mathematics

Johannes Widmann

Johannes Widmann is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Johannes Widmann rather than just read about it. In short: Johannes Widmann (c. 1460 – after 1498) was a German mathematician. 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.

Key takeaways

Johannes Widmann belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Johannes Widmann to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Johannes Widmann from memory before moving on to harder problems.

Reference excerpt

Johannes Widmann (c. 1460 – after 1498) was a German mathematician. 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, Bohemia, Widmann attended the University of Leipzig in the 1480s. In 1482 he earned his "Baccalaureus" (Bachelor of Art degree) and in 1485 his "Magister" (doctorate). Widman published Behende und hübsche Rechenung auff allen Kauffmanschafft (German; i.e. Nimble and neat calculation in all trades), his work making use of the signs, in Leipzig in 1489. Further editions were published in Pforzheim, Hagenau, and Augsburg. 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 Leipzig. When Adam Ries was in Erfurt 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, 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.

Illustrations

Worked examples

Example 1 — a first encounter with Johannes Widmann

Start with the simplest possible case. Write down what Johannes Widmann claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Johannes Widmann before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Johannes Widmann ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Johannes Widmann

In research: Johannes Widmann appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Johannes Widmann in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Johannes Widmann is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1460s births, 15th-century German mathematicians, 15th-century German writers, so understanding it makes those chapters shorter.
In everyday life: Look for Johannes Widmann outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Johannes Widmann in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Johannes Widmann means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Johannes Widmann out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Johannes Widmann in simple terms?

Why does Johannes Widmann matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Johannes Widmann?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Johannes Widmann.