mathematics

Luther P. Eisenhart

Luther P. Eisenhart 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 Luther P. Eisenhart rather than just read about it. In short: Luther Pfahler Eisenhart (13 January 1876 – 28 October 1965) was an American mathematician, best known today for his contributions to semi-Riemannian geometry. Life Eisenhart was born in York, Pennsylvania, and graduated from Gettysburg College in 1896.

Key takeaways

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

Reference excerpt

Luther Pfahler Eisenhart (13 January 1876 – 28 October 1965) was an American mathematician, best known today for his contributions to semi-Riemannian geometry.

Life Eisenhart was born in York, Pennsylvania, and graduated from Gettysburg College in 1896. He earned his doctorate in 1900 at Johns Hopkins University, where he was influenced (at long range) by the work of Gaston Darboux and at shorter range by that of Thomas Craig. During the next two decades, Eisenhart's research focused on moving frames after the French school, but around 1921 took a different turn when he became enamored of the mathematical challenges and entrancing beauty of a new theory of gravitation, Albert Einstein's general theory of relativity. Eisenhart played a central role in American mathematics in the early twentieth century. He served as chairman of the mathematics department at Princeton University and later as Dean of the Graduate School there from 1933 to 1945. He is widely credited with guiding the development in America of the mathematical background needed for the further development of general relativity, through his influential textbooks and his personal interaction with Albert Einstein, Oswald Veblen, and John von Neumann at the nearby Institute for Advanced Study, as well as with gifted students such as Abraham Haskel Taub. In the early 40s he chaired the "Reference Committee", formed in June 1940 for editors of scientific journals to send the papers submitted to them, in order to check that the papers did not contain results (especially regarding nuclear physics) whose public knowledge could be detrimental to the US war efforts. Eisenhart was an elected member of both the American Philosophical Society and the United States National Academy of Sciences. Eisenhart indirectly contributed to popularization of science. In 1939, as Dean of the Graduate School, he hosted a tea for incoming students including Richard Feynman. When asked by Eisenhart's wife "would you like cream or lemon in your tea?", Feynman, uncomfortable in the situation, stammered "both please." This elicited the condescending response "Surely You're Joking, Mr. Feynman!" a phrase later immortalized as the title of the future Nobel Laureate's best selling memoir.

Publications Eisenhart, Luther Pfahler (1923). Transformations of Surfaces. Princeton: Princeton University Press. LCCN 62011699. Eisenhart, Luther Pfahler (1933). Continuous Groups of Transformations. Princeton: Princeton University Press. LCCN 61003361/L. Eisenhart, Luther Pfahler (1926). Riemannian Geometry (PDF). Princeton: Princeton University Press. OCLC 5836010. Eisenhart, Luther Pfahler (1939). Coordinate Geometry. Dover Publishing. Eisenhart, Luther Pfahler (1927). Non-Riemannian geometry (PDF). New York: American Mathematical Society. Eisenhart, Luther Pfahler (1909). A treatise on the differential geometry of curves and surfaces. Boston: Ginn and Company.

Notes

External links

O'Connor, John J.; Robertson, Edmund F., "Luther P. Eisenhart", MacTutor History of Mathematics Archive, University of St Andrews Luther P. Eisenhart at the Mathematics Genealogy Project National Academy of Sciences Biographical Memoir

Illustrations

Worked examples

Example 1 — a first encounter with Luther P. Eisenhart

Start with the simplest possible case. Write down what Luther P. Eisenhart 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 Luther P. Eisenhart 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 Luther P. Eisenhart 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 Luther P. Eisenhart

In research: Luther P. Eisenhart 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 Luther P. Eisenhart 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: Luther P. Eisenhart is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1876 births, 1965 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Luther P. Eisenhart 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 Luther P. Eisenhart in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Luther P. Eisenhart means in your own words.
Compare your version with the excerpt and mark what you missed.
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Frequently asked questions

What is Luther P. Eisenhart in simple terms?

Luther Pfahler Eisenhart (13 January 1876 – 28 October 1965) was an American mathematician, best known today for his contributions to semi-Riemannian geometry. Life Eisenhart was born in York, Pennsylvania, and graduated from Gettysburg College in 1896.

Why does Luther P. Eisenhart 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 Luther P. Eisenhart?

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 Luther P. Eisenhart.