ArticleslgStudy

mathematics

Lipman Bers

Lipman Bers 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 Lipman Bers rather than just read about it. In short: Lipman Bers (Latvian: Lipmans Berss; May 22, 1914 – October 29, 1993) was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also known for his work in human rights activism.

Key takeaways

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

Reference excerpt

Lipman Bers (Latvian: Lipmans Berss; May 22, 1914 – October 29, 1993) was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also known for his work in human rights activism.

Biography Bers was born in Riga, then under the rule of the Russian Tsars, and spent several years as a child in Saint Petersburg after his hometown fell to invading Germany in 1915; his family returned to Riga in approximately 1919, by which time it was part of independent Latvia. In Riga, his mother was the principal of a Jewish elementary school, and his father became the principal of a Jewish high school, both of which Bers attended, with an interlude in Berlin while his mother, by then separated from his father, attended the Berlin Psychoanalytic Institute. After high school, Bers studied at the University of Zurich for a year, but had to return to Riga again because of the difficulty of transferring money from Latvia in the international financial crisis of the time. He continued his studies at the University of Riga, where he became active in socialist politics, including giving political speeches and working for an underground newspaper. In the aftermath of the 1934 Latvian coup d'état by right-wing leader Kārlis Ulmanis, Bers was targeted for arrest but fled the country, first to Estonia and then to Czechoslovakia. Bers begun his studies at the University of Prague with Rudolf Carnap, but when Carnap moved to the US he switched to Charles Loewner, who would eventually become his thesis advisor. He received his Ph.D. in 1938. In Prague, he lived with an aunt, and married his wife Mary (née Kagan) whom he had met in elementary school and who had followed him from Riga. Having applied for postdoctoral studies in Paris, he was given a visa to go to France soon after the Munich Agreement, by which Nazi Germany annexed the Sudetenland. He and his wife Mary had a daughter in Paris. They were unable to obtain a visa there to emigrate to the US, as the Latvian quota had filled, so they escaped to the south of France ten days before the fall of Paris, and eventually obtained an emergency US visa in Marseilles, one of a group of 10,000 visas set aside for political refugees by Eleanor Roosevelt. The Bers family rejoined Bers' mother, who had by then moved to New York City and become a psychoanalyst, married to thespian Boris Tumarin. At this time, Bers worked for the YIVO Yiddish research agency. Bers spent World War II teaching mathematics as a research associate at Brown University, where he was joined by Loewner. After the war, Bers found an assistant professorship at Syracuse University (1945–1951), before moving to New York University (1951–1964) and then Columbia University (1964–1984), where he became the Davies Professor of Mathematics, and where he chaired the mathematics department from 1972 to 1975. His move to NYU coincided with a move of his family to New Rochelle, New York, where he joined a small community of émigré mathematicians. He was a visiting scholar at the Institute for Advanced Study in 1949–51. He was a Vice-President (1963–65) and a President (1975–77) of the American Mathematical Society, chaired the Division of Mathematical Sciences of the United States National Research Council from 1969 to 1971, chaired the U.S. National Committee on Mathematics from 1977 to 1981, and chaired the Mathematics Section of the National Academy of Sciences from 1967 to 1970. Late in his life, Bers suffered from Parkinson's disease and strokes. He died on October 29, 1993.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Lipman Bers

Start with the simplest possible case. Write down what Lipman Bers 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 Lipman Bers 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 Lipman Bers 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 Lipman Bers

In research
Lipman Bers 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 Lipman Bers 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
Lipman Bers is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1914 births, 1993 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Lipman Bers 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Lipman Bers in 20 minutes

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

Frequently asked questions

What is Lipman Bers in simple terms?

Lipman Bers (Latvian: Lipmans Berss; May 22, 1914 – October 29, 1993) was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also known for his work in human rights activism.

Why does Lipman Bers 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 Lipman Bers?

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 Lipman Bers.

Tags

  • 1914 births
  • 1993 deaths
  • 20th-century American mathematicians
  • 20th-century Latvian Jews
  • 20th-century Latvian mathematicians
  • Columbia University faculty
  • Complex analysts
  • Fellows of the American Academy of Arts and Sciences
  • Fellows of the American Association for the Advancement of Science
  • Institute for Advanced Study visiting scholars
  • Latvian emigrants to the United States
  • Mathematical analysts

Keep exploring