About the cover: Kummer's tables

Harold M. Edwards
2006 Bulletin of the American Mathematical Society  
The meticulously drafted table on the cover gives a startling glimpse of Ernst Eduard Kummer's method of work. Although anyone who reads Kummer's papers can see that he thought algorithmically and that his discoveries were based on the experience of extensive calculations, this table reveals that the scope of his calculations was beyond what anyone today would think was feasible without computing machines. The story behind the tables is told in a communication Kummer made to the Berlin Academy
more » ... the Berlin Academy in 1850 [3], in which he explains that his work in 1846-7 on the arithmetic of cyclotomic integers had led him to conjecture a certain reciprocity law for this arithmetic. (He doesn't use the modern term "cyclotomic integers" and calls them "complex numbers", but he was dealing with a very special integral domain contained within the field of complex numbers, namely, for a fixed prime λ, the integral domain generated over the integers by a primitive λth root of unity.) The exact statement of his conjecture is not difficult to give, as the interested reader can see by reading his statement of it in the paper. (For an explanation in English, see [1] .) But the subject here is not the law itself but the extensive tables Kummer compiled to convince himself of its truth. The tables were enough to convince him that his conjecture was correct, or at least to be convinced enough to want to tell his mentor and cousin by marriage,
doi:10.1090/s0273-0979-06-01139-6 fatcat:3yvgiqds6rcxvo7vm2ubjfmn7u