We present the notions of category theory which are of use in Boolean valued analysis and describe the Boolean toposes that form the backstages of Boolean valued universes.

This is a brief overview of the worldline and memes of Yurii Reshetnyak (1929–1921), the Russian leader of geometric analysis.

We overview the main ideas and techniques of the functional-analytical approach to some extremal problems of convex geometry that stem from the Queen Dido problem.

The aim of the present article is to extend the Stone-Weierstrass theorem to functions ranging in a lattice normed space and admitting order rather than topological approximation. We proceed with the machinery of Boolean-valued transfer from lattice normed space to normed space.

We implement the Boolean valued analysis of Banach spaces. The realizations of Banach spaces in a Boolean valued universe are lattice normed spaces. We present the basic techniques of studying these objects as well as the Boolean valued approach to injective Banach lattices.

This is a brief overview of the worldline, contributions, and memes of Aleksandr Alexandrov (1912–1999), the first and foremost Russian geometer of the twentieth century.

This is a brief overview of the worldline and memes of Sergei Sobolev (1908–1989), a cofounder of distribution theory.

In the history of infinitesimal calculus, we trace innovation from Leibniz to Cauchy and reaction from Berkeley to Mansion and beyond. We explore 19th century infinitesimal lores, including the approaches of Simeon-Denis Poisson, Gaspard-Gustave de Coriolis, and Jean-Nicolas Noel. We examine contrasting historiographic approaches to such lores, in the work of Laugwitz, Schubring, Spalt, and others, and address a recent critique by Archibald et al. We argue that the element of contingency in this history is more prominent than many modern historians seem willing to acknowledge.

Leibniz scholarship is currently an area of lively debate. We respond to some recent criticisms by Archibald et al.

An erased Kantorovich space is the lattice ordered additive groupof a Kantorovich space. We study the special role of erased Kantorovich spacesin extending positive, dominated, and lattice homomorphismsand also the existence of unbounded polar-preserving group homomorphisms.Our method of study is Boolean-valued analysis.

This is an overview of the worldline, contribution, and memes of Leonid Kantorovich (1912-1986).

This is an overview of the life and contributions of Leonid Kantorovich, a renowned Russian mathematician and economist.

This is an overview of the worldline and contribution of Aleksandr Alexandrov (1912-1999).

We provide a version of Korovkin-type theorems for monotone sublinear operators in vector lattices and discuss the possibilities of further extensions and generalizations. .

The paper provides a brief overview of the origins, methods and results of Boolean valued analysis. Boolean valued representations of some mathematical structures and mappings are given in tabular form. A list of some problems arising outside the theory of Boolean valued models, but solved using the Boolean valued approach, is given. The relationship between the Kantorovich’s heuristic principle and the Boolean valued transfer principle is also discussed.

This is a short tribute to Aleksandr Alekseevich Borovkov on the occasion of his 90th birthday.March 6, 2021 is the ninetieth birthday of Aleksandr Borovkov, an outstanding mathematician who specializes in probability and statistics.The general public respects the latter areas of science but stumbles in understanding them.So the essence of probability and statistics needs short explanation.Kutateladze, S.S., A few words about probability and statistics (on the Occasion of the 90th birthday of Aleksandr Borovkov).

This is a continuation of the authors' previous study of the geometric characterizations of the preduals of injective Banach lattices. We seek the properties of the unit ball of a Banach space which make the space isometric or isomorphic to an injective Banach lattice. The study bases on the Boolean valued transfer principle for injective Banach lattices. The latter states that each such lattice serves as an interpretation of an AL-space in an appropriate Boolean valued model of set theory. External identification of the internal Boolean valued properties of the corresponding AL-spaces yields a characterization of injective Banach lattices among Banach spaces and ordered Banach spaces. We also describe the structure of the dual space and present some dual characterization of injective Banach lattices.

On 2 October, 2020, just over two months before his centenary, the outstanding representative of the St Petersburg School of Geometry, honourary member of the St Petersburg Mathematical Society, Professor Viktor Abramovich Zalgaller passed away. He was born on 25 December 1920 in the village of Parfino, Novgorod Province, in the family of engineer Abram Leont’evich Zalgaller and attorney Tat’yana Markovna Shabad-Zalgaller. In 1922 the family moved to Petrograd. In 1931 his father was convicted under Article 581 and spent 16 years in Ukhtpechlag2, in prison, and then in exile. After graduating from School no. 103 in the Smol’ninskii district of Leningrad in 1937, Viktor enrolled in the Faculty of Mathematics and Mechanics of Leningrad University. His abilities were noticed by L. V. Kantorovich, his lecturer on mathematical analysis, who asked the third-year student to prepare a textbook based on his notes. In 1940, as part of a mobilisation announced by the Young Communist League, Zalgaller was transferred to the Aviation Institute. There he received an engineering education, which played a significant role in his further research career. In the first days of the war he volunteered for the People’s Militia (Second Division) and was sent to the front almost immediately. During almost the entire war he was a signaller. The combat path of Viktor Zalgaller was not easy: the defence of Leningrad, the Oranienbaum Bridgehead, an injury during the lifting of the Leningrad blockade, the storming of Vyborg, battles in the Baltic states, the storming of Danzig, reaching the Elbe. . . Zalgaller was awarded the Order of the Red Star, the medal “For Courage”, three medals “For Battle Merit”, the medal “For the Defence of Leningrad”, and others. He met the end of the war as

This is a short obituary of Yuri Reshetnyak (1929-2021)