Related papers: Post-human mathematics
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
New understandings of the functioning of human brains engaged in mathematics raise interesting questions for mathematics educators. Novel lines of research are suggested by neuroscientific findings, and new light is shed on some…
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
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…
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
Mathematics is one of the most powerful conceptual systems developed and used by the human species. Dreams of automated mathematicians have a storied history in artificial intelligence (AI). Rapid progress in AI, particularly propelled by…
In this article, I discuss the relationship of mathematics to the physical world, and to other spheres of human knowledge. In particular, I argue that Mathematics is created by human beings, and the number $\pi$ can not be said to have…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
Computers have already changed the way that humans do mathematics: they enable us to compute efficiently. But will they soon be helping us to reason? And will they one day start reasoning themselves? We give an overview of recent…
Humans are the most effective integrators and producers of information, directly and through the use of information-processing inventions. As these inventions become increasingly sophisticated, the substantive role of humans in processing…
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…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
Today we live in computational abundance whereby our everyday lives and the environment that surrounds us are suffused with digital technologies. This is a world of anticipatory technology and contextual computing that uses smart diffused…
Post-human design runs the risk of obscuring the fact that AI technology actually imports a Cartesian humanist logic, which subsequently influences how we design and conceive of so-called smart or intelligent objects. This leads to unwanted…
The complexity of cultures in the modern world is now beyond human comprehension. Cognitive sciences cast doubts on the traditional explanations based on mental models. The core subjects in humanities may lose their importance. Humanities…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical…
The speed and transformative power of human cultural evolution is evident from the change it has wrought on our planet. This chapter proposes a human computation program aimed at (1) distinguishing algorithmic from non-algorithmic…
Computers have a direct impact on our lives nowadays. Human's interaction with the computer has modified with the passage of time as improvement in technology occurred the better the human computer interaction became. Today we are…
The widespread availability of generative artificial intelligence tools poses new challenges for school mathematics education, particularly regarding the formative role of traditional mathematical tasks. In post-AI educational contexts,…