101 citations · 389 across the 22 of their papers we have counts for
25 papers
Time and periodicity from Ptolemy to Schroedinger: paradigm shifts vs continuity
Yuri I. Manin
I briefly consider the Kuhnian notion of "paradigm shifts" applied to the history of mathematics and argue that the succession and intergenerational continuity of mathematical thou…
Cognitive networks: brains, internet, and civilizations
Dmitrii Yu. Manin, Yuri I. Manin
In this short essay, we discuss some basic features of cognitive activity at several different space-time scales: from neural networks in the brain to civilizations. One motivation…
Neural codes and homotopy types: mathematical models of place field recognition
Yuri I. Manin
This note is a brief survey of some results of the recent collaboration of neurobiologists and mathematicians dedicated to stimulus reconstruction from neuronal spiking activity. T…
Forgotten Motives: the Varieties of Scientific Experience
Yuri I. Manin
Personal recollections about Alexandre Grothendieck and early days of his theory of motives
Arithmetic Differential Equations of Painleve' VI Type
Alexandru Buium, Yuri I. Manin
Using the description of Paileve' VI family of differential equations in terms of a universal elliptic curve, going back to R. Fuchs (cf. [Ma96]), we translate it into the realm of…
Complexity vs Energy: Theory of Computation and Theoretical Physics
Yuri I. Manin
This paper is a survey dedicated to the analogy between the notions of {\it complexity} in theoretical computer science and {\it energy} in physics. This analogy is not metaphorica…