mathematics

Georg Bohlmann

Georg Bohlmann 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 Georg Bohlmann rather than just read about it. In short: Georg Bohlmann (23 April 1869 – 25 April 1928) was a German mathematician who specialized in probability theory and actuarial mathematics. Life and career Georg Bohlmann went to school in Berlin and Leipzig and took his Abitur at the Wilhelms-Gymnasium in Berlin in 1888.

Key takeaways

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

Reference excerpt

Georg Bohlmann (23 April 1869 – 25 April 1928) was a German mathematician who specialized in probability theory and actuarial mathematics.

Life and career Georg Bohlmann went to school in Berlin and Leipzig and took his Abitur at the Wilhelms-Gymnasium in Berlin in 1888. After that, he began studying mathematics at the University of Berlin under Leopold Kronecker, Lazarus Fuchs, and Wilhelm Dilthey. As he advanced in his studies, Lie groups became the focus of his interest. Since this area was poorly represented at Berlin, he moved to the University of Halle, where he obtained his doctorate in 1892 under Albert Wangerin with a dissertation on the topic Ueber eine gewisse Klasse continuierlicher Gruppen und ihren Zusammenhang mit den Additionstheoremen ("On a certain class of continuous groups and their relation to addition theorems"). After that, he worked at the Meteorological Institute of Berlin, where presumably his interest in applied mathematics developed. At the invitation of Felix Klein, he moved to the University of Göttingen, where he habilitated in 1894. In 1895, he was involved in starting a seminar on actuarial science at Göttingen. However, since he held no permanent position there, he went to Berlin in 1903 to work as the Chief Actuary for the German subsidiary of the New York Mutual Life Insurance Company. In 1901, he wrote the entry on life insurance mathematics in the Enzyklopädie der mathematischen Wissenschaften ("Encyclopaedia of Mathematical Sciences") in which he gave axioms for probability theory long before Andrey Kolmogorov did so in 1933. In particular, he was the first to give the modern definition of statistical independence. Compared to the current structure of probability theory, his work only lacked the technical condition of sigma additivity. However, in contrast to Kolmogorov, Bohlmann failed to prove significant theorems within his axiomatic framework. As a result, his fundamental contributions to probability theory gained very little attention. In particular, though Kolmogorov had visited Göttingen several times in the late 1920s, he had no knowledge of Bohlmann's work. Bohlmann was an invited speaker in the International Congress of Mathematicians in 1908 at Rome.

Publications Lebensversicherungsmathematik (Life Insurance Mathematics), Enzyklopädie der Mathematischen Wissenschaften, 1901 Continuierliche Gruppen von quadratischen Transformationen der Ebene (Continuous groups of quadratic transformations of the plane), Göttinger Nachrichten, 1896, pp. 44–54 Ein Ausgleichungsproblem (A stabilization problem), Göttinger Nachrichten, 1899, pp. 260–271 Die Grundbegriffe der Wahrscheinlichkeitsrechnung in ihrer Anwendung auf die Lebensversicherung (The basic concepts of probability theory and its applications to life insurance), Atti del IV Congresso internazionale dei Matematici III, Rome 1909, pp. 244–278 Anthropometrie und Lebensversicherung (Anthropometry and life insurance), Zeitschrift für die gesamte Versicherungs-Wissenschaft 14, 1914, pp. 743–786

References

Ulrich Krengel, 100 Jahre Versicherungsmathematik an den Universitäten (100 years of actuarial science at universities), Blätter der deutschen Gesellschaft für Versicherungsmathematik 22, 1996, p. 663 Ulrich Krengel, On the contributions of Bohlmann to probability theory (PDF: 6.4 MB), Electronic Journal for History of Probability and Statistics, 2011 Peter Koch, Geschichte der Versicherungswissenschaft in Deutschland (History of actuarial science in Germany), Verlag Versicherungswirtschaft, Karlsruhe 1998, ISBN 3-88487-745-3

External links Geschichte der Stochastik in Göttingen (History of Stochastics in Göttingen), Ulrich Krengel and Axel Munk

Illustrations

Worked examples

Example 1 — a first encounter with Georg Bohlmann

Start with the simplest possible case. Write down what Georg Bohlmann 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 Georg Bohlmann 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 Georg Bohlmann 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 Georg Bohlmann

In research: Georg Bohlmann 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 Georg Bohlmann 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: Georg Bohlmann is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1869 births, 1928 deaths, 19th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Georg Bohlmann 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 Georg Bohlmann in 20 minutes

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

Frequently asked questions

What is Georg Bohlmann in simple terms?

Georg Bohlmann (23 April 1869 – 25 April 1928) was a German mathematician who specialized in probability theory and actuarial mathematics. Life and career Georg Bohlmann went to school in Berlin and Leipzig and took his Abitur at the Wilhelms-Gymnasium in Berlin in 1888.

Why does Georg Bohlmann 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 Georg Bohlmann?

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 Georg Bohlmann.