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In 1903, Epstein published his proof of meromorphic continuation and a functional equation for Dirichlet series associated with quadratic forms, now called Epstein zeta-functions. However, already in 1889 (or even earlier) Hurwitz was aware of these results as his mathematical diaries and some unpublished notes (in an almost final form) found in his estate at the ETH Zurich show. In this article we present and analyze Hurwitz's notes and compare his reasoning with Epstein's paper in detail.

That Euler was quite aware of the subtleties of assigning a sum to a divergent series is amply demonstrated in his paper De seriebus divergentibus which appeared in Novi commentarii academiae scientiarum Petropolitanae 5 (1754/55), 205–237 (= Opera Omnia (1) 14, 585–617) in the year 1760. The first half of this paper contains a detailed exposition of Euler's views which should be more readily accessible to the mathematical community.The authors present here a translation from Latin of the summary and first twelve sections of Euler's paper with some explanatory comments. The remainder of the paper, treating Wallis' hypergeometric series and other technical matter, is described briefly. Appended is a short bibliography of works concerning Euler which are available to the English-speaking reader.

The collection of Riemann's mathematical papers preserved in Gottingen University Library since 1895 includes none of Riemann's scientific correspondence nor any of his more personal papers. The present report gives an account of the documents (correspondence, lecture notes, etc.) discovered outside Gottingen in the course of a larger research project on Riemann, and briefly describes the history of the Riemann Nachlass. At the same time, readers are kindly requested to inform the author of the whereabouts of any further material relating to Riemann, so that it can be included in the collection of texts and sources currently in preparation.

The paper aims to give an insight into the meaning of Kronecker's program of Arithmetisierung of the whole mathematics through a reappraisal of the realization of a small part of it in the reinterpretation of numerical notions such as that of integer, rational, and algebraic number in terms of the fundamental notion of natural number. It tries to convey the flavor of Kronecker's strong and deliberate opposition to both the abstract and the set-theoretic trend which were blossoming during the last three decades of the 19th century, showing at the same time how an attentive reading of Kronecker's papers on the foundations of mathematics can shed some light on how one of his most celebrated aphorisms should properly be understood.ResumenL'articolo intende dare un'idea del significato del programma di Kronecker (di ciò che egli chiamò la Arithmetisirung dell'intera matematica) esponendo e commentando la realizzazione di una porzione specifica di esso: la reinterpretazione nella “aritmetica generale” della nozione di numero intero, di numero razionale e di numero algebrico. Esso mette in luce l'opposizione decisa e consapevole di Kronecker sia alla tendenza astratta sia a quella insiemistica che cominciavano a entrare nella matematica durante gli ultimi trent'anni del secolo XIX, mostrando al tempo stesso come un'attenta lettura dei lavori di Kronecker sui fondamenti della matematica possa far meglio capire il senso in cui egli intendesse uno dei suoi più celebri aforismi.

This paper is concerned with (a) a brief outline of Chebyshev's life; (b) certain background material in connection with Chebyshev's work on approximation and integration in finite terms; (c) the question of whether he already was in Paris in 1842, 10 years prior to his established and presumed first trip to Western Europe; d) his contacts with Catalan, Liouville, Hermite, Lucas, d'Ocagne, Laussedat, and Dwelshauvers-Dery; (e) his contacts with Dirichlet, Borchardt, Kronecker, and Weierstrass; and (f) Chebyshev's last two trips to the West. It is argued that the great Russian scientist did not work in isolation at St. Petersburg. Instead, he was in personal contact, at least until 1884, with many of the greatest European scientists of the time.

One of the significant contributions of Chinese mathematicians is the method of solving numerical equations of higher degree. A number of scholarly works have established similarities between ancient and medieval Chinese root-extraction procedures and Horner's method of solving a numerical equation of any degree. The conceptual development of the Chinese methods, which began with the procedures of extracting square and cube roots during the Han dynasty, culminated in the solution of higher numerical equations in the 13th and the beginning of the 14th centuries. This paper attempts to show the intimate role played by the triangular array of numbers (known in the West as the Pascal triangle) in the process of the development of the Chinese methods, especially when the original geometrical concept was being replaced by the more general algebraic method.