did not actually state the theorem in such terms, and Leibniz did not state it at all. Leibniz was defending the association of the divergent series with the value 1⁄2, while Frobenius' theorem is stated in terms of convergent sequences and the epsilon-delta formulation of the limit of a function. Frobenius' theorem was soon followed with further generalizations by Otto Hölder and Thomas Joannes Stieltjes in 1882. Again, to a modern reader their work strongly suggests new definitions of the sum of a divergent series, but those authors did not yet make that step. Ernesto Cesàro proposed a systematic definition for the first time in 1890. Since then, mathematicians have explored many different summability methods for divergent series. Most of these, especially the simpler ones with historical parallels, sum Grandi's series to 1⁄2. Others, motivated by Daniel Bernoulli's work, sum the series to another value, and a few do not sum it at all. Notes References Cited primary sources The full texts of many of the following references are publicly available on the Internet from Google Books; the Euler archive at Dartmouth College; DigiZeitschriften, a service of Deutsche Forschungsgemeinschaft; or Gallica, a service of the Bibliothèque nationale de France. Written November 9, 1844. Written in October 1879. Cited secondary sources Volume 1, Parte III, Cap. 1, "La questione della serie di Grandi (1696 - 1715)", pp. 296–345. Reiff's German-language work "History of infinite Series" is frequently cited by other sources when they deal with the history of Grandi's series. Hardy (p. 21) calls it "useful but uninspiring and not always accurate." D. J. Struik, editor, A source book in mathematics, 1200-1800 (Princeton University Press, Princeton, New Jersey, 1986). , (pbk). See in particular pp. 178–180 in regard to the versiera (i.e. witch of Agnesi) and Maria Gaetana Agnesi (1718–1799) of Milan, sister of the composer Maria Teresa Agnesi, the first important woman mathematician since Hypatia (fifth century A.D.). Further reading Grandi's series Grandi's Series Grandi's series, History of Parity (mathematics)