Johannes Widmann (c. 1460 – after 1498) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. The + and - symbols first appeared in print in his book ''Mercantile Arithmetic'' or ''Behende und hüpsche Rechenung auff allen Kauffmanschafft'' published in Leipzig in 1489 in reference to surpluses and deficits in business problems. Born in

Eger Eger ( , ; ; also known by other alternative names) is the county seat of Heves County, and the second largest city in Northern Hungary (after Miskolc). A city with county rights. Eger is best known for its castle, thermal baths, baroque build ...

Bohemia Bohemia ( ; cs, Čechy ; ; hsb, Čěska; szl, Czechy) is the westernmost and largest historical region of the Czech Republic. Bohemia can also refer to a wider area consisting of the historical Lands of the Bohemian Crown ruled by the Bohem ...

, Widmann attended the

University of Leipzig Leipzig University (german: Universität Leipzig), in Leipzig in Saxony, Germany, is one of the world's oldest universities and the second-oldest university (by consecutive years of existence) in Germany. The university was founded on 2 Decemb ...

in the 1480s. In 1482 he earned his "

Baccalaureus A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six ye ...

" (Bachelor of Art degree) and in 1485 his " Magister" (doctorate). Widman published ''Behende und hübsche Rechenung auff allen Kauffmanschafft'' (

German German(s) may refer to: * Germany (of or related to) ** Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ge ...

; i.e. Nimble and neat calculation in all trades), his work making use of the signs, in

Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as wel ...

in 1489. Further editions were published in

Pforzheim Pforzheim () is a city of over 125,000 inhabitants in the federal state of Baden-Württemberg, in the southwest of Germany. It is known for its jewelry and watch-making industry, and as such has gained the nickname "Goldstadt" ("Golden City") ...

Hagenau Haguenau (; Alsatian: or ; and historically in English: ''Hagenaw'') is a commune in the Bas-Rhin department of France, of which it is a sub-prefecture. It is second in size in the Bas-Rhin only to Strasbourg, some to the south. To the n ...

, and

Augsburg Augsburg (; bar , Augschburg , links=https://en.wikipedia.org/wiki/Swabian_German , label=Swabian German, , ) is a city in Swabia, Bavaria, Germany, around west of Bavarian capital Munich. It is a university town and regional seat of the ' ...

. Handwritten entries in a surviving collection show that after earning his "Magister" Widman announced holding lectures on e.g. calculating on the lines of a calculating board and on algebra. There is evidence that the lecture on algebra actually took place, making it the first known university lecture on this topic. Around 1495 Widmann published the Latin writings ''Algorithmus integrorum cum probis annexis'', ''Algorithmus linealis'', ''Algorithmus minutiarum phisicarum'', ''Algorithmus minutiarum vulgarium'', ''Regula falsi apud philosophantes augmenti et decrementi appellata und Tractatus proportionum plusquam aureus''. He died in

. When

Adam Ries Adam Ries (17 January 1492 – 30 March 1559) was a German mathematician. He is also known by the name Adam Riese. Life Almost nothing is known about Ries' childhood, youth and education. The exact year of his birth is not known. The caption o ...

was in

Erfurt Erfurt () is the capital and largest city in the Central German state of Thuringia. It is located in the wide valley of the Gera river (progression: ), in the southern part of the Thuringian Basin, north of the Thuringian Forest. It sits i ...

between 1518 and 1522 he got to know Widmann's algebra lecture script (today in the Saxon State Library) wherefrom he took examples for his own writings.

References

Sources

* Barbara Gärtner, ''Johannes Widmanns „Behende und hübsche Rechenung“. Die Textsorte „Rechenbuch“ in der Frühen Neuzeit'', Tübingen 2000. (Germanistische Linguistik. 222.) *

M. Cantor Moritz Benedikt Cantor (23 August 1829 – 10 April 1920) was a German historian of mathematics. Biography Cantor was born at Mannheim. He came from a Sephardi Jewish family that had emigrated to the Netherlands from Portugal, another branch of ...

, ''Vorlesungen über Geschichte der Mathematik'' II (Leipzig, 1913), pp. 228s. *K. Fogel, ''Merchants' aids in practical arithmetic from the Middle Ages'' (Russian), Istor.-Mat. Issled. No. 23 (1978), pp. 235–249; 359. *W. Kaunzner and H. Wussing (eds.), ''Adam Ries, Coss'' (B.G. Teubner Verlagsgesellschaft mbH, Stuttgart, 1992). *Karl Röttel, ''Johannes Widmann – Am Wendepunkt der Mathematikgeschichte''. In: Schatzkammer der Rechenkunst. Annaberg-Buchholz 2008. *K. Vogel,'' Biography in Dictionary of Scientific Biography'' (New York 1970-1990). * Franz Xaver Wilhelm, ''Zur Biographie des Mathematikers Johann Widmann von Eger. In: Mitteilungen des Vereins für Geschichte der Deutschen in Böhmen'', Volume 45 (1907), pp. 429–430. 1460s births People from Cheb Medieval German mathematicians Algebraists 15th-century German mathematicians 15th-century German writers 15th-century Latin writers Leipzig University faculty Year of death unknown {{Germany-mathematician-stub