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Computability in principle and in practice in algebraic number theory: Hensel to Zassenhaus

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History of algebraic number theory
Philosophy of mathematical practice
Kurt Hensel
Helmut Hasse
Olga Taussky
Hans Zassenhaus

In the early years of algebraic number theory, different mathematicians built the theory in terms of different objects, and according to different rules, some seeking always to demonstrate that the objects were computable in principle. Later, prominently in the era in which electronic computers were becoming available for academic research, efforts were initiated by some to compute the objects of the theory in practice. By examining writings, research, and correspondence of mathematicians spanning these early and late computational periods, we seek to demonstrate ways in which ideas from the old tradition influenced the new. Among the connections we seek are personal influence on problem selection, and borrowing of computational methods. In particular, we examine such links among the works of Kurt Hensel, Helmut Hasse, Olga Taussky, and Hans Zassenhaus.

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Copyright remains with the author. The author granted permission for the file to be printed and for the text to be copied and pasted.
Michael Monagan
Science: Department of Mathematics
Thesis type: 
(Thesis) M.Sc.