mathematics

Max Shiffman

Max Shiffman 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 Max Shiffman rather than just read about it. In short: Max Shiffman (30 October 1914, New York City – 2 July 2000, Hayward, California) was an American mathematician, specializing in the calculus of variations, partial differential equations, and hydrodynamics. He was a Guggenheim Fellow for the academic year 1951–1952.

Key takeaways

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

Reference excerpt

Max Shiffman (30 October 1914, New York City – 2 July 2000, Hayward, California) was an American mathematician, specializing in the calculus of variations, partial differential equations, and hydrodynamics. He was a Guggenheim Fellow for the academic year 1951–1952.

Biography Max Shiffman graduated with a bachelor's degree from City College of New York (CNNY) and then graduated in 1938 with a Ph.D. from New York University (NYU). His thesis was entitled The Plateau Problem for Minimal Surfaces of Arbitrary Topological Structure and his thesis advisor was Richard Courant. According to Peter Lax, Shiffman was "Courant's most brilliant student in America". Shiffman gave a one-hour address at a meeting of the American Mathematical Society. He was an instructor at CCNY in 1939–42. In 1942 at NYU he joined a research project funded by the Office of Scientific Research and Development. From 1945 to 1948 he was an associate professor at NYU, where he influenced many graduate students, including Clifford Gardner, Joe Keller, Martin Kruskal, Peter Lax, Cathleen Morawetz, and Louis Nirenberg. In 1948 Gábor Szegő hired Shiffman as a full professor at Stanford University. Szegő also brought to the Stanford mathematics department Donald C. Spencer, Albert Charles Schaeffer, Paul Garabedian, and Richard E. Bellman. Shiffman and Bellman introduced a number of modern mathematics courses at Stanford. Shiffman was the first to teach at Stanford a course on functional analysis. Merrill M. Flood's 1952 introduction to non-Soviet mathematicians of Kantorovich's 1939 paper Mathematical Methods of Organizing and Planning Production is due to Shiffman in 1949.

His brilliant career came to a tragic halt in 1951, due to a schizophrenic breakdown. He recovered and continued his research and teaching until a second breakdown in 1956. With the support of his friends and a generous trustee of Stanford University, he was admitted to Chestnut Lodge, a prestigious psychiatric institute. After nine years of therapy he was transferred to Agnews State Hospital in California, where Max took advantage of a state law and sued in court to be released; he convinced a jury that he was mentally competent. From 1965 to 1967 Shiffman held at Stanford a research appointment, mainly due to the efforts of Donald C. Spencer. At California State University, Hayward Shiffman was a full professor from 1967 to 1981, when he retired as professor emeritus.

Much of Shiffman’s work dealt with Plateau’s problem. He showed that if a boundary curve spans two minimal surfaces that are relative minima, then it also spans one which is not a relative minimum. In one of his last publications he showed that a doubly connected minimal surface whose boundary consists of two circles on parallel planes intersects any other parallel plane in a circle. Shiffman also worked on problems of conformal mapping, and the differentiability and analyticity of solutions of double integral variational problems. ... Shiffman used variational methods to study the flow of fluids, incompressible and compressible. He proved a basic theorem about compressible flows around bodies with prescribed subsonic speed at infinity; he showed that such flows are smooth until the flow becomes sonic. The technical tool he used, altering the equation of state, is called “shiffmanization” by cognoscenti. In the summer of 1949 Shiffman gave a new proof of von Neumann's minimax theorem with a generalization to concave-convex functions. Maurice Sion generalized Shiffman's result to Sion's minimax theorem, published in 1958. In 1938 Bella Manel, a mathematics graduate student at NYU, married Max Shiffman. She received her PhD in 1939 with thesis advisor Richard Courant. Max and Bella Shiffman divorced in 1957, after the birth of their two sons. Upon his death Max Shiffman was survived by his sons, Bernard, a professor of mathematics, and David, an owner of an investment company, and by five grandchildren.

Selected publications Shiffman, M. (1939). "The Plateau Problem for Non-Relative Minima". Proceedings of the National Academy of Sciences. 25 (4): 215–220. Bibcode:1939PNAS...25..215S. doi:10.1073/pnas.25.4.215. PMC 1077750. PMID 16588292. Shiffman, Max (1939). "The Plateau Problem for Minimal Surfaces of Arbitrary Topological Structure". American Journal of Mathematics. 61 (4): 853–882. doi:10.2307/2371631. JSTOR 2371631. Shiffman, Max (1942). "Unstable Minimal Surfaces with Several Boundaries". Annals of Mathematics. 43 (2): 197–222. doi:10.2307/1968866. JSTOR 1968866. Shiffman, M. (1942). "Unstable Minimal Surfaces with Any Rectifiable Boundary". Proceedings of the National Academy of Sciences. 28 (3): 103–108. Bibcode:1942PNAS...28..103S. doi:10.1073/pnas.28.3.103. PMC 1078423. PMID 16578029. Shiffman, Max (1947). "Differentiability and Analyticity of Solutions of Double Integral Variational Problems". The Annals of Mathematics. 48 (2): 274–284. doi:10.2307/1969170. JSTOR 1969170.1947 Shiffman, Max; Spencer, D. C. (1947). "The flow of an ideal incompressible fluid about a lens" (PDF). Quarterly of Applied Mathematics. 5 (3): 270–288. doi:10.1090/qam/22494. Shiffman, M. (1952). "On the Existence of Subsonic Flows of a Compressible Fluid". Proceedings of the National Academy of Sciences. 38 (5): 434–438. Bibcode:1952PNAS...38..434S. doi:10.1073/pnas.38.5.434. PMC 1063580. PMID 16589119. Shiffman, M. (2016-03-02). "Games of Timing". In Kuhn, Harold William; Tucker, Albert William (eds.). Contributions to the Theory of Games (AM-28). Princeton University Press. pp. 97–124. ISBN 9781400881970; reprint of 1953 original{{cite book}}: CS1 maint: postscript (link) Shiffman, Max (1956). "On Surfaces of Stationary Area Bounded by Two Circles, or Convex Curves, in Parallel Planes". Annals of Mathematics. 63 (1): 77–90. doi:10.2307/1969991. JSTOR 1969991.

References

Worked examples

Example 1 — a first encounter with Max Shiffman

Start with the simplest possible case. Write down what Max Shiffman 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 Max Shiffman 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 Max Shiffman 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 Max Shiffman

In research: Max Shiffman 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 Max Shiffman 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: Max Shiffman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1914 births, 2000 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Max Shiffman 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 Max Shiffman in 20 minutes

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

Frequently asked questions

What is Max Shiffman in simple terms?

Why does Max Shiffman 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 Max Shiffman?

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 Max Shiffman.