 By 1902, both Whitehead and Russell had reached this same conclusion. Both men were in the initial stages of preparing second volumes to their earlier books on related topics: Whitehead’s 1898 A Treatise on Universal Algebra and Russell’s 1903 The Principles of Mathematics. Since their research overlapped considerably, they began collaborating on what would eventually become Principia Mathematica. By agreement, Russell worked primarily on the philosophical parts of the project, including the book’s philosophically rich Introduction, the theory of  descriptions,  and the no-class theory (in which set or class terms become meaningful only when placed in well-defined contexts), all of which can still be read fruitfully even by non-specialists. The two men then collaborated on the technical derivations. As Russell writes,