& centerdot; This article offers a his-torical and mathematical reading of Andrej N. Kolmogorov's essay "the general theory of dynamical systems and classical mechanics", based on a close textual analysis. The essay is re-interpreted as a scientific manifesto that reframes classical mechanics through a combination of measure-theoretic and spectral perspectives, with particular attention to its rhetori-cal architecture. The analysis brings into view the intersections, within the theory of dynamical systems, be-tween classical mechanics, ergodic theory, and operator theory through a network of references spanning four decades (1917-1954) and different na-tional traditions. It also highlights the dramatic structure of the text, in- tended to draw attention to "old-fashioned" open problems in classical mechanics and to a new approach-imbuing it with a sense of pathos likely derived from its origin as a lecture presented during the 1954 Amsterdam International Congress of Mathematicians. In this sense, the scope of Kolmogorov's text goes far beyond the presentation of early in-stances of what would later become KAM theorems-thus establishing the essay as a landmarkwriting in modern mathematics. The rhetorical architec-ture culminates in the recognition of two paradigmatic regimes of conser-vative dynamics: global transitivity with continuous spectrum, versus invariant tori and quasi-periodic motions with discrete spectrum.
This study explores the contributions of Arab mathematicians to Diophantine analysis across both the eastern and western regions of the Islamic world during the medi-eval period. It focuses particularly on problems that can be reformulated as indeterminate equations of the second degree-or systems thereof- and examines the dual use of algebraic and arithmetic methods in their solution. Through a comparative analysis of these approaches within the Arabic mathematical tradition and those found in Diophantus's Arithmetica, the study highlights the distinctive methodologies and innovations that emerged within classical Islamic mathematics.
Established in April 1930, the Volta Foundation was one of the centers annexed to the Reale Accade-mia d'Italia and played a central role in the fascist foreign policy of science because it financed dozens of foreign travel fellowships and nine inter-national conferences, the first dedi-cated to Nuclear Physics (1931) and the last one before the war on con-temporary Mathematics and its ap-plications (1939). Postponed due to the outbreak of the war, and finally cancelled, the 1939 Volta Conference deserves an in-depth analysis under a double perspective: political and mathematical. Beyond the exclusion of Jewish mathematicians, its organ-zation was in fact an exercise of science anti-diplomacy. Considering the extensive correspondence kept in the archives of the Royal Academy of Italy and the Italian Mathematical Union, the paper will focus on the behind-the-scenes to this virtual con-erence, scrutinizing the practice of international cooperation and propa-gandistic uses of mathematics in fas-cist Italy.
The paper studies the presence of Sergei Bernstein at Khar-kiv university during two decades, in the turmoil of events that happened in Ukraine in the Great War and its aftermath. The mathmatician's ap-parent refusal to emigrate during the 1920s is examined as well as his suc- cessful career, leading to a transfer to Leningrad and Moscow in spite of his rather open opposition to some aspects of the Soviet ideology. Some particularities of the local situation in Kharkiv may have played a role in this singular evolution.
The article traces Enrico Giusti's long engagement with Leonardo Pisano's writings, beginning with the 2002 centenary of the Liber abbaci and culminating in the editions of Leonardo's complete works prepared in the final years of his life. It outlines the principal stages of this editorial enterprise and emphasises the inter-play of philological precision and mathematical insight that defines Giusti's contribution to the critical study of scientific and mathematical texts.
