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Artificial intelligence is transforming mathematics at a speed and scale that demand active engagement from the mathematical community. We examine five areas where this transformation is particularly pressing: values, practice, teaching,…

History and Overview · Mathematics 2026-05-11 Johan Commelin , Mateja Jamnik , Rodrigo Ochigame , Lenny Taelman , Akshay Venkatesh

The game of chess as always been viewed as an iconic representation of intellectual prowess. Since the very beginning of computer science, the challenge of being able to program a computer capable of playing chess and beating humans has…

Other Computer Science · Computer Science 2012-03-16 Frederic Prost

The importance of knowing ICT training and motivation -so relevant in today's society- which currently offers the first year college students, mostly in degrees in Education, focuses the object of interest in this study. The following…

Computers and Society · Computer Science 2016-05-24 Maria Isabel Ponce-Escudero , Jose Gomez-Galan

We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…

History and Overview · Mathematics 2007-05-23 Palle E. T. Jorgensen

Uncovering the structure of socioeconomic systems and timely estimation of socioeconomic status are significant for economic development. The understanding of socioeconomic processes provides foundations to quantify global economic…

Physics and Society · Physics 2019-07-02 Jian Gao , Yi-Cheng Zhang , Tao Zhou

Social evolutionary theory seeks to explain increases in the scale and complexity of human societies, from origins to present. Over the course of the twentieth century, social evolutionary theory largely fell out of favor as a way of…

Multiagent Systems · Computer Science 2025-02-27 David H. Wolpert , Kyle Harper

The formation and development of the human person is most influenced by the environment in which it lives, studies, works. Therefore, the problem of the creation of such a high-tech information and communication educational and scientific…

History and Overview · Mathematics 2018-09-11 Kateryna Slovak , Serhiy Semerikov , Yu. V. Tryus

The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation,…

Artificial Intelligence · Computer Science 2025-02-10 Simon Zhang

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

Logic · Mathematics 2008-03-25 Wesley Calvert , Julia F. Knight

Turing's (1936) paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure…

Logic · Mathematics 2015-06-23 S. Barry Cooper

Computational thinking is a way of reasoning about the world in terms of data. This mindset channels number crunching toward an ambition to discover knowledge through logic, models and simulations. Here we show how computational cognitive…

Physics and Society · Physics 2020-07-21 Massimo Stella , Anastasiya Kapuza , Catherine Cramer , Stephen Uzzo

Computer programming is undergoing a true transformation driven by powerful new tools for automatic source code generation based on large language models. This transformation is also manifesting in introductory programming courses at…

Computers and Society · Computer Science 2025-07-02 Clemente Rubio-Manzano , Jazna Meza , Rodolfo Fernandez-Santibanez , Christian Vidal-Castro

The shortage of people trained in STEM fields is becoming acute, and universities and colleges are straining to satisfy this demand. In the case of computer science, for instance, the number of US students taking introductory courses has…

There is one, and only one way, consistent with fundamental physics, that the efficiency of general digital computation can continue increasing indefinitely, and that is to apply the principles of reversible computing. We need to begin…

Emerging Technologies · Computer Science 2018-03-09 Michael P. Frank

We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…

Computational Complexity · Computer Science 2011-04-19 Joost J. Joosten , Fernando Soler-Toscano , Hector Zenil

The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in…

Quantum Physics · Physics 2007-05-23 Anders K. H. Bengtsson

Quantum computing is a growing field at the intersection of physics and computer science. The goal of this article is to highlight a successfully trialled quantum computing course for high school students between the ages of 15 and 18 years…

Physics Education · Physics 2024-06-19 Ciaran Hughes , Joshua Isaacson , Anastasia Perry , Ranbel Sun , Jessica Turner

Animation, which is basically a form of pictorial presentation, has become the most prominent feature of technology-based learning environments. It refers to simulated motion pictures showing movement of drawn objects. Recently, educational…

Graphics · Computer Science 2013-12-09 Sajid Musa , Rushan Ziatdinov , Carol Griffiths

By nature, transmissible human knowledge is enumerable: every sentence, movie, audio record can be encoded in a sufficiently long string of 0's and 1's. The works of G\"odel, Turing and others showed that there are inherent limits and…

Other Computer Science · Computer Science 2020-01-30 Frédéric Prost

A key mission of computer science is to enable people realize their creative ideas as naturally and painlessly as possible. Software engineering is at the center of this mission -- software technologies enable reification of ideas into…

Software Engineering · Computer Science 2016-02-04 Mehrdad Afshari , Zhendong Su