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ZbMATH Open

ZbMATH Open 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 ZbMATH Open rather than just read about it. In short: zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society, FIZ Karlsruhe, and the Heidelberg Academy of Sciences. zbMATH is distributed by Springer Science+Business Media.

Key takeaways

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

Reference excerpt

zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society, FIZ Karlsruhe, and the Heidelberg Academy of Sciences. zbMATH is distributed by Springer Science+Business Media. It uses the Mathematics Subject Classification codes for organising reviews by topic.

History Mathematicians Richard Courant, Otto Neugebauer, and Harald Bohr, together with the publisher Ferdinand Springer, took the initiative for a new mathematical reviewing journal. Harald Bohr worked in Copenhagen. Courant and Neugebauer were professors at the University of Göttingen. At that time, Göttingen was considered one of the central places for mathematical research, having appointed mathematicians like David Hilbert, Hermann Minkowski, Carl Runge, and Felix Klein, the great organiser of mathematics and physics in Göttingen. His dream of a building for an independent mathematical institute with a spacious and rich reference library was realised four years after his death. The credit for this achievement is particularly due to Richard Courant, who convinced the Rockefeller Foundation to donate a large amount of money for the construction. The service was founded in 1931, by Otto Neugebauer as Zentralblatt für Mathematik und ihre Grenzgebiete. It contained the bibliographical data of all recently published mathematical articles and book, together with peer reviews done by mathematicians over the world. In the preface to the first volume, the intentions of Zentralblatt are formulated as follows:

Zentralblatt für Mathematik und ihre Grenzgebiete aims to publish—in an efficient and reliable manner—reviews of the entire world literature in mathematics and related areas in issues initially appearing monthly. As the name suggests, the main focus of the journal is mathematics. However, those areas that are closely related to mathematics will be treated as seriously as the so-called pure mathematics.

Zentralblatt and the Jahrbuch über die Fortschritte der Mathematik had in essence the same agenda, but Zentralblatt published several issues per year. An issue was published as soon as sufficiently many reviews were available, in a frequency of three or four weeks. In the late 1930s, it began rejecting some Jewish reviewers and a number of reviewers in England and United States resigned in protest. Some of them helped start Mathematical Reviews, a competing publication. The electronic form was provided under the name INKA-MATH (acronym for Information System Karlsruhe-Database on Mathematics) since at least 1980. The name was later shortened to Zentralblatt MATH. In addition to the print issue, the services were offered online under the name zbMATH since 1996. Since 2004 older issues were incorporated back to 1826. The printed issue was discontinued in 2013. Since January 2021, the access to the database is now open under the name zbMATH Open.

Jahrbuch über die Fortschritte der Mathematik The Jahrbuch über die Fortschritte der Mathematik (Yearbook on the Progress of Mathematics) was internationally the first comprehensive journal of abstracts in the history of mathematics. It contains information about almost all of the most important publications in mathematics and their areas of application from the period 1868 to 1942. The Jahrbuch was written in 1868 by the mathematicians Carl Ohrtmann (1839–1885) and Felix Müller (1843–1928). It appeared annually with a few exceptions and initially contained 880 references per year (1868) and up to 7000 references in the later phase (around 1930). Some of the mathematical abstracts were written by famous mathematicians such as Felix Klein, Sophus Lie, Richard Courant, or Emmy Noether. During WW II publication of the Jahrbuch was stopped. The Jahrbuch's founding concept was characterized by its documentary completeness. The Jahrbuch only appeared when all papers in a year had been completely processed. This was later paid for with a great loss of relevance. In addition, there was since 1931 the Zentralblatt MATH, which surpassed the Jahrbuch in terms of speed of publication.

Services The Zentralblatt MATH abstracting service provides reviews (brief accounts of contents) of current articles, conference papers, books and other publications in mathematics, its applications, and related areas. The reviews are predominantly in English, with occasional entries in German and French. Reviewers are volunteers invited by the editors based on their published work or a recommendation by an existing reviewer. Zentralblatt MATH is provided both over the Web and in printed form. The service reviews more than 2,300 journals and serials worldwide, as well as books and conference proceedings. Zentralblatt MATH is now edited by the European Mathematical Society, FIZ Karlsruhe, and the Heidelberg Academy of Sciences.

The database also incorporates the 200,000 entries of the earlier similar publication Jahrbuch über die Fortschritte der Mathematik from 1868 to 1942, added in 2003. As of January 2021, the complete database is accessible for free. Previously, only the first three records in a search were available without a subscription.

Awards In 2024, zbMATH Open is awarded the Demailly prize for open science.

See also All-Russian Mathematical Portal List of academic databases and search engines Mathematical Reviews, published in the United States MathSciNet Referativny Zhurnal, published in the former Soviet Union and now in Russia

References

External links

Official website Jahrbuch database Archived 2013-07-23 at the Wayback Machine

Worked examples

Example 1 — a first encounter with ZbMATH Open

Start with the simplest possible case. Write down what ZbMATH Open 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 ZbMATH Open 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 ZbMATH Open 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 ZbMATH Open

In research
ZbMATH Open 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 ZbMATH Open 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
ZbMATH Open is common in secondary-school and first-year university syllabi. It links to neighbouring topics Bibliographic databases and indexes, Mathematical databases, Online databases, so understanding it makes those chapters shorter.
In everyday life
Look for ZbMATH Open 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 ZbMATH Open in 20 minutes

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

Frequently asked questions

What is ZbMATH Open in simple terms?

zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society…

Why does ZbMATH Open 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 ZbMATH Open?

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 ZbMATH Open.

Tags

  • Bibliographic databases and indexes
  • Mathematical databases
  • Online databases
  • Publications established in 1931

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