70 citations · 229 across the 50 of their papers we have counts for
6 papers · 1 filter
Constructive mathematics and teaching
Alexander Shen
Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This qu…
Mathematical works of Vladimir A. Uspensky: A commentary
Alexander Shen
Vladimir Andreevich Uspensky [1930-2018] was one of the Soviet pioneers of the theory of computation and mathematical logic in general (and my teacher and thesis advisor). This pap…
Rod in a train: a mechanical problem of H.Whitney, or Much Ado About Nothing
Alexander Shen
In 1941 a mechanical problem about a rod in a moving train (there is a initial position such that rod does not touch the floor while train is moving) was published by R.Courant and…
Algorithms and Geometric Constructions
Vladimir Uspenskiy, Alexander Shen
It is well known that several classical geometry problems (e.g., angle trisection) are unsolvable by compass and straightedge constructions. But what kind of object is proven to be…
Algorithmic Information Theory and Foundations of Probability
Alexander Shen
The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.
Algorithmic information theory and martingales
Laurent Bienvenu, Alexander Shen
The notion of an individual random sequence goes back to von Mises. We describe the evolution of this notion, especially the use of martingales (suggested by Ville), and the develo…