mathematics

Hans Samelson

Hans Samelson 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 Hans Samelson rather than just read about it. In short: Hans Samelson (3 March 1916 – 22 September 2005) was a German-American mathematician who worked in differential geometry, topology and the theory of Lie groups and Lie algebras—important in describing the symmetry of analytical structures. Career and personal life The eldest of three sons, Samelson was born on 3 March 1916, in Strassburg, Germany (now Strasbourg, France).

Key takeaways

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

Reference excerpt

Hans Samelson (3 March 1916 – 22 September 2005) was a German-American mathematician who worked in differential geometry, topology and the theory of Lie groups and Lie algebras—important in describing the symmetry of analytical structures.

Career and personal life The eldest of three sons, Samelson was born on 3 March 1916, in Strassburg, Germany (now Strasbourg, France). His brother Klaus later became a mathematician and early computer science pioneer in Germany. His parents—one of Protestant and one of Jewish background—were both pediatricians. He spent most of his youth in Breslau, Silesia, Germany (now Wrocław, Poland), and began his advanced mathematical education there, at the University of Breslau. His family helped him leave Nazi Germany in 1936 for Zurich, Switzerland, where he studied with the geometer Heinz Hopf and received his doctorate in 1940 from the Swiss Federal Institute of Technology. In 1941, he accepted a position at the Institute for Advanced Study in Princeton and immigrated to the United States; he arrived by ship six months before the United States entered World War II and acquired U.S. citizenship several years later. After leaving Princeton, he held faculty positions at the University of Wyoming (1942–1943), Syracuse University (1943–1946) and the University of Michigan (1946–1960) before coming to Stanford in 1960. He was recognized with the Dean's Award for Distinguished Teaching in 1977. He served as chair of the Mathematics Department from 1979 to 1982. Though he became emeritus in 1986, he remained professionally active throughout his retirement, publishing articles on both contemporary and historical mathematical topics. One solved an architectural puzzle associated with the construction of the Brunelleschi Dome in Florence, Italy. He was active in the Palo Alto Friends Meeting (Quakers) during his retirement, serving as treasurer for several years.

Worked examples

Example 1 — a first encounter with Hans Samelson

Start with the simplest possible case. Write down what Hans Samelson 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 Hans Samelson 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 Hans Samelson 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 Hans Samelson

In research: Hans Samelson 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 Hans Samelson 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: Hans Samelson is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1916 births, 2005 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Hans Samelson 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 Hans Samelson in 20 minutes

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

Frequently asked questions

What is Hans Samelson in simple terms?

Why does Hans Samelson 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 Hans Samelson?

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 Hans Samelson.