Dmitry Semionovitch Mirimanoff (; 13 September 1861,

Pereslavl-Zalessky Pereslavl-Zalessky (, ), formerly known as Pereyaslavl-Zalessky, or simply Pereyaslavl, is a town in Yaroslavl Oblast, Russia, located on the main Moscow–Yaroslavl road and on the southeastern shore of Lake Pleshcheyevo at the mouth of the ...

Russia Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...

– 5 January 1945,

Geneva Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...

Switzerland Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. Switzerland ...

) was a member of the

Moscow Mathematical Society The Moscow Mathematical Society (MMS) is a society of Moscow mathematicians aimed at the development of mathematics in Russia. It was created in 1864, and Victor Vassiliev is the current president. History The first meeting of the society w ...

in 1897. And later became a doctor of

mathematical sciences The Mathematical Sciences are a group of areas of study that includes, in addition to mathematics, those academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper. Statisti ...

in 1900, in Geneva, and taught at the universities of

and

Lausanne Lausanne ( , ; ; ) is the capital and largest List of towns in Switzerland, city of the Swiss French-speaking Cantons of Switzerland, canton of Vaud, in Switzerland. It is a hilly city situated on the shores of Lake Geneva, about halfway bet ...

. Mirimanoff made notable contributions to

axiomatic set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

and to number theory (relating specifically to

Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive number, positive integers , , and satisfy the equation for any integer value of greater than . The cases ...

, on which he corresponded with

Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...

before the

First World War World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

Jean A. Mirimanoff. Private correspondence with Anton Lokhmotov. (2009)). In 1917, he introduced, though not as explicitly as

John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...

later, the

cumulative hierarchy In mathematics, specifically set theory, a cumulative hierarchy is a family of sets W_\alpha indexed by ordinals \alpha such that * W_\alpha \subseteq W_ * If \lambda is a limit ordinal, then W_\lambda = \bigcup_ W_ Some authors additionally re ...

of sets and the notion of

von Neumann ordinals In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets. A finite set can be enumerated by successively labeling each element with the least ...

; although he introduced a notion of regular (and well-founded set) he did not consider regularity as an axiom, but also explored what is now called

non-well-founded set theory Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axio ...

and had an emergent idea of what is now called

bisimulation In theoretical computer science a bisimulation is a binary relation between state transition systems, associating systems that behave in the same way in that one system simulates the other and vice versa. Intuitively two systems are bisimilar if ...

Life

Dmitry Semionovitch was born in

, on 13 September 1861. His parents were Semion Mirimanovitch Mirimanoff () and Maria Dmitrievna Rudakova (). Around 1885, Dmitry Mirimanoff met a French lady Malvina Geneviève Valentine Adriansen in

Nice Nice ( ; ) is a city in and the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly one million Russian Russian(s) may refer to: *Russians (), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *A citizen of Russia *Russian language, the most widely spoken of the Slavic languages *''The Russians'', a b ...

and accepted

Russian Orthodox Christianity The Russian Orthodox Church (ROC; ;), also officially known as the Moscow Patriarchate (), is an autocephaly, autocephalous Eastern Orthodox Church, Eastern Orthodox Christian church. It has 194 dioceses inside Russia. The Primate (bishop), p ...

. They married in

on 25 October 1897 and had two sons: Alexander (later Alexandre) Dmitrievitch Mirimanoff (), born in Oranienbaum (now Lomonossov) in 1898, and Andreï (later André) Dmitrievitch Mirimanoff (), born in Geneva in 1902. The family lived in

(first, in

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

, then in

St Petersburg Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

) until 1900 when they moved to Geneva (in search of a better climate for Dmitry Mirimanoff's bad health). After the 1917 revolutions they never visited Russia, although Dmitry's sisters Sophia and Lydia remained there. Dmitry Mirimanoff became a

Swiss citizen The primary law governing nationality of Switzerland is the Federal Act on Swiss Citizenship, which came into force on 1 January 2018. Switzerland is a member state of the European Free Trade Association (EFTA) and the Schengen Area. All Swiss ...

on 17 September 1926. He later died on 5 January 1945 in Geneva.

Work

Set theory

Mirimanoff in a 1917 paper introduced the concept of well-founded set and the notion of rank of a set.cf. and Mirimanoff called a set ''x'' "regular" (French: "ordinaire") if every descending chain ''x'' ∋ ''x₁'' ∋ ''x₂'' ∋ ... is finite. Mirimanoff however did not consider his notion of regularity (well-foundedness) as an axiom to be observed by all sets; in later papers Mirimanoff also explored what are now called non-well-founded sets ("extraordinaire" in Mirimanoff's terminology).

Reflection method

In 2008
Marc Renault
published an article in which he pointed out that it is Dmitry Mirimanoff who should be credited for creating " the reflection method" for solving Bertrand's ballot problem, not Désiré André to whom it had been long credited. Therefore,

Donald Knuth Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of comp ...

, who has read Renault's article, will credit Mirimanoff instead of André in future printings of Volume 1 of his monograph

The Art of Computer Programming ''The Art of Computer Programming'' (''TAOCP'') is a comprehensive multi-volume monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. it consists of published volumes 1, 2, 3, 4A, and 4 ...

.Donald E. Knuth. Private correspondence with Anton Lokhmotov. (2009)

References

External links