Related papers: Post-human mathematics
Can computers overcome human capabilities? This is a paradoxical and controversial question, particularly because there are many hidden assumptions. This article focuses on that issue putting on evidence some misconception related with…
The last two decades have seen tremendous advances in Artificial Intelligence. The exponential growth in terms of computation capabilities has given us hope of developing humans like robots. The question is: are we there yet? Maybe not.…
What constitutes human creativity, and is it possible for computers to exhibit genuine creativity? We argue that achieving human-level intelligence in computers, or so-called Artificial General Intelligence, necessitates attaining also…
Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we…
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…
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
Artificial computing machinery transforms representations through an objective process, to be interpreted subjectively by humans, so the machine and the interpreter are different entities, but in the putative natural computing both…
In the very large debates on ethics of algorithms, this paper proposes an analysis on human responsibility. On one hand, algorithms are designed by some humans, who bear a part of responsibility in the results and unexpected impacts.…
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards…
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…
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,…
As far as algorithmic thinking is bound by symbolic paper-and-pencil operations, the Church-Turing thesis appears to hold. But is physics, and even more so, is the human mind, bound by symbolic paper-and-pencil operations? What about the…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
The fundamental role of mathematics as an inspiration for artists, but also as a tool for art creation, is presented in this paper following different art fields, like architecture, sculpture, painting, photography, literature and poetry,…
There are inherent limits in classical computation for it to serve as an adequate model of human cognition. In particular, non-commutativity, while ubiquitous in physics and psychology, cannot be sufficiently handled. We propose that we…
General wisdom is, mathematical operation is needed to generate number by numbers. It is pointed out that without any mathematical operation true random numbers can be generated by numbers through algorithmic process. It implies that human…
Recent progress in artificial intelligence (AI) has renewed interest in building systems that learn and think like people. Many advances have come from using deep neural networks trained end-to-end in tasks such as object recognition, video…
The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically…