Dmitry Mirimanoff


Dmitry Semionovitch Mirimanoff became a doctor of mathematical sciences in 1900, in Geneva, and taught at the universities of Geneva and Lausanne. Mirimanoff made notable contributions to axiomatic set theory and to number theory. In 1917, he introduced, though not as explicitly as John von Neumann later, the cumulative hierarchy of sets and the notion of von Neumann ordinals; although he introduced a notion of regular he did not consider regularity as an axiom, but also explored what is now called non-well-founded set theory and had an emergent idea of what is now called bisimulation.
Mirimanoff became a member of the Moscow Mathematical Society in 1897.

Life

Dmitry Semionovitch Mirimanoff was born in Pereslavl-Zalessky, Russia, on 13 September 1861.
His parents were Semion Mirimanovitch Mirimanoff and Maria Dmitrievna Rudakova.
He was a great grandson of David A. Mirimanian , a member of an old Armenian family settled in Georgia and an honorary citizen of Tiflis.
Around 1885, Dmitry Mirimanoff met a French lady Malvina Geneviève Valentine Adriansen in Nice.
Geneviève Adriansen learnt Russian and accepted Russian Orthodox Christianity.
They married in Geneva on 25 October 1897 and had two sons: Alexander Dmitrievitch Mirimanoff, born in Oranienbaum in 1898, and Andreï Dmitrievitch Mirimanoff, born in Geneva in 1902.
The family lived in Russia until 1900 when they moved to Geneva.
After the 1917 revolutions they never visited Russia, although Dmitry's sisters Sophia and Lydia remained there.
Dmitry Mirimanoff became a Swiss citizen on 17 September 1926.
Dmitry Mirimanoff 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. Mirimanoff called a set x "regular" if every descending chain x ∋ x1 ∋ x2 ∋... is finite. Mirimanoff however did not consider his notion of regularity as an axiom to be observed by all sets; in later papers Mirimanoff also explored what are now called non-well-founded sets.

Fermat's last theorem

Reflection method

In 2008, 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, 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.