I imagine Bertrand Russell's motivation for participating in the project leading to the Principia Mathematica was an attempt to justify logicism and reject Kant's synthetic a priori, but what was Alfred North Whitehead's motivation?
Perhaps it was just an interesting research project for him, but I wonder if he had reasons coming from a philosophical view of what mathematics was?
Here is a sketch of Whitehead's life from Wikipedia:
Elected a fellow of Trinity in 1884, Whitehead would teach and write on mathematics and physics at the college until 1910, spending the 1890s writing his Treatise on Universal Algebra (1898), and the 1900s collaborating with his former pupil, Bertrand Russell, on the first edition of Principia Mathematica.
This would put him in his late 40s to earthly 50s when Principia Mathematica appeared (1910-1913).
Wikipedia contributors. (2019, June 24). Alfred North Whitehead. In Wikipedia, The Free Encyclopedia. Retrieved 15:56, July 11, 2019, from https://en.wikipedia.org/w/index.php?title=Alfred_North_Whitehead&oldid=903296135