Related papers: Mathematical Monsters
This essay inquires how mathematical beings could be inserted into the architecture of modes of existence proposed by Bruno Latour in the framework of his pluralist and renewed ontology of the modern world. After a description of the…
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in…
Mathematical challenges punctuate the history of early modern mathematics. While cultural historians have attempted to contextualize these challenges among contemporary practices, in particular duels or advertisements in a competitive…
With the increasing adoption of Artificial Intelligence (AI) in all fields and daily activities, a heated debate is found about the advantages and challenges of AI and the need for navigating the concerns associated with AI to make the best…
This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were…
We usually construct mathematical objects that are accessible, on which we can put our hands, but a huge part of the mathematical existing is actually wild. Here we explore part of the wild world: its inhabitants are knots that are…
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…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…
The 19th century impressionist movement, as a reaction to "art pompier", is proposed as a comparison with modern evolutions in mathematics.
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
How many odd numbers are there? How many even numbers? From Galileo to Cantor, the suggestion was that there are the same number of odd, even and natural numbers, because all three sets can be mapped in one-one fashion to each other. This…
In the words of the twentieth-century British mathematician G. H. Hardy, "the human function is to 'discover or observe' mathematics" (1). For centuries, starting from the ancient Greeks, mankind has hunted for beauty and order in arts and…
Large Language Models (LLMs) are reshaping organizational knowing by unsettling the epistemological foundations of representational and practice-based perspectives. We conceptualize LLMs as Haraway-ian monsters, that is, hybrid,…
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 nature of the existence, revealed through Human cognitive system, has been evolving since the development of the languages. Part of such revelations were the geometrical forms and the numbers, whose beauty and order, wondrous and…
The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the…