mathematics

Martin Grötschel

Martin Grötschel 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 Martin Grötschel rather than just read about it. In short: Martin Grötschel (born 10 September 1948) is a German mathematician known for his research on combinatorial optimization, polyhedral combinatorics, and operations research. From 1991 to 2012 he was Vice President of the Zuse Institute Berlin (ZIB) and served from 2012 to 2015 as ZIB's President.

Key takeaways

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

Reference excerpt

Martin Grötschel (born 10 September 1948) is a German mathematician known for his research on combinatorial optimization, polyhedral combinatorics, and operations research. From 1991 to 2012 he was Vice President of the Zuse Institute Berlin (ZIB) and served from 2012 to 2015 as ZIB's President. From 2015 to 2020 he was President of the Berlin-Brandenburg Academy of Sciences and Humanities (BBAW).

Biography Grötschel was born in Schwelm, Germany, and earned a diploma in mathematics with a minor in economics in 1973 from the University of Bochum. He completed a doctorate in 1977 at the University of Bonn under the supervision of Bernhard Korte, and obtained his habilitation at Bonn in the field of operations research in 1981. One year later he was appointed full professor of applied mathematics at the University of Augsburg. From 1991 until his retirement at the end of September 2015, he was, while also engaged at ZIB, full professor for information technology at Technische Universität Berlin. Martin Grötschel was a member of the Executive Committee of the German Mathematical Society (Deutsche Mathematiker-Vereinigung (DMV)) from 1989 to 1996 and from 1993 to 1994 its President. From 1999 to 2014 he was a member of the Executive Committee of the International Mathematical Union (IMU) and from 2007 to 2014 IMU's General Secretary. Since 2011 he has been a member of the Executive Board of the Einstein Foundation Berlin and was from 2011 to 2015 its Chair. He was co-founder and longstanding Chair of the DFG Research Center Matheon "Mathematics for key technologies". Martin Grötschel has been married since 1976 to his wife Iris Grötschel and has three daughters.

Work Martin Grötschel is one of the most internationally renowned experts in the field of combinatorial optimization. Martin Grötschel's main mathematical research fields are graph theory, linear and mixed-integer optimization and operations research. Already in his doctoral thesis, Grötschel achieved significant progress in the development of solution methods of the Traveling Salesman Problem, in particular, he contributed significantly to understanding the cutting-plane method. His publications together with L. Lovász and A. Schrijver on the ellipsoid method and its application in the combinatorial and convex optimization gained worldwide recognition. In recent years Martin Grötschel has mainly dealt (besides addressing "classical" mathematical problems) with mathematical modelling and solving real-world problems in economy and industry. The application areas he has worked in include optimization of production planning and control, public transport and energy systems, logistics and telecommunication. Since the early 1990s Grötschel has been working intensively in the fields of electronic information and communication, library systems, Open Access and Open Science and thereto participated in numerous national and international bodies and initiatives. The promotion of digital humanities is one of the main goals of Grötschel's BBAW presidency.

Awards and honors Grötschel was one of the winners of the Fulkerson Prize of the American Mathematical Society in 1982 for his work with László Lovász and Alexander Schrijver on applications of the ellipsoid method to combinatorial optimization. In 2006 the same trio won the John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences. The Society for Industrial and Applied Mathematics and Mathematical Optimization Society gave Grötschel the George B. Dantzig Prize in 1991, and the Deutsche Forschungsgemeinschaft gave him the Gottfried Wilhelm Leibniz Prize in 1995. In 2004 he was awarded the EURO Gold Medal, the highest distinction within Operations Research in Europe. He was an invited speaker at the 2006 International Congress of Mathematicians. Grötschel received honorary doctorates from the University of Karlsruhe in 2006, from the Vietnamese Academy of Sciences and Technology (VAST) in 2007, from the Otto-von-Guericke-Universität Magdeburg in 2008 and from the University of Augsburg in 2011. Since 2011 he has been Distinguished Affiliated Professor at the Technical University of Munich. Grötschel is member of seven national and international scientific academies: In 1995 he was a member the Berlin-Brandenburg Academy of Sciences and Humanities, in 1999 he became Foreign Member of the US National Academy of Engineering (NAE) for "contributions to combinatorial optimization and its applications", since 2003 he has been a member of the Deutsche Akademie der Technikwissenschaften (acatech), since 2005 of the German National Academy of Sciences Leopoldina, since 2015 of the Chinese Academy of Sciences (CAS) as Foreign Member, since 2016 of The World Academy of Sciences (TWAS) for the advancement of science in the developing countries as Fellow, and in 2017 he was elected a member of the Academy of Europe Academia Europaea. In 2013, a festschrift was published in his honor.

Selected publications Grötschel, Martin; Lucas, Klaus; Mehrmann, V. L., eds. (2010). Production factor mathematics. Heidelberg: Springer. ISBN 978-3-642-11248-5. OCLC 668095703. Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419 Graham, Ronald L.; Grötschel, Martin; Lovász, László (1995). Handbook of combinatorics. Amsterdam: Elsevier. ISBN 0-444-88002-X. OCLC 32626230.

References

External links Grötschel's homepage at Zuse Institute Berlin

Illustrations

Worked examples

Example 1 — a first encounter with Martin Grötschel

Start with the simplest possible case. Write down what Martin Grötschel 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 Martin Grötschel 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 Martin Grötschel 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 Martin Grötschel

In research: Martin Grötschel 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 Martin Grötschel 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: Martin Grötschel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1948 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Martin Grötschel 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 Martin Grötschel in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Martin Grötschel 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 Martin Grötschel out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Martin Grötschel in simple terms?

Why does Martin Grötschel 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 Martin Grötschel?

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 Martin Grötschel.