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This text presents the ideas of a particular group of mathematicians of the late 18th century known as "the German combinatorial school" and its influence. The book tackles several questions concerning the emergence and historical development of the German combinatorial analysis, which was the unfinished scientific research project of that group of mathematicians. The historical survey covers the three main episodes in the evolution of that research project: its theoretical antecedents (which go back to the innovative ideas on mathematical analysis of the late 17th century) and first formulation, its consolidation as a foundationalist project of mathematical analysis, and its dissolution at the beginning of the 19th century. In addition, the book analyzes the influence of the ideas of the combinatorial school on German mathematics throughout the 19th century.
List of contents
1. A History of the Binomial and Multinomial Theorems.- 2. The Emergence of the German Combinatorial Analysis.- 3. The Consolidation of the German Combinatorial Analysis.- 4. The Decline of the German Combinatorial Analysis.- 5. A Combinatorial Current of Thought.- Epilogue.
Report
"This book is the first extensive study of Combinatorial Analysis, a movement and style of mathematics that was popular in the German-speaking states at the end of the 18th century. ... With Noble's study, historians of mathematics now finally have a detailed insight in how Combinatorial Analysis developed from being a one-man's project to a research programme that was joined ... ." (Maarten Bullynck, Historia Mathematica, November 23, 2024)
"Taken as an intellectual chapter in the history of mathematics, Noble's monograph stands apart for its exhaustive account of an unfinished scientific research project associated with this school, namely the German combinatorial analysis. ... This volume is suitable for advanced students and researchers in the history of 18th century German mathematics." (Judith R. Goodstein, Mathematical Reviews, May, 2023)
