. Bollobas, A. Connes, D. McDuff and P. Sarnak.

A. Borel, [Art and science][3] (Math. Intelligencer vol.5 1983, translation from German). A text for a general audience about the relationship between art and mathematics.

R. P. Langlands [Is there beauty in mathematical theories?][4], this text is actually about number theory, old and new.

T. Gowers [The two cultures of mathematics][5], another take on the dichotomy between problem solving and theory building.

A. Connes [A view of mathematics][6], a thorough exposition of A. Connes'philosophical stance about space and physics. Targeted at a scientific audience.

D. Mumford, [the dawning of the age of stochasticity][7], from algebraic geometry to statistics.

Y. Manin, [Interrelations between Mathematics and Physics][8], on the divergence between mathematics and physics in the XXe century.

M. Gromov, [ergobrain][9], one of the most surprising inquiry about life and mathematics.

I end that list with a text from a french mathematician about the future of mathematics: Poincare, [l'avenir des mathematiques][10].


  [1]: http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-87-3600-02
  [2]: https://press.princeton.edu/chapters/gowers/gowers_VIII_6.pdf
  [3]: http://www.forthelukeofmath.com/documents/borel.pdf
  [4]: http://publications.ias.edu/sites/default/files/ND.pdf
  [5]: https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf
  [6]: http://www.alainconnes.org/docs/maths.pdf
  [7]: http://www.dam.brown.edu/people/mumford/beyond/.../2000b--DawningAgeStoch-NC.pdf
  [8]: https://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_3_157-168.pdf
  [9]: http://www.ihes.fr/~gromov/PDF/ergobrain.pdf
  [10]: http://www.mathunion.org/ICM/ICM1908.1/Main/icm1908.1.0167.0182.ocr.pdf