Related papers: Tolstoy's Mathematics in "War and Peace"
This article reviews and develops an epistemological tradition in the philosophy of science, known as convergentism, which holds that inference methods should be assessed based on their ability to converge to the truth across a range of…
The article attempts to demonstrate the rich history of one truly remarkable problem situated at the confluence of probability theory and theory of numbers - finding the probability of co-primality of two randomly selected natural numbers.…
In a series of lectures given in 2003 soon after receiving the Fields Medal for his results in the Algebraic Geometry Vladimir Voevodsky (1966-2017) identifies two strategic goals for mathematics, which he plans to pursue in his further…
This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to…
Can we avoid wars at the crossroads of history? This question has been pursued by individuals, scholars, policymakers, and organizations throughout human history. In this research, we attempt to answer the question based on the recent…
Karl Pearson is the leading figure of XX century statistics. He and his co-workers crafted the core of the theory, methods and language of frequentist or classical statistics -- the prevalent inductive logic of contemporary science.…
An explanation for the political processes leading to the sudden collapse of empires and states would be useful for understanding both historical and contemporary political events. We seek a general description of state collapse spanning…
These are notes on the impact of Lagrange's memoir on the construction of geographical maps. We mention the relations of some ideas and questions introduced in this memoir with other notions that appeared later in the works of several…
In tug-of-war, two players compete by moving a counter along edges of a graph, each winning the right to move at a given turn according to the flip of a possibly biased coin. The game ends when the counter reaches the boundary, a fixed…
Beginning in the 1970s, statistician-cum-logician Per Martin-L\"of wrote a series of papers developing what became Martin-L\"of type theory, realizing a system where the distinction between mathematics and programming disappears. Inspired…
This paper gives a short review of the history of statistical physics starting from D. Bernoulli's kinetic theory of gases in the 18th century until the recent new developments in nonequilibrium kinetic theory in the last decades of this…
Douglas Walton's multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
When people mention the mathematical achievements of Euclid, his geometrical achievements always spring to mind. But, his Number-Theoretical achievements (See Books 7, 8 and 9 in his magnum opus \emph{Elements} [1]) are rarely spoken. The…
Game theory is the study of tractable games which may be used to model more complex systems. Board games, video games and sports, however, are intractable by design, so "ludological" theories about these games as complex phenomena should be…
The Colonel Blotto game, first introduced by Borel in 1921, is a well-studied game theory classic. Two colonels each have a pool of troops that they divide simultaneously among a set of battlefields. The winner of each battlefield is the…
The mathematical analysis was conceived in XVII century in Newton and Leibniz works. The problem of logical rigor in definitions was considered by Arnauld and Nicole in "Logique ou l'art de penser". They were the first, who distinguished…
The accepted lore is that Operational Research traces its roots back to the First and Second World Wars, when scientific research was used to improve military operations. In this essay we provide a different perspective on the origins of…
Rationality has been an intriguing topic for several decades. Even the scope of definition of rationality across different subjects varies. Several theories (e.g., game theory) initially evolved on the basis that agents (e.g., humans) are…
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…