**Jakob Kulik**'s first name is, in addition to the common form Jakob, sometimes written as Jacob or Yakov. When he was born in Lvov, the city was known as Lemberg and was part of the Austrian Empire. Today the usual spelling of the city is Lviv and it is in Ukraine. Although Lvov was in the Austrian Empire, the inhabitants were largely Polish speaking and, indeed, Kulik's family considered themselves Polish. He attended the Philosophy Faculty of Lvov University and, after graduating, began to study law at the university. However, he soon lost interest in law as he became more and more fascinated by mathematics. He never completed his law degree.

In 1814 a competition was announced for the position of professor of elementary mathematics at the Lyceum in Olomouc (the German name for the town is Olmütz). Kulik entered the competition and was judged the best applicant, worthy of a professorship. He accepted the position and, while teaching in Olomouc, he undertook research towards a doctorate. While still undertaking research for his doctorate, he moved from Olomouc to Graz in 1816 when he was appointed Professor of Physics and Applied Mathematics at the Lyceum there. In the following year of 1817 he took on additional duties, teaching astronomy at the Joanneum in Graz. He received his doctorate in 1822 for a thesis which studied the rainbow, then, from 1826, he was Professor of Higher Mathematics at the Charles University of Prague. In November 1848, the year of revolution when many students joined in an insurrection, the library of the University of Lvov was destroyed by fire. Kulik donated over 1000 books to help rebuild the collection at the University in the town of his birth where he had studied. He remained in Prague until his death in 1863. He was buried in the Vysehrad Cemetery in that city.

Kulik wrote textbooks on mathematics and mechanics, for example publishing *Lehrbuch der höheren Analysis* (1^{st} edition 1831, 2^{nd} edition 1844) and *Anfangsgründe der höheren mechanik* in 1846. He also published his thousand-year calendar *Der tausendjährige Kalender* in 1831 (with a 2^{nd} edition 1834). The calendar claims to be:-

... a useful handbook for historians, archivists, judges, lawyers, country clergymen, and even for those who wish to determine chronological data occurring in old manuscripts, history books, and documents.

Kulik is best known, however, for producing numerous mathematical tables including an unpublished table of divisors of integers consisting of 4212 pages. His first publication of mathematical tables was *Handbuch mathematischer* (1824). The contents are described by Raymond Archibald [1]:-

In the 'Handbuch' are30tables including the following:1-2:

All factors of numbers up to21500and the smallest factors up to67100.3-4

: Squares and cubes of numbers up to1000and higher powers of numbers up to100.5:

Square roots and cube roots of numbers up to1000.15, 19:

Natural and logarithmic sin and tan.16:

Natural secants.28: 11

-place log of prime numbers up to1811.

Clearly Kulik intended this as part of a larger work which was never completed [1]:-

In the "Vorerinnerung," dated November,1823, Kulik states that his 'Tafeln' are an extract from a larger work, to be published in the year1824, and entitled 'Collectio tabularum mathematico-physicarum locupletissima, vollständige Sammlung mathematisch-physicalischer Tafeln'. Among various volumes of tables which Kulik wrote I do not find that this one is ever mentioned, not even in the bibliography sent by Kulik to Poggendorff(1863)nearly40years later.

Perhaps some of the tables which Kulik intended for this larger publication were contained in his next volume which was published in 1825, namely *Divisores numerorum decies centena millia non excedentium. Accedunt tabulae auxiliares ad calculandos numeri cujuscunque divisores destinatae. Tafeln der einfachen Faktoren aller Zahlen unter Einer Million nebst Hülfstafeln zur Bestimmung der Factoren jeder grösseren Zahl.* Unlike the earlier work, the tables presented here are all related to primes and factors. He continued to work on producing various tables, some of which he did not publish until many years after he had begun the work. The next tables he published were: conversion tables *Toasirtafeln, zur leichtern Berechnung des Längen- Flächenund Kubik-Inhaltes und der verschiedenen Münz- Mass- und Gewichts-Beträge* (1833); a table of squares and cubes *Tafeln der Quadrat- und Kubik-Zahlen aller natürlichen Zahlen bis hundert Tausend, nebst ihrer Anwendung auf die Zerlegung grosser Zahlen in ihre Faktoren *(1848); multiplication tables *Neue Multiplikationstafeln: ein unentbehrliches Hülfsmittel für Jedermann, um schnell, sicher und ohne Ermüdung zu rechnen* (1851); and tables of hyperbolic sectors and elliptic arcs *Tafeln der hyperbolischen Sektoren und der Längen elliptischer Bögen und Quadranten* (1851).

Kulik's most impressive work, however, if one is just thinking about the sheer magnitude of the task, was his unpublished tables of factors. He did publish a description of the unpublished tables in 1860 and, in 1866, Józeph Petzval also described Kulik's tables. In [4] Howard Eves states that Kulik's greatest achievement was the construction of these factor tables:-

His as yet unpublished manuscript is the result of a twenty-year hobby, and covers all numbers up to100,000,000.

Similar statements are made in many other books, see for example Leonard Dickson's comments in [3]. Kulik's manuscripts are kept in the archives of the Austrian Academy of Sciences (Kaiserliche Akademie der Wissenschaften in Wien) in Vienna, and Novy has studied them and has written [6] and [7] to correct false statements about them such as the one by Eves above. Novy gives the following summary of his article [6]:-

The manuscript tables of J P Kulik(1793-1863), kept in the Archives of the Austrian Academy of Sciences of Vienna, are commonly alleged to give the least divisors of all numbers up to100million. The incorrectness of this assertion is demonstrated by an analysis of the manuscript materials including the unknown auxiliary computations made by Kulik. In the paper it is shown that the computations are incomplete, and that the least divisors of only certain numbers are entered in the tables, starting at the23rd million. In comparison with the preserved part of the tables(the tables from13,000,000to23,000,000are lost), the auxiliary computations reaching in a complete succession up to20million may be of greater value, although diminishingly so going up to80million. A description of Kulik's methods of computation is also given, and documents are referred to which substantiate the hypothesis that Kulik was helped in his work by collaborators. Meanwhile, we also give the basic dates for the rest of the tables(especially of trigonometric functions)deposited in Kulik's Nachlass in Vienna.

Novy is even more direct in his criticisms of the unpublished tables in [7]:-

... the manuscript of Kulik's tables of divisors is essentially useless beginning with the third volume; the second volume, which has been lost, could perhaps tell us more about the real value of the manuscript.

Kulik's methods of calculating his tables and other manuscripts left by him are, however, very interesting and are discussed in [7]. Other work by Kulik which we have not mentioned above includes: *Theorie und Tafeln der Kettenlinie* (1832); *Untersuchungen über die Kettenbrückenlinie* (1838); and *Über die Tafel primitiver Wurzeln* (1853).

The Union of Czech Mathematicians and Physicists began its existence on 28 May 1862 when the Society for Open Lectures in Mathematics and Physics in Prague was founded. Initially it was a student Society for students at the Charles University of Prague, but university teachers quickly supported the Society. In particular Kulik gave strong support and in the year after the Society was founded he donated a large part of his extensive library of mathematics books to the Society. When he died the rest of his library was left to the Society.

Let us end this biography by quoting the mathematician Frantisek Josef Studnicka (1836-1903), a colleague of Kulik's at the Charles University of Prague, who wrote of Kulik's death (see [10]):-

He stopped calculating and living.

**Article by:** *J J O'Connor* and *E F Robertson*