Michael Stifel

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Michael Stifel
Born 1487
Died April 19, 1567
Nationality German
Fields Theology, mathematics
Institutions University of Jena
Alma mater University of Halle-Wittenberg
Known for Arithmetica integra cf. Logarithms
Michael Stifel's Arithmetica Integra (1544), p. 225.

Michael Stifel or Styfel (1487 – April 19, 1567) was a German monk and mathematician. He was an Augustinian who became an early supporter of Martin Luther. He was later appointed professor of mathematics at Jena University.


Stifel was born in Esslingen am Neckar. He joined the Order of Saint Augustine and was ordained a priest in 1511. Tensions in the abbey grew after he published the poem Von der Christförmigen, rechtgegründeten leer Doctoris Martini Luthers (1522, i.e. On the Christian, righteous doctrine of Doctor Martin Luther) and came into conflict with Thomas Murner. Stifel then left for Frankfurt, and soon went to Mansfeld, where he began his mathematical studies. In 1524 upon a recommendation by Luther Stifel was called to the Jörger on Tollet Palace in Tollet close to Grieskirchen, Upper Austria.[1] Stifel returned to Wittenberg in 1527 and then married and became minister in Lochau, where George Spalatin frequently resided. Stifel married the widow of his predecessor in the ministry. The tranquil life in Lochau again led him to mathematical studies and he performed, what he called "Wortrechnung" (i.e. word-calculation), studying the statistical properties of letters and words in the bible. In 1532 Stifel published anonymously his "Ein Rechenbuchlin vom EndChrist. Apocalyps in Apocalypsim" (A Book of Arithmetic about the AntiChrist. A Revelation in the Revelation). This predicted that Judgement Day the world would end at 8am on October 19, 1533. The German saying "to talk a Stiefel" or "to calculate a Stiefel" (Stiefel is the German word for boot) meaning to say or calculate something based on a wrong track can be traced back to this incident.[2] When this prediction failed, he did not make any other predictions. In 1535 he became minister in Holzdorf near Wittenberg and stayed there for 12 years.

In 1541, during his time as minister in Holzdorf, he registered for mathematics at the University of Wittenberg[3] to extend his mathematical knowledge. In 1558 Stifel became first professor of mathematics at the new founded University of Jena.[4]


Stifel's most important work Arithmetica integra (1544) contained important innovations in mathematical notation. It has the first use of multiplication by juxtaposition (with no symbol between the terms) in Europe. He is the first to use the term "exponent" and also included the following rules for calculating powers: q^m q^n = q^{m+n} and \tfrac{q^m}{q^n} = q^{m-n}.[5] The book contains a table of integers and powers of 2 that some have considered to be an early version of a logarithmic table.[6][7][8]

Stifel was the first, who had a standard method to solve quadratic equations. He was able to reduce the different cases known to one case, because he uses both positive and negative coefficients. He called his method/rule AMASIAS. Stifel, however does not show the negative results.[9][10]

Further topics dealt with in the Arithmetica integra are negative numbers (which Stifel calls numeri absurdi) and sequences.


  1. ^ report (in german) letter of Martin Luther to Countess Dorothea Jörger regarding a request of Michael Stifel
  2. ^ Stiefel (einen Stiefel reden / schreiben) Retrieved 01/11/2012
  3. ^ Album academiae vitebergensis 1502–1560, Leipzig 1841
  4. ^ Uni Jena, list of prominent persons (in german)
  5. ^ Michael Stifel (1544). arithmetica integra. Johann Petreium, Nuremberg. p. 237. 
  6. ^ Michael Stifel (1544). arithmetica integra. Johann Petreium, Nuermberg. p. 249B. 
  7. ^ Walter William Rouse Ball (1908). A short account of the history of mathematics. Macmillan and Co. p. 216. 
  8. ^ Vivian Shaw Groza and Susanne M. Shelley (1972). Precalculus mathematics. 9780030776700. p. 182. ISBN 978-0-03-077670-0. 
  9. ^ Michael Stifel (1544). arithmetica integra. Johann Petreium, Nuremberg. p. 240B. 
  10. ^ Bertram Maurer (1999). Abhandlung über Leben und Werk Stifels / scientific paper regarding life and work of Michael Stifel (in german). Kolping-Kolleg Stuttgart. 


  • Stifel, Michael (1544). "Arithmetica integra"
  • Stifel, Michael (1544). "Arithmetica integra"/"Vollständiger Lehrgang der Arithmetik". german translation by Eberhard Knobloch and Otto Schönberger, Königshausen & Neumann, Würzburg 2007, ISBN 978-3-8260-3561-6.
  • Anon. (Stifel, Michael) (1532). "Ein Rechenbuchlin vom EndChrist. Apocalyps in Apocalypsim" (A Book of Arithmetic about the AntiChrist. A Revelation in the Revelation).
  • Koetsier, Teun and Karin Reich (2005). Michael Stifel and his numerology. pp. 291–310 in Koetsier and Bergmans (2005).
  • Koetsier, Teun and Luc Bergmans (2005). Mathematics and the Divine: A Historical Study. Elsevier.

External links[edit]