Related papers: Is Mathematics Obsolete?
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…
{\bf Abstract.} The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to a well-known open problem. It has two objectives. The first is to reconcile the way of…
Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions,…
Current advances in Artificial Intelligence and machine learning in general, and deep learning in particular have reached unprecedented impact not only across research communities, but also over popular media channels. However, concerns…
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…
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…
Despite many recent advancements in language modeling, state-of-the-art language models lack grounding in the real world and struggle with tasks involving complex reasoning. Meanwhile, advances in the symbolic reasoning capabilities of AI…
The capabilities of modern artificial intelligence (AI) as a ``scientific collaborator'' are explored by engaging it with three nuanced problems in quantum optics: state populations in optical pumping, resonant transitions between decaying…
Aristotle is generally accepted as the father of logic. The ideas that he raised in his study of logical reasoning carried the development of science over the centuries. Today, in the era of AI, this title of the fatherhood of logic has a…
Artificial intelligence (AI) is reshaping how research is conceived, conducted, and communicated across fields from chemistry to biomedicine. This commentary examines how AI is transforming the research workflow. AI systems now help…
A few remarks on how mathematics quests for freedom.
Neurosymbolic artificial intelligence (AI) systems combine neural network and classical symbolic AI mechanisms to exploit the complementary strengths of large scale, generalizable learning and robust, verifiable reasoning. Numerous…
Knowledge representation and reasoning in neural networks have been a long-standing endeavor which has attracted much attention recently. The principled integration of reasoning and learning in neural networks is a main objective of the…
Can we define what it means to be "creative," and if so, can our definition drive artificial intelligence (AI) systems to feats of creativity indistinguishable from human efforts? This mixed question is considered from technological and…
Reasoning has long been understood as a pathway between stages of understanding. Proper reasoning leads to understanding of a given subject. This reasoning was conceptualized as a process of understanding in a particular way, i.e.,…
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 chapter provides an overview of the different Artificial Intelligence (AI) systems that are being used in contemporary digital tools for Mathematics Education (ME). It is aimed at researchers in AI and Machine Learning (ML), for whom…
The advances in language-based Artificial Intelligence (AI) technologies applied to build educational applications can present AI for social-good opportunities with a broader positive impact. Across many disciplines, enhancing the quality…
The evolution of mathematics is shaped importantly by interestingness: researchers choose which problems to pursue, and students choose which problems to engage with, based on expectations of interest and challenge. As AI systems,…
The research on and application of artificial intelligence (AI) has triggered a comprehensive scientific, economic, social and political discussion. Here we argue that statistics, as an interdisciplinary scientific field, plays a…