Michael Stifel

Last updated
Michael Stifel
Michael Stifel.jpeg
Contemporain gravure of Michael Stifel
Born1487
DiedApril 19, 1567
NationalityGerman
Alma mater University of Wittenberg
Known forArithmetica integra (containing an early version of logarithms)
Scientific career
FieldsTheology, mathematics
Institutions University of Jena
Michael Stifel's Arithmetica Integra (1544), p. 225. Michael Stifel's Arithmetica Integra (1544) p225.tif
Michael Stifel's Arithmetica Integra (1544), p. 225.

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

Contents

Life

Stifel was born in Esslingen am Neckar in southern Germany. 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 by the Jörger family tk serve at their residence, Tollet Castle in Tollet (close to Grieskirchen, Upper Austria). [1] Due to the tense situation in the Archduchy of Austria in the wake of the execution of Leonhard Kaiser in Schärding, Stifel returned to Wittenberg in 1527. At this time Stifel started writing a book collecting letter transcripts of Martin Luther, completed in 1534. [2]

By intercession of Martin Luther, Stifel became minister in Lochau (now Annaburg). Luther also confirmed his marriage to the widow of his predecessor in the ministry. Michael Stifel was fascinated regarding the properties and possibilities of numbers; he studied number theory and numerology. He also performed the "Wortrechnung" (i.e. word-calculation), studying the statistical properties of letters and words in the bible (a common method at that time). 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 would occur and 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 an unusual track, can be traced back to this incident. [3] 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. He studied "Die Coss" (the first algebra book written in German) by Christoph Rudolff and Euclid's Elements in the Latin edition by Campanus of Novara. Jacob Milich supported his scientific development and encouraged him to write a comprehensive work on arithmetic and algebra. [4] [5] In 1541 he registered for mathematics at the University of Wittenberg [6] to extend his mathematical knowledge. In 1558 Stifel became first professor of mathematics at the new founded University of Jena. [7]

Mathematics

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: and . [8] The book contains a table of integers and powers of 2 that some have considered to be an early version of a logarithmic table. Stifel explicitly points out, that multiplication and division operations in the (lower) geometric series can be mapped by addition and subtraction in the (upper) arithmetic series. On the following page 250, he shows examples also using negative exponents. He also realized that this would create a lot of work. So he wrote, that regarding this issue marvelous books could be written, but he himself will refrain and keep his eyes shut. [9] [10] [11]

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. The letters A, M, A/S, I, A/S each are representing a single operation step when solving a quadratic equation. Stifel, however avoided to show the negative results. [12] [13]

Another topic dealt with in the Arithmetica integra are negative numbers (which Stifel calls numeri absurdi). Negative numbers were refused and considered as preposterous by the authorities at that time. Stifel however, used negative numbers equal to the other numbers. He also discussed the properties of irrational numbers and if the irrationals are real numbers, or only fictitious (AI page 103). Stifel found them very useful for mathematics, and not dispensable. Further issues were a method of calculating roots of higher order by using binomial coefficients [14] and sequences.

Notes

  1. publication of kathpress (2013), letter of Martin Luther to Countess Dorothea Jörger regarding a request of Michael Stifel (in German)
  2. Michael Stifel, collection of handwritten transcripts (1534), "Martin Luther Briefe and Sermone; Michael Stifel Passionsharmonie" (Latin/German), Wittenberg, digitized version of University Library Jena
  3. Stiefel (einen Stiefel reden / schreiben) Retrieved 01/11/2012
  4. Kurt Vogel (1981), Stifel, Michael Complete Dictionary of Scientific Biography. 2008. on Encyclopedia.com. 6 Dec. 2014 <http://www.encyclopedia.com>[ permanent dead link ]. (the years at Holzdorf)
  5. Moritz Cantor (1857), "Petrus Ramus, Michael Stifel, Hieronymus Cardanus, drei mathematische Charakterbilder aus dem 16. Jahrhundert"(German) essay in "Zeitschrift für Mathematik und Physik /Literaturzeitung Band 2" (1857), Digitized version of the Heidelberg University Library
  6. Album academiae vitebergensis 1502–1560, Leipzig 1841
  7. Uni Jena, prominent persons. "Namhafte Hochschullehrer und Studenten aus der Jenaer Universitätsgeschichte" (selection, in German) on http://www.uni-jena.de
  8. Michael Stifel (1544). arithmetica integra. Johann Petreium, Nuremberg. p.  237. arithmetica integra.
  9. Michael Stifel (1544). arithmetica integra. Johann Petreium, Nuermberg. p. 249B. arithmetica integra.
  10. Walter William Rouse Ball (1908). A short account of the history of mathematics. Macmillan and Co. p.  216. arithmetica integra logarithms.
  11. Vivian Shaw Groza and Susanne M. Shelley (1972). Precalculus mathematics. 9780030776700. p. 182. ISBN   978-0-03-077670-0.
  12. Michael Stifel (1544). arithmetica integra. Johann Petreium, Nuremberg. p. 240B. arithmetica integra.
  13. Bertram Maurer (1999). Abhandlung über Leben und Werk Stifels / scientific paper regarding life and work of Michael Stifel (in german). Kolping-Kolleg Stuttgart.
  14. Bertram Maurer (1999). Abhandlung über Leben und Werk Stifels / scientific paper regarding life and work of Michael Stifel (in german). Kolping-Kolleg Stuttgart.

