Related papers: Database-Driven Mathematical Inquiry
Building machines that can understand text like humans is an AI-complete problem. A great deal of research has already gone into this, with astounding results, allowing everyday people to discuss with their telephones, or have their reading…
We summarize math search engines and search interfaces produced by the Document and Pattern Recognition Lab in recent years, and in particular the min math search interface and the Tangent search engine. Source code for both systems are…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
All but a few digital computers used for scientific computations have supported floating-point and digital arithmetic of rather limited numerical precision. The underlying assumptions were that the systems being studied were basically…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
Probabilistic databases (PDBs) model uncertainty in data in a quantitative way. In the established formal framework, probabilistic (relational) databases are finite probability spaces over relational database instances. This finiteness can…
As the use of technology increases and data analysis becomes integral in many businesses, the ability to quickly access and interpret data has become more important than ever. Information retrieval technologies are being utilized by…
Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains…
Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this…
Provenance, or information about the sources, derivation, custody or history of data, has been studied recently in a number of contexts, including databases, scientific workflows and the Semantic Web. Many provenance mechanisms have been…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
Data science and technology offer transformative tools and methods to science. This review article highlights latest development and progress in the interdisciplinary field of data-driven plasma science (DDPS). A large amount of data and…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…
In the article, proposed is a new e-learning information technology based on an ontology driven learning engine, which is matched with modern pedagogical technologies. With the help of proposed engine and developed question database we have…
Any act of problem-solving combines prior knowledge, local search, and a third element that is less often discussed: the extraction of information from search to update understanding. I propose a model of mathematical problem-solving as a…
An introduction to the emerging fusion of machine learning and causal inference. The book presents ideas from classical structural equation models (SEMs) and their modern AI equivalent, directed acyclical graphs (DAGs) and structural causal…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
We discuss whether science is in the process of being transformed from a quest for causality to a quest for correlation in light of the recent development in artificial intelligence. We observe that while a blind trust in the most seductive…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…