Did Whitehead express his motivation for writing with Russell the Principia Mathematica?

Question

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).

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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

Answer 1

Alfred North Whitehead started his academic career in 1884 as a mathematician. Only towards the '20s Whitehead turned his attention to philosophy.

See Alfred North Whitehead :

Whitehead’s intellectual life is often divided into three main periods. The first corresponds roughly to his time at Cambridge from 1884 to 1910. It was during these years that he worked primarily on issues in mathematics and logic. It was also during this time that he collaborated with Russell.

By the early 1900s, both Whitehead and Russell had completed books on the foundations of mathematics. Whitehead’s 1898 A Treatise on Universal Algebra had resulted in his election to the Royal Society. Russell’s 1903 The Principles of Mathematics had expanded on several themes initially developed by Whitehead. Russell’s book also represented a decisive break from the neo-Kantian approach to mathematics Russell had developed six years earlier in his Essay on the Foundations of Geometry. Since the research for a proposed second volume of Russell’s Principles overlapped considerably with Whitehead’s own research for a planned second volume of his Universal Algebra, the two men began collaboration on what eventually would become Principia Mathematica (1910, 1912, 1913). According to Whitehead, they initially expected the research to take about a year to complete. In the end, they worked together on the project for a decade.

And see A.N. Whitehead's Autobiographical Notes :

My first book, A Treatise on Universal Algebra, was published in February, 1898. [...] The Treatise on Universal Algebra led to my election to the Royal Society in 1903. [...] In 1903 Bertrand Russell published The Principles of Mathematics. This was also a "first volume." We then discovered that our projected second volumes were practically on identical topics, so we coalesced to produce a joint work. We hoped that a short period of one year or so would complete the job. Then our horizon extended and, in the course of eight or nine years, Principia Mathematica was produced.

See also Ivor Grattan-Guinness, Intersections in the Philosophy of Mathematics of A.N. Whitehead (2002).