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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

New information concerning Isaac Wolfram's life and calculations


Author: R. C. Archibald
Journal: Math. Comp. 4 (1950), 185-200
MSC: Primary 01.0X
MathSciNet review: 0037814
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  • [1] R. C. A., MTAC, v. 1, p. 57; Wolfram, and Peters & Stein errata.
  • [2] R. C. A., MTAC, v. 2, p. 161-163; Wolfram errata.
  • [3] R. C. A., MTAC, v. 2, p. 340, and v. 3, p. 171; Wolfram and Lambert.
  • [4] R. C. A., ``Wolfram's table,'' Scripta Mathematica, v. 4, 1936, p. 99-100, 293.
  • [5] C. R. Cosens, ``A note on the errors in W. Thiele's table of hyperbolic logarithms to 48 decimals, with some remarks on previous tables taken from the original work of Wolfram.'' Unpublished manuscript dated August 7, 1939 and sent to me in that month. Mr. Cosens (of the Engineering Laboratory, University of Cambridge) computed a number of ln $ x$, to 52D, in testing the accuracy of the table. In writing my paper, some of Mr. Cosens' material has been useful. He had not seen the 1778 edition of Wolfram when he wrote his note.
  • [6] J. H. Lambert, Beyträge zum Gebrauche der Mathematik und deren Anwendungen. Berlin, 3v., 1765, 1770, 1772; v. 3, p. [vi-xi] of the Vorrede contains Wolfram's list of 70 errors in Table I of no. 7 as well as in the Sherwin-Sharp and Clausberg tables. See no. 9(a)(XVIII-XX); v. 2 contains a complete factor table (p. 42-53 + large folding plate.)
  • [7] J. H. Lambert, Zusätze zu den logarithmischen und trigonometrischen Tabellen. Berlin, 1770.
  • [8] J. C. Schulze, ``Zusätze und Verbesserungen der Berliner Sammlung trigonometrischer Tafeln,'' Berliner Astronomisches Jahrbuch für das Jahr 1783, Berlin, 1780, p. 191; six missing logarithms, calculated by Wolfram are given, as well as the note by Barzellini, of a Wolfram error. Barzellini's calculation of the values of the 6 missing lns agreed with that of W.
  • [9] Deutscher gelehrter Briefwechsel Joh. Heinr. Lamberts. Edited by Johann (III) Bernoulli, Berlin, (a) v. 4, 1784; (b) v. 5, 1785, p. 1-242, and 1787, p. 243-502. (a): Correspondence between Wolfram and Lambert, Letters XVIII-XXXIX, 5 March 1772- 9 August 1777, p. 436-536. XVIII W(L), = letter from W. to L., dated Namur 5 March, 1772 (436-440); XIX L(W) Berlin 21 March, 1772 (441-445); XX W(L) Namur 3 August, 1772 (445-469) (see no. 6, above); XXI L(W) Berlin 19 December, 1772 (469-476); XXII W(L) Namur 8 February, 1773 (477-484); XXIII L(W) Berlin 13 March, 1773 (484-492); XXIV W(L) Namur 5 April, 1773 (493-496); XXV W(L) Namur 26 July, 1773 (497-500); XXVI L(W) Berlin 21 August, 1773 (501-507); XXVII W(L) Danzig 29 July, 1774 (507-509); XXVIII L(W) Berlin 11 August, 1774 (509-512); XXIX L(W) 28 August, 1774 (513); XXX W(L) Danzig 6 September, 1774 (514-516); XXXI W(L) Nimwegen 14 April, 1775 (516-519), notes on L(W) (519); XXXII W(L) Nimwegen 2 April, 1776 (520-522); XXXIII Nimwegen 18 October, 1776 (523-524); XXXIV L(W) Berlin 30 Nov. 1776 (528-529); XXXV W(L) Nimwegen (528-530); XXXVI W(L) Nimwegen 24 January, 1777 (530); XXXVII L(W) Berlin 8 March, 1777 (531-534); XXXVIII W(L) Nimwegen 18 April, 1777 (535); XXXIX L(W) Berlin 9 August, 1777 (536). On p. 531-532 and 536 there are references to another letter W(L) dated 21 March, 1777. In editing these letters Bernoulli supplied annotations. The Nimwegen here evidently corresponds to Mr. Kemperman's Nijmegen. Lambert died in the month following the one in which he wrote his last letter to W. (b); P. 353-464 constitute supplements to (a), p. 474f, 491, 500, 503, 508, 517, 523, 529. There are many new tables, new Wolfram letters and other valuable material. There are references to 5 other W. letters: to L.(14 October, 1773, p. 368; 30 December, 1773, p. 368, 383; 17 March 1774, p. 392, and for all 3 to v. 4, p. 508); to Schulze (28 April, 1779, p. 463-464), and to Geheim Kriegsrath Davisson in Dantzig (Helvoetsluys, 2 March, 1781, p. 461-463). In connection with this last letter W. records errors in his table at 1900, 4357, 7247, 8963.
  • [10] P. Erman, Académie R. d. Sciences ..., Berlin, Mémoires, MDCCXCIV et MDCCXCV, Berlin, 1799, p. 55-70.
  • [10a] J. C. Burckhardt, Tables des Diviseurs. Paris, 1817, p. [iii]; correction of ln 7853.
  • [11] J. B. J. Delambre, Histoire de l'Astronomie Moderne. V. 1, Paris, 1821, p. 501, 511-513, 519.
  • [12] J. P. Kulik, ``Auszug aus einem Briefe . . . 1824, May 13,'' Astron. Nachrichten, v. 3, 1824, cols. 191-192; list of 17 common errors in Wolfram and Vega tables (K. was incorrect in listing an error in ln 1658) and a description of the partial publication of an extension of this table; also idem, v. 4, cols. 47-48, April, 1825; further details of this publication. Earlier recordings of two W. errors noted by K. are 4891 (Barzellini), 7853 (Burckhardt), 1900 (Wolfram).
