Big Math and the One-Brain Barrier: The Tetrapod Model of Mathematical Knowledge

Carette, Jacques; Farmer, William M.; Kohlhase, Michael; Rabe, Florian

doi:10.1007/s00283-020-10006-0

Cited by 12 publications

(5 citation statements)

References 25 publications

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“…The Tetrapod project [Carette et al, 2020a] envisions a software system in which 5 aspects of doing mathematics are integrated. These 5 aspects are organization, inference, computation, narration, and concretization.…”

Section: Broader Contextmentioning

confidence: 99%

Leveraging the Information Contained in Theory Presentations

Carette

Farmer

Sharoda

2020

Lecture Notes in Computer Science

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Building a large library of mathematical knowledge is a complex and labour-intensive task. By examining current libraries of mathematics, we see that the human effort put in building them is not entirely directed towards tasks that need human creativity.Instead, a non-trivial amount of work is spent on providing definitions that could have been mechanically derived.In this work, we propose a generative approach to library building, so definitions that can be automatically derived are computed by meta-programs. We focus our attention on libraries of algebraic structures, like monoids, groups, and rings. These structures are highly inter-related and their commonalities have been well-studied in universal algebra. We use theory presentation combinators to build a library of algebraic structures. Definitions from universal algebra and programming languages meta-theory are used to derive library definitions of constructions, like homomorphisms and term languages, from algebraic theory presentations. The result is an interpreter that, given 227 theory expressions, builds a library of over 5000 definitions. This library is, then, exported to Agda and Lean.iii To my family, You are my greatest blessing iv I would like to express my sincere thanks to my supervisors Dr. Jacques Carette and Dr. William Farmer for their continuous support to my learning journey. Your expertise and feedback were invaluable in shaping this research direction and throughout my studies. I learned from you a lot about how to do research and communicate it. I

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Section: Broader Contextmentioning

confidence: 99%

Leveraging the Information Contained in Theory Presentations

Carette

Farmer

Sharoda

2020

Lecture Notes in Computer Science

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“…В настоящее время происходящие изменения в инфраструктуре научных коммуникаций поставили целый ряд новых задач по управлению знаниями, а каждый этап жизненного цикла научной публикации предполагает его сопровождение специализированными программными инструментами (например, [1][2][3][4]).…”

Section: Introductionunclassified

Extraction Of Wikidata Knowledge For The Metadata Formation For Documents of Digital Mathematical Collections

Gafurova¹,

Елизаров²,

Lipachev³

2022

RDLJ

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Methods for creating digital mathematical collections that include unstructured sets of documents are presented. These sets contain materials from scientific conferences, as well as articles from the archives of mathematical journals of the "pre-digital" period. Using the software tools of the metadata factory of the digital mathematical library Lobachevskii DML, a mandatory set of metadata for digital collection documents was formed. To refine and replenish the metadata sets, knowledge extraction methods from Wikidata were used. To search Wikidata for information about digital collection documents and their authors, a system of SPARQL queries has been developed. A set of Wikidata entities is defined, which determine the features of the search, as well as the subsequent filtering of the results. Methods for clarifying and supplementing the bibliographic references given in the articles are proposed. When forming the metadata of documents of retrocollections, a search was made in Wikidata for information about the years of life of the authors of articles, as well as URLs of web pages with information about articles and their authors. The results of the formation of several new digital collections of the Lobachevskii-DML digital library are presented.

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“…Currently, information and communication technologies (ICT) are being actively developed and implemented in research and development, which makes it possible to use the entire body of accumulated scientific knowledge when conducting new research. In turn, such use requires the creation of a complex of new technologies that provide optimal management of existing knowledge, the organization of effective access to them, as well as the exchange and reuse of new types of knowledge structures (see, for example, [2]).…”

Section: Introductionmentioning

confidence: 99%

Digital Libraries and the Common Digital Space of Mathematical Knowledge

Елизаров

Lipachev

2021

Preprint

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We present the results of the development of a range of semantic services for the integrated management of electronic scientific collections. The goals of these developments are the formation of a unified digital space of mathematical knowledge, as well as information support for research activities in the field of mathematics and computer science. The digital collections we create and the semantic services we develop form the backbone of the Lobachevskii-DML digital math library. In implementing this study, we used approaches that are consistent with the widely discussed and accepted concepts of building the World Digital Mathematical Library (WDML).

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Big Math and the One-Brain Barrier: The Tetrapod Model of Mathematical Knowledge

Cited by 12 publications

References 25 publications

Leveraging the Information Contained in Theory Presentations

Leveraging the Information Contained in Theory Presentations

Extraction Of Wikidata Knowledge For The Metadata Formation For Documents of Digital Mathematical Collections

Digital Libraries and the Common Digital Space of Mathematical Knowledge

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