Related papers: Tolstoy's Mathematics in "War and Peace"
This paper attributes the sudden emergence of mathematical probability and statistics in the second half of the seventeenth century to Calvin's Reformed theology. Calvin accommodated Epicurean chance with Stoic determinism and synthesised…
Interest in the mathematical structure of poetry dates back to at least the 19th century: after retiring from his mathematics position, J. J. Sylvester wrote a book on prosody called $\textit{The Laws of Verse}$. Today there is interest in…
The aim of this article has been to put together various aspects of the personality of the Italian mathematician Francesco Severi: the mathematical, the political, the institutional, academic and philosophical one. We tried in particular to…
The game theory techniques are used to find the equilibrium of a market. Game theory refers to the ways in which strategic interactions among economic agents produce outcomes with respect to the preferences (or utilities) of those agents,…
The calculus of relations was introduced by De Morgan and Peirce during the second half of the 19th century, as an extension of Boole's algebra of classes. Later developments on quantification theory by Frege and Peirce himself, paved the…
We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are…
As the etymology of the word shows, logic is intimately related to language, as exemplified by the work of philosophers from Antiquity and from the Middle-Age. At the beginning of the XX century, the crisis of the foundations of mathematics…
Based on the nine-palace diagram, we establish the systematical geometric theory of arithmetic, which can realize the arithmetical addition, subtraction, multiplication, division and other operations thoroughly in the mind. In this paper,…
Building on the collaborative Equational Theories project initiated by Terence Tao fifteen months ago, and combining it with ideas coming from machine learning and finite model theory, we construct a latent space of equational theories…
The purpose of this paper is to emphasize the role of language in the process of teaching and learning mathematics. We will begin with the definition of mathematics given by Cassiodorus (in its essential features repeated in Kolmogorov's…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
This essay traces the history of three interconnected strands. Firstly, changes in the concept of number, secondly, the study of the qualities of number, which evolved into number theory, and thirdly, the nature of mathematics itself, from…
A few remarks on how mathematics quests for freedom.
This paper is devoted to show that the last quarter of the past century can be considered as the golden age of the Mathematical Finance. In this period the collaboration of great economists and the best generation of probabilists, most of…
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…
Andrei Kolmogorov's Grundbegriffe der Wahrscheinlichkeits-rechnung put probability's modern mathematical formalism in place. It also provided a philosophy of probability--an explanation of how the formalism can be connected to the world of…
The effect of Richard T. Cox's contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra.…
Since Kolmogorov's theory, turbulence has been studied using various methods, many of which could be now be understood in a probabilistic framework. Herein, a comprehensive review of the advances made on stochastic theory of turbulence…
Littlewood--Paley theory began with the classic paper of Littlewood and Paley (J.\ E.\ Littlewood, R.\ E.\ A.\ C.\ Paley, {\em Theorems on Fourier Series and Power Series}. J. Lond. Math. Soc. (1), {\bf 6} (1931), 230--33). We discuss this…
Forcing was first introduced by Paul J. Cohen in his work on the independence of the Continuum Hypothesis. Other formulations of forcing appeared using Model Theory, Boolean-valued Models, and Topos Theory. There is a folkloric claim that…