  • [13] C. Gudermann, J. f. d. reine u. angew. Math., v. 9, 1831, p. 362; notes Wolfram error at 1099 (earlier reported by Kulik).
  • [14] A. De Morgan, article ``Table,'' (a) Penny Cyclopaedia, Suppl., v. 2, London, 1846, p. 600-603; (b) English Cyclopaedia, Arts and Sciences Section, London, v. 7, 1861, cols. 1000-1001; high praise of Wolfram's work but inaccurate description of its contents.
  • [15] P. Gray, Tables for the Formation of Logarithms & Antilogarithms, to Twelve Places, London, 1865, p. 39; Wolfram error in connection with 1409 noted.
  • [16] A. F. D. Wackerbarth, R. A. S., Mo. Not., v. 27, 1867, p. 254; Wolfram error in connection with 1099 noted (already published by Kulik and Gudermann).
  • [17] D. Bierens de Haan, ``Bouwstoffen voor de Geschiedenis der wis- en natuurkundige Wetenschappen in de Nederlanden,'' Akad. v. Wetenschappen, Afd. Natuurk., Verslagen, s. 2, v. 10, 1876, p. 189-191, 202-204; also reprinted in a volume with the above title, 1878, p. 199-201, 212-214.
  • [18] J. W. L. Glaisher, Report of the Committee on Mathematical Tables. London, 1873, p. 69, 126. In the Wolfram paragraph on p. 126, line 8, for 47 read 43; and in the last line, for 38, read 39.
  • [19] A. Steinhauser, Hilfstafeln zur präcisen Berechnung zwanzigstelliger Logarithmen. . . . Vienna, 1880, p. iii, 1; Wolfram error in connection with 6343.
  • [20] D. Bierens de Haan, Bibliographie Néerlandaise Historique--Scientifique des Ouvrages Importants . . . sur les Sciences Mathématiques et Physiques. Rome, 1883, p. 309-310.
  • [21] M. Cantor, Vorlesungen über Geschichte d. Mathematik. V. 4, Leipzig, 1908, p. 299, 436, 438; notably trivial.
  • [22] R. Mehmke & M. d'Ocagne, Encycl. d. Mathématiques, t. 1, v. 4, fasc. 2, 1908, p. 306.
  • [23] J. Henderson, Bibliotheca Tabularum Mathematicarum. Part I. Cambridge, 1926; p. 138, 178, three inaccurate statements: (i) about Wolfram's table; (ii) that Gray noted the error discovered by Gudermann (see note 13); (iii) that Wolfram calculated the common logarithm table, p. 259, only once (see note 8); p. 191 more than one misleading statement about the Thiele table.
  • [24] F. J. Duarte, Nouvelles Tables de Log n! à 33 Décimales depuis n = l jusqu'au = 3000. Geneva and Paris, 1927, p. iii; errors noted in Wolfram's table in connection with 829, 1087, 1409, 1900. On July 23, 1874, T. M. Simkiss reported the 829 case to J. W. L. Glaisher but his result was unpublished before 1928; earlier recordings 1087 (Peters & Stein), 1409 (Gray), 1900 (Wolfram and Kulik).
  • [25] F. J. Duarte, Nouvelles Tables Logarithmiques. Paris, 1933, p. xxii; eleven Wolfram (1794 table) errors, including 3 of these listed in no. 24--the other 8 being in connection with 3571, 3967, 6343, 7247, 7853, 8837, 8963, 9623--earlier recordings being 3571 (Peters & Stein), 6343 (Steinhauser), 7247 and 8963 (Wolfram), 7853 (Kulik).
  • [26] MNYMTP, Table of Natural Logarithms. V. 1-4, Washington, 1941, p. xi, xi, xi, xiii, respectively. W. errors are noted in 829, 1099, 1409, 1937, 1938, 2093, 3571, 4757, 6343, 7853, 8023, 8837, 9623, but the first announcement was made only in connection with 2093 and 8023.
  • [27] FMR, Index. 1946, p. 176-177, 432, 437, 440, 443; inaccurate contents descriptions for Thiele and Wolfram.
  • [28] J. H. Lambert, Opera Mathematica, ed. by A. Speiser. Zürich, v. 1, 1946, p. xiv, xx, 123, 205; v. 2, 1948, p. ix, 70-71. We find in these v. various parts of Beytrdge,' v. 1-3, and the essential parts of the Zusätze.'
  • [30] In no bibliography except the British Museum Catalogue of Printed Books, and the catalogue of the Royal Observatory Library, Edinburgh, could I find any reference to a Sarganeck: J. J. Schmidt, Biblishcer Mathematicus, Oder Erläuterung der Heil. Schrift aus den Mathematischen Wissenschaften ... Als ein Anhang ist beygefüget Herrn Georg Sarganeck's Versuch einer Anwendung der Mathematic in dem Articul von der Grösse der Sünden-Schulden. Zullichau, 1736, 27 plates, 11 ff + 672 p. + 16 ff.
  • [31] A. G. Kästner published 10 volumes beginning with this word, hence it is not easy to determine which one refers to the Leibniz series; perhaps it was Anfangsgründe der Analysis des Unendlichen. Leipzig, 1760.

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DOI: http://dx.doi.org/10.1090/S0025-5718-1950-0037814-2
PII: S 0025-5718(1950)0037814-2
Article copyright: © Copyright 1950 American Mathematical Society