Related papers: On definitions of "mathematician"
Ambiguity is shown in the context of the differential calculus of several variables and with the help of the language of category theory, a way to solve it in its most general form is offered. It is also shown that this new definition is…
Recent concern about harms of information technologies motivate consideration of regulatory action to forestall or constrain certain developments in the field of artificial intelligence (AI). However, definitional ambiguity hampers the…
This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already…
The concepts of precision, and accuracy are domain and problem dependent. The simplified numeric hard and soft measures used in the fields of statistical learning, many types of machine learning, and binary or multiclass classification…
Social computing encompasses the mechanisms through which people interact with computational systems: crowdsourcing systems, ranking and recommendation systems, online prediction markets, citizen science projects, and collaboratively edited…
Defining artificial intelligence (AI) is a persistent challenge, often muddied by technical ambiguity and varying interpretations. Commonly used definitions heavily emphasize technical properties of AI but neglect the human purpose of it.…
The field of data science currently enjoys a broad definition that includes a wide array of activities which borrow from many other established fields of study. Having such a vague characterization of a field in the early stages might be…
Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the province of humans. As these tools become…
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
This is a survey of results on definability and undefinability in models of arithmetic. The goal is to present a stark difference between undefinability results in the standard model and much stronger versions about expansions of…
Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…
The field of ethnomathematics holds significance in the pursuit of comprehending how students can grasp, express, manipulate, and ultimately apply mathematical concepts. However, ethnomathematics is also considered a complex concept in…
In recent years, promising mathematical models have been suggested which aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully…
Classification systems are evaluated in a countless number of papers. However, we find that evaluation practice is often nebulous. Frequently, metrics are selected without arguments, and blurry terminology invites misconceptions. For…
In psychiatry, we often speak of constructing "models." Here we try to make sense of what such a claim might mean, starting with the most fundamental question: "What is (and isn't) a model?". We then discuss, in a concrete measurable sense,…
Writing assignments in any mathematics course always present several challenges, particularly in lower-level classes where the students are not expecting to write more than a few words at a time. Developed based on strategies from several…
In this paper we provide an exhaustive survey of the current state of the mathematics of filtration enlargement and an interpretation of the key results of the literature from the viewpoint of mathematical finance. The emphasis is on…
The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main…
Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…