Related papers: Mathematical reasoning and the computer
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…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their…
Neural network models can now recognise images, understand text, translate languages, and play many human games at human or superhuman levels. These systems are highly abstracted, but are inspired by biological brains and use only…
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…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
In the present study, we investigate and compare reasoning in large language models (LLM) and humans using a selection of cognitive psychology tools traditionally dedicated to the study of (bounded) rationality. To do so, we presented to…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
A machine thinking model is proposed in this report based on recent advances of computer vision and the recent results of neuroscience devoted to brain understanding. We deliver the result of machine thinking in the form of sentences of…
Machines have achieved a broad and growing set of linguistic competencies, thanks to recent progress in Natural Language Processing (NLP). Psychologists have shown increasing interest in such models, comparing their output to psychological…
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…
Neural networks are computing models that have been leading progress in Machine Learning (ML) and Artificial Intelligence (AI) applications. In parallel, the first small scale quantum computing devices have become available in recent years,…
The development of highly fluent large language models (LLMs) has prompted increased interest in assessing their reasoning and problem-solving capabilities. We investigate whether several LLMs can solve a classic type of deductive reasoning…
Visual perception and language understanding are - fundamental components of human intelligence, enabling them to understand and reason about objects and their interactions. It is crucial for machines to have this capacity to reason using…
Creating learning models that can exhibit sophisticated reasoning skills is one of the greatest challenges in deep learning research, and mathematics is rapidly becoming one of the target domains for assessing scientific progress in this…
We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition - complementary to and in contrast with the more formalistic approach of automated…
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…
We propose Neural Reasoner, a framework for neural network-based reasoning over natural language sentences. Given a question, Neural Reasoner can infer over multiple supporting facts and find an answer to the question in specific forms.…
In recent years, the dramatic progress in machine learning has begun to impact many areas of science and technology significantly. In the present perspective article, we explore how quantum technologies are benefiting from this revolution.…