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Heinrich Guggenheimer

Heinrich Guggenheimer 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 Heinrich Guggenheimer rather than just read about it. In short: Heinrich Walter Guggenheimer (July 21, 1924 – March 4, 2021) was a German-born Swiss and American mathematician and educator, who has contributed to knowledge in differential geometry, topology, algebraic geometry, and convexity. He was Jewish and has also contributed volumes on Jewish sacred literature.

Key takeaways

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

Reference excerpt

Heinrich Walter Guggenheimer (July 21, 1924 – March 4, 2021) was a German-born Swiss and American mathematician and educator, who has contributed to knowledge in differential geometry, topology, algebraic geometry, and convexity. He was Jewish and has also contributed volumes on Jewish sacred literature.

Life and career Heinrich Walter Guggenheimer was born on July 21, 1924, in Nuremberg, Germany. He is the son of Marguerite Bloch and the physicist Siegfried Guggenheim (physicist). He studied in Zürich, Switzerland at the Eidgenössische Technische Hochschule, receiving his diploma in 1947 and a D.Sc. in 1951. His dissertation was titled "On complex analytic manifolds with Kahler metric". It was published in Commentarii Mathematici Helvetici (in German). Guggenheimer began his teaching career at the Hebrew University as a lecturer, 1954–56. He was a professor at the Bar Ilan University, 1956–59. In 1959, he immigrated to the United States, becoming a naturalized citizen in 1965. Washington State University was his first American post, where he was an associate professor. After one year he moved to University of Minnesota where he was raised to a full professor in 1962. While in Minnesota, he wrote Differential Geometry (1963), a textbook treating "classical problems with modern methods". According to Robert Hermann in 1979, "Among today's treatises, the best one from the point of view of the Erlangen Program is Differential Geometry by H. Guggenheimer, Dover Publications, 1977." In 1967 Guggenheimer published Plane Geometry and its Groups (Holden Day), and moved to New York City to teach at Polytechnic University, now called New York University Tandon School of Engineering. In 1977, he published Applicable Geometry: Global and Local Convexity. Until 1995 Guggenheimer produced a steady stream of papers in mathematical journals. As a supervisor of graduate study in Minnesota and New York, he had six students proceed to Ph.D.s with theses supervised by him, two in Minnesota and four in New York. See the link to the Mathematics Genealogy Project below. Guggenheimer has also contributed to literature on Judaism. In 1966, he wrote "Logical problems in Jewish tradition". The next year he contributed "Magic and Dialectic" to Diogenes where he examines the supposition that "knowledge of the right name gives power over the bearer of that name". In 1995 Guggenheimer presented The Scholar's Haggadah, which makes a bilingual comparison of variances in the traditions of Passover observance, including Ashkenazic, Sephardic, and Oriental sources. One of its most significant contributions to Haggadah scholarship was the identification of references to the Haggadah's text in verses from the Septuagint, the third century B.C.E. Greek translation of the Pentateuch. His study of the Jerusalem Talmud provided text and commentary. He died in March 2021 at the age of 96.

Family On June 6, 1947, Guggenheimer married Eva Auguste Horowitz. Together with his wife they wrote Jewish Family Names and their Origins: an Etymological Dictionary (1992). They have two sons, Michael, a professor of Arabic, and Tobias I. S., an architect, and two daughters Dr. Esther Furman, a biochemist, and Hanna Y. Guggenheimer, an artist.

Notes

References Allen G. Debus, "Heinrich Walter Guggenheimer", Who's Who in Science, 1968. Heinrich Guggenheimer at Mathematics Genealogy Project. "Guggenheimer, Heinrich Walter" in American Men and Women of Science, 25th edition, Gale, 2008.

Worked examples

Example 1 — a first encounter with Heinrich Guggenheimer

Start with the simplest possible case. Write down what Heinrich Guggenheimer 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 Heinrich Guggenheimer 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 Heinrich Guggenheimer 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 Heinrich Guggenheimer

In research
Heinrich Guggenheimer 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 Heinrich Guggenheimer 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
Heinrich Guggenheimer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1924 births, 2021 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Heinrich Guggenheimer 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 Heinrich Guggenheimer in 20 minutes

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

Frequently asked questions

What is Heinrich Guggenheimer in simple terms?

Heinrich Walter Guggenheimer (July 21, 1924 – March 4, 2021) was a German-born Swiss and American mathematician and educator, who has contributed to knowledge in differential geometry, topology, algebraic geometry, and convexity. He was Jewish and has also contributed volumes on Jewish sacred liter…

Why does Heinrich Guggenheimer 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 Heinrich Guggenheimer?

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 Heinrich Guggenheimer.

Tags

  • 1924 births
  • 2021 deaths
  • 20th-century American mathematicians
  • 21st-century American mathematicians
  • Differential geometers
  • Emigrants from Nazi Germany to Switzerland
  • German emigrants to the United States
  • Jewish emigrants from Nazi Germany to Switzerland
  • Polytechnic Institute of New York University faculty
  • Scientists from Nuremberg

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