Related Research Articles

Arithmetic Elementary branch of mathematics

Arithmetic is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis. The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider part of number theory.

Diophantus Alexandrian Greek mathematician

Diophantus of Alexandria was an Alexandrian Hellenistic mathematician, who was the author of a series of books called Arithmetica, many of which are now lost. His texts deal with solving algebraic equations. While reading Claude Gaspard Bachet de Méziriac's edition of Diophantus' Arithmetica, Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted in the margin without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat's Last Theorem. This led to tremendous advances in number theory, and the study of Diophantine equations and of Diophantine approximations remain important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. This term was rendered as adaequalitas in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought.

Number theory Branch of mathematics

Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of objects made out of integers or defined as generalizations of the integers. Number theory seeks to understand the properties of integer systems in spite of their apparent complexity.

Number Mathematical description of the common concept

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. For being manipulated, individual numbers need to be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows representing any number by a combination of ten basic numerals called digits. In addition to their use in counting and measuring, numerals are often used for labels, for ordering, and for codes. In common usage, a numeral is not clearly distinguished from the number that it represents.

Exponentiation Mathematical operation

Exponentiation is a mathematical operation, written as bn, involving two numbers, the baseb and the exponent or powern. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases:

Negative number Real number that is strictly less than zero

In mathematics, a negative number is a real number that is less than zero. Negative numbers represent opposites. If positive represents a movement to the right, negative represents a movement to the left. If positive represents above sea level, then negative represents below sea level. If positive represents a deposit, negative represents a withdrawal. They are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, a decrease in some quantity may be thought of as a negative increase. If a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common sense idea of an opposite is reflected in arithmetic. For example, −(−3) = 3 because the opposite of an opposite is the original value.

Mathematical table Tables used to quickly evaluate mathematical functions

Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Tables of trigonometric functions were used in ancient Greece and India for applications to astronomy and celestial navigation. They continued to be widely used until electronic calculators became cheap and plentiful, in order to simplify and drastically speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks, and specialized tables were published for numerous applications.

University of Jena university located in Jena, Thuringia, Germany

The University of Jena, officially the Friedrich-Schiller University of Jena is a public research university located in Jena, Thuringia, Germany.

Zenzizenzizenzic Obsolete mathematical notation representing the eighth power of a number

Zenzizenzizenzic is an obsolete form of mathematical notation representing the eighth power of a number, dating from a time when powers were written out in words rather than as superscript numbers. This term was suggested by Robert Recorde, a 16th-century Welsh writer of popular mathematics textbooks, in his 1557 work The Whetstone of Witte ; he wrote that it "doeth represent the square of squares squaredly".

Nicomachus of Gerasa was an important ancient mathematician best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek. He was born in Gerasa, in the Roman province of Syria. He was a Neopythagorean, who wrote about the mystical properties of numbers.

Johannes Bugenhagen German theologian

Johannes Bugenhagen, also called Doctor Pomeranus by Martin Luther, introduced the Protestant Reformation in the Duchy of Pomerania and Denmark in the 16th century. Among his major accomplishments was organization of Lutheran churches in Northern Germany and Scandinavia. He has also been called the second Apostle of the North.

Martin Eichler German mathematician

Martin Maximilian Emil Eichler was a German number theorist.

Johannes Petreius German printer

Johann(es) Petreius was a German printer in Nuremberg.

History of logarithms

The history of logarithms is the story of a correspondence between multiplication on the positive real numbers and addition on the real number line that was formalized in seventeenth century Europe and was widely used to simplify calculation until the advent of the digital computer. The Napierian logarithms were published first in 1614. Henry Briggs introduced common logarithms, which were easier to use. Tables of logarithms were published in many forms over four centuries. The idea of logarithms was also used to construct the slide rule, which became ubiquitous in science and engineering until the 1970s. A breakthrough generating the natural logarithm was the result of a search for an expression of area against a rectangular hyperbola, and required the assimilation of a new function into standard mathematics.

Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra.

Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Classically, discrete dynamics refers to the study of the iteration of self-maps of the complex plane or real line. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational, p-adic, and/or algebraic points under repeated application of a polynomial or rational function. A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures.

Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

Andreas Poach was a German Lutheran theologian and Reformer.

The year 1544 in science and technology involved some significant events.

Stanisław Knapowski Polish mathematician

Stanisław Knapowski was a Polish mathematician who worked on prime numbers and number theory. Knapowski published 53 papers despite dying at only 36 years old.

References