Related papers: Post-human mathematics
Having a computer do the work for you has become more and more common over time. But in the entertainment area, where a human is a creator, we want to avoid having too much influence on technology. On the other hand, inspiration is still…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…
As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…
Generative AI techniques have opened the path for new generations of machines in diverse domains. These machines have various capabilities for example, they can produce images, generate answers or stories, and write codes based on the…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
Creativity is perhaps what most differentiates humans from other species. It involves the capacity to shift between divergent and convergent modes of thought in response to task demands. Divergent thought has been characterized as the kind…
Recent developments in computer programming and in mathematics suggest that there is a strong case for a new way of introducing programming to enhance the learning of school mathematics. The article describes a collaboration of mathematics…
Human cognitive performance is enhanced by the use of tools. For example, a human can produce a much greater, and more accurate, volume of mathematical calculation in a unit of time using a calculator or a spreadsheet application on a…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The new field of hypercomputation studies models of computation…
Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind,…
We are at the dawn of a new era, where advances in computer power, broadband communication and digital sensor technologies have led to an unprecedented flood of data inundating our surrounding. It is generally believed that means such as…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however,…
It has been proposed that human physical reasoning consists largely of running "physics engines in the head" in which the future trajectory of the physical system under consideration is computed precisely using accurate scientific theories.…
This piece plays with the idea of the Computocene: an era defined not merely by the ubiquity of computers, but by their deepening role in how we observe, interpret, and make sense of the world. Rather than emphasizing automation, speed,…
Human computation is an approach to solving problems that prove difficult using AI only, and involves the cooperation of many humans. Because human computation requires close engagement with both "human populations as users" and "human…
Relentless progress in artificial intelligence (AI) is increasingly raising concerns that machines will replace humans on the job market, and perhaps altogether. Eliezer Yudkowski and others have explored the possibility that a promising…
The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even to the way we interpret mathematical…
Human-AI co-creativity represents a transformative shift in how humans and generative AI tools collaborate in creative processes. This chapter explores the synergies between human ingenuity and AI capabilities across four levels of…