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José Luis Massera

José Luis Massera 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 José Luis Massera rather than just read about it. In short: José Luis Massera (Genoa, Italy, June 8, 1915 – Montevideo, September 9, 2002) was a Uruguayan dissident and mathematician who researched the stability of differential equations. Massera's lemma is named after him.

José Luis Massera — main illustration
José Luis Massera — illustration

Key takeaways

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

Reference excerpt

José Luis Massera (Genoa, Italy, June 8, 1915 – Montevideo, September 9, 2002) was a Uruguayan dissident and mathematician who researched the stability of differential equations. Massera's lemma is named after him. He published over 40 papers during 1940–1970. A militant Communist, he was a political prisoner during 1975–1984. In the 1930s, Julio Rey Pastor gave regular weekend lectures on topology in Montevideo to a group that included Massera. Stimulated by contact with Argentine mathematics, the 1950s saw Uruguay develop a fine school in mathematics, of which Massera was very much a part. Massera developed new notions of stability, and published several foundational papers and an influential textbook. His results in (Massera 1950) on periodic differential equations have been heavily cited and are referred to as Massera's theorem. His work in (Massera 1949) and (Massera 1956) on the converse to Lyapunov's criterion is also influential, and contain the well known Massera's lemma. His textbook (Massera & Schäffer 1966) is also heavily cited. After military intervention in Uruguay in 1973, Massera was arrested on October 22, 1975 in Montevideo and was held in solitary confinement for nearly a year. During this time he was subjected to repeated torture resulting in injuries including a fractured pelvis. In October 1976 he was taken from solitary confinement, tried and convicted for "subversive association", and given a 24-year prison sentence. On June 22, 1979, as a consequence of a proposal put forward by Gaetano Fichera and unanimously approved by the whole Mathematics Faculty Council of the Sapienza University of Rome, he was awarded the laurea honoris causa while still being under conviction. He was released in 1984.

Honors The outer main-belt asteroid 10690 Massera, discovered by American astronomer Schelte Bus at the Australian Siding Spring Observatory in 1981, was named in his memory on 13 April 2017 (M.P.C. 103976).

Selected works Massera, José Luis (1949), "On Liapounoff's conditions of stability", Annals of Mathematics, Second Series, 50 (3), The Annals of Mathematics, Vol. 50, No. 3: 705–721, doi:10.2307/1969558, JSTOR 1969558, MR 0035354, Zbl 0038.25003. Massera, José Luis (1950), "The existence of periodic solutions of systems of differential equations", Duke Mathematical Journal, 17 (4): 457–475, doi:10.1215/S0012-7094-50-01741-8, MR 0040512, Zbl 0038.25002. Massera, José Luis (1956), "Contributions to stability theory", Annals of Mathematics, Second Series, 64 (1), The Annals of Mathematics, Vol. 64, No. 1: 182–206, doi:10.2307/1969955, JSTOR 1969955, MR 0079179, Zbl 0070.31003. Massera, José Luis; Schäffer, Juan Jorge (1966), Linear differential equations and function spaces, Pure and Applied Mathematics, Vol. 21, Boston, MA: Academic Press, MR 0212324, Zbl 0243.34107

References

Biographical references Vernacchia-Galli, Jole (1986), "José Luis Massera", Regesto delle lauree honoris causa dal 1944 al 1985, Studi e Fonti per la storia dell'Università di Roma (in Italian and Spanish), vol. 10, Roma: Edizioni Dell'Ateneo, pp. 559–605. The "regest of honoris causa degrees from 1944 to 1985" (English translation of the title) is a detailed and carefully commented regest of all the documents of the official archive of the Sapienza University of Rome pertaining to the honoris causa degrees, awarded or not. It includes all the awarding proposals submitted during the considered period, detailed presentations of the work of the candidate, if available, and precise references to related articles published on Italian newspapers and magazines, if the laurea was awarded.

Illustrations

José Luis Massera illustration

Worked examples

Example 1 — a first encounter with José Luis Massera

Start with the simplest possible case. Write down what José Luis Massera 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 José Luis Massera 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 José Luis Massera 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 José Luis Massera

In research
José Luis Massera 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 José Luis Massera 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
José Luis Massera is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1915 births, 2002 deaths, 20th-century Uruguayan mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for José Luis Massera 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 José Luis Massera in 20 minutes

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

Frequently asked questions

What is José Luis Massera in simple terms?

José Luis Massera (Genoa, Italy, June 8, 1915 – Montevideo, September 9, 2002) was a Uruguayan dissident and mathematician who researched the stability of differential equations. Massera's lemma is named after him.

Why does José Luis Massera 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 José Luis Massera?

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 José Luis Massera.

Tags

  • 1915 births
  • 2002 deaths
  • 20th-century Uruguayan mathematicians
  • Fellows of The World Academy of Sciences
  • Italian emigrants to Uruguay
  • Mathematical analysts
  • Members of the Senate of Uruguay
  • Prisoners and detainees of Uruguay
  • Science and technology in Uruguay
  • University of the Republic (Uruguay) alumni
  • Uruguayan communists
  • Uruguayan prisoners and detainees

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