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Solomon Mikhlin

Solomon Mikhlin 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 Solomon Mikhlin rather than just read about it. In short: Solomon Grigor'evich Mikhlin (Russian: Соломо́н Григо́рьевич Ми́хлин, real name Zalman Girshevich Mikhlin) (the family name is also transliterated as Mihlin or Michlin) (23 April 1908 – 29 August 1990) was a Soviet mathematician of who worked in the fields of linear elasticity, singular integrals and numerical analysis: he is best known for the introduction of the symbol of a singular integral operator, which eventu…

Solomon Mikhlin — main illustration
Solomon Mikhlin — illustration

Key takeaways

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

Reference excerpt

Solomon Grigor'evich Mikhlin (Russian: Соломо́н Григо́рьевич Ми́хлин, real name Zalman Girshevich Mikhlin) (the family name is also transliterated as Mihlin or Michlin) (23 April 1908 – 29 August 1990) was a Soviet mathematician of who worked in the fields of linear elasticity, singular integrals and numerical analysis: he is best known for the introduction of the symbol of a singular integral operator, which eventually led to the foundation and development of the theory of pseudodifferential operators.

Biography He was born in Kholmech, Rechytsa District, Minsk Governorate (in present-day Belarus) on 23 April 1908; Mikhlin (1968) himself states in his resume that his father was a merchant, but this assertion could be untrue since, in that period, people sometimes lied on the profession of parents in order to overcome political limitations in the access to higher education. According to a different version, his father was a melamed, at a primary religious school (kheder), and that the family was of modest means: according to the same source, Zalman was the youngest of five children. His first wife was Victoria Isaevna Libina: Mikhlin's book (Mikhlin 1965) is dedicated to her memory. She died of peritonitis in 1961 during a boat trip on Volga. In 1940 they adopted a son, Grigory Zalmanovich Mikhlin, who later emigrated to Haifa, Israel. His second wife was Eugenia Yakovlevna Rubinova, born in 1918, who was his companion for the rest of his life.

Education and academic career

He graduated from a secondary school in Gomel in 1923 and entered the State Herzen Pedagogical Institute in 1925. In 1927 he was transferred to the Department of Mathematics and Mechanics of Leningrad State University as a second year student, passing all the exams of the first year without attending lectures. Among his university professors there were Nikolai Maximovich Günther and Vladimir Ivanovich Smirnov. The latter became his master thesis supervisor: the topic of the thesis was the convergence of double series, and was defended in 1929. Sergei Lvovich Sobolev studied in the same class as Mikhlin. In 1930 he started his teaching career, working in some Leningrad institutes for short periods, as Mikhlin himself records on the document (Mikhlin 1968). In 1932 he got a position at the Seismological Institute of the USSR Academy of Sciences, where he worked till 1941: in 1935 he got the degree of Doctor of Sciences in Mathematics and Physics, without having to earn the Candidate of Sciences degree, and finally in 1937 he was promoted to the rank of professor. During World War II he became professor at the Kazakh University in Alma Ata. Since 1944 S.G. Mikhlin has been professor at the Leningrad State University. From 1964 to 1986 he headed the Laboratory of Numerical Methods at the Research Institute of Mathematics and Mechanics of the same university: since 1986 until his death he was a senior researcher at that laboratory.

Honours He received the order of the Badge of Honour (Russian: Орден Знак Почёта) in 1961: the name of the recipients of this prize was usually published in newspapers. He was awarded of the Laurea honoris causa by the Karl-Marx-Stadt (now Chemnitz) Polytechnic in 1968 and was elected member of the German Academy of Sciences Leopoldina in 1970 and of the Accademia Nazionale dei Lincei in 1981. As Fichera (1994, p. 51) states, in his country he did not receive honours comparable to his scientific stature, mainly because of the racial policy of the communist regime, briefly described in the following section.

Influence of communist antisemitism He lived in one of the most difficult periods of contemporary Russian history. The state of mathematical sciences during this period is well described by Lorentz (2002): marxist ideology rise in the USSR universities and Academia was one of the main themes of that period. Local administrators and communist party functionaries interfered with scientists on either ethnical or ideological grounds. As a matter of fact, during the war and during the creation of a new academic system, Mikhlin did not experience the same difficulties as younger Soviet scientists of Jewish origin: for example he was included in the Soviet delegation in 1958, at the International Congress of Mathematicians in Edinburgh. However, Fichera (1994, pp. 56–60), examining the life of Mikhlin, finds it surprisingly similar to the life of Vito Volterra under the fascist regime. He notes that antisemitism in communist countries took different forms compared to his nazist counterpart: the communist regime aimed not to the brutal homicide of Jews, but imposed on them a number of constrictions, sometimes very cruel, in order to make their life difficult. During the period from 1963 to 1981, he met Mikhlin attending several conferences in the Soviet Union, and realised how he was in a state of isolation, almost marginalized inside his native community: Fichera describes several episodes revealing this fact. Perhaps, the most illuminating one is the election of Mikhlin as a member of the Accademia Nazionale dei Lincei: in June 1981, Solomon G. Mikhlin was elected Foreign Member of the class of mathematical and physical sciences of the Lincei. At first time, he was proposed as a winner of the Antonio Feltrinelli Prize, but the almost sure confiscation of the prize by the Soviet authorities induced the Lincei members to elect him as a member: they decided to honour him in a way that no political authority could alienate. However, Mikhlin was not allowed to visit Italy by the Soviet authorities, so Fichera and his wife brought the tiny golden lynx, the symbol of the Lincei membership, directly to Mikhlin's apartment in Leningrad on 17 October 1981: the only guests to that "ceremony" were Vladimir Maz'ya and his wife Tatyana Shaposhnikova.

They just have power, but we have theorems. Therefore we are stronger!

Death According to Fichera (1994, pp. 60–61), which refers a conversation with Mark Vishik and Olga Oleinik, on 29 August 1990 Mikhlin left home to buy medicines for his wife Eugenia. On a public transport, he suffered a lethal stroke. He had no documents with him, therefore he was identified only some time after his death: this may be the cause of the difference in the death date reported on several biographies and obituary notices. Fichera also writes that Mikhlin's wife Eugenia survived him only a few months.

Work

… excerpt ends here. Continue reading the full article.

Illustrations

Solomon Mikhlin illustration

Worked examples

Example 1 — a first encounter with Solomon Mikhlin

Start with the simplest possible case. Write down what Solomon Mikhlin 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 Solomon Mikhlin 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 Solomon Mikhlin 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 Solomon Mikhlin

In research
Solomon Mikhlin 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 Solomon Mikhlin 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
Solomon Mikhlin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1908 births, 1990 deaths, Belarusian Jews, so understanding it makes those chapters shorter.
In everyday life
Look for Solomon Mikhlin 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 Solomon Mikhlin in 20 minutes

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

Frequently asked questions

What is Solomon Mikhlin in simple terms?

Solomon Grigor'evich Mikhlin (Russian: Соломо́н Григо́рьевич Ми́хлин, real name Zalman Girshevich Mikhlin) (the family name is also transliterated as Mihlin or Michlin) (23 April 1908 – 29 August 1990) was a Soviet mathematician of who worked in the fields of linear elasticity, singular integrals a…

Why does Solomon Mikhlin 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 Solomon Mikhlin?

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 Solomon Mikhlin.

Tags

  • 1908 births
  • 1990 deaths
  • Belarusian Jews
  • Herzen University alumni
  • Jewish scientists
  • Mathematical analysts
  • Mathematical physicists
  • People from Minsk Governorate
  • People from Rechytsa district
  • Soviet mathematicians

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