Related papers: Post-human mathematics
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays,…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
``The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words…
When we want to predict the future, we compute it from what we know about the present. Specifically, we take a mathematical representation of observed reality, plug it into some dynamical equations, and then map the time-evolved result back…
This essay discusses whether computers, using Artificial Intelligence (AI), could create art. First, the history of technologies that automated aspects of art is surveyed, including photography and animation. In each case, there were…
This paper addresses the question of how able the current trends of Artificial Intelligence (AI) are in managing to take the responsibility of a full course of mathematics at a college level. The study evaluates this ability in four…
This paper discusses digital online mathematics examinations -- a discussion ranging from high school to university level examinations. In particular, we consider the nature of mathematical writing, what is distinctive about mathematical…
Politics today is largely about the art of messaging to influence the public, but the mathematical theory of messaging -- information and communication theory -- can turn this art into a precise analysis, both qualitative and quantitative,…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical…
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
Some of the strongest evidence that human minds should be thought about in terms of symbolic systems has been the way they combine ideas, produce novelty, and learn quickly. We argue that modern neural networks -- and the artificial…
The ability to represent scientific data and concepts visually is becoming increasingly important due to the unprecedented exponential growth of computational power during the present digital age. The data sets and simulations scientists in…
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
Mammalian brain is one of the most complex objects in the known universe, as it governs every aspect of animal's and human behavior. It is fair to say that we have a very limited knowledge of how the brain operates and functions.…
Human beings are considered as the most intelligent species on Earth. The ability to think, to create, to innovate, are the key elements which make humans superior over other existing species on Earth. Machines lack all those elements,…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
In today's education systems, there is a deep concern about the importance of teaching code and computer programming in schools. Moving digital learning from a simple use of tools to understanding the processes of the internal functioning…