\input zb-basic \input zb-matheduc \iteman{ZMATH 2007a.00238} \itemau{Otte, Michael} \itemti{Russel's introduction to mathematical philosophy.} \itemso{Educ. Mat. Pesqui. 3, No. 1, 11-55 (2001).} \itemab Summary: Bertrand Russell is an important and interesting figure, undoubtedly the most read, honored, and reviled English-speaking philosopher of the twentieth century. And his Introduction of Mathematical Philosophy' is no less fascinating. Indeed, Russell's above-mentioned work, published in 1918, has sometimes rightly been called an admirable exposition of the monumental work Principia Mathematica'. The main object of Russell's book is number, and everything belonging to number, to arithmetic, and to the logic of arithmetic. The foundations of arithmetic always remained the focus of Russell's interest in logic and mathematics, and his views had a profound influence on the reform movement of mathematics education that began around 1960. Since the beginning of the $19^{th}$ century, mathematics showed a strong tendency towards arithmetization, because space and the continuum seemed beset with seemingly intractable otherness. By the end of the $19^{th}$ century, even number appeared not to be so transparent and so immediately given anymore and the question 'what numbers are' arose to explain and to complete the foundations of arithmetic itself by means of logical analysis and set theoretical construction. \itemrv{~} \itemcc{E20 E60} \itemut{foundation of mathematics; mathematics and philosophy; concept of number; set theory; new maths; history of mathematics} \itemli{} \end