Article Title：Algebras, projective geometry, mathematical logic, and constructing the world: Intersections in the philosophy of mathematics of A.N. Whitehead
Abstract：
A. N. Whitehead (1861-1947) contributed notably to the foundations of pure and applied mathematics, especially from the late 1890s to the mid 1920s. An algebraist by mathematical tendency, he surveyed several algebras in his book Universal Algebra (1898). Then in the 1900s he joined Bertrand Russell in an attempt to ground many parts of mathematics in the newly developing mathematical logic. In this connection he published in 1906 a long paper on geometry, space and time, and matter. The main outcome of the collaboration was a three-volume work, Principia Mathematica (1910-1913): he was supposed to write a fourth volume on parts of geometries, but he abandoned it after much of it was done. By then his interests had switched to educational issues, and especially to space and time and relativity theory, where his earlier dependence upon logic was extended to an ontology of events and to a general notion of process, especially in human experience. These innovations led to somewhat revised conceptions of logic and of the philosophy of mathematics. (C) 2002 Elsevier Science (USA).
Keywords: Whitehead; foundations of mathematics; Principia Mathematica; process philosophy
DOI: 10.1006/hmat.2002.2356
Source：HISTORIA MATHEMATICA
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