The digital mathematical library Lobachevskii DML is one of the national initiatives that have emerged in the past decade in different countries of the world. During this time, the formed technical and organizational conditions allowed making mathematicians' dreams of a global World Digital Mathematical Library (WDML) a reality. Following the vision approved by the International Mathematical Union, we started the Lobachevskii DML project in 2017 - the year of the 225-th anniversary of the birth of the brilliant mathematician Nikolai Ivanovich Lobachevskii, the founder of non-Euclidean geometry, the rector of the Kazan University. The main task of Lobachevskii DML project is the development of tools for managing mathematical content, which take into account not only the specifics of mathematical texts, but also the features of processing Russian-language texts. A particular task of creating this digital library is the integration of mathematical resources of Kazan University. Therefore, the original goal of the project was to build up a sound basis for a digital archive comprising the relevant mathematical literature published for 213 years of the existence of Kazan University and stored in the libraries of the University and Kazan. According to our assumption, the digital library Lobachevskii DML should be endowed with all conceivable necessary functions and services, making it a comprehensive and up-to-date live DML, generally respected and used by the local as well as the global mathematical community. From the very beginning, we had in mind that the Lobachevskii DML should constitute a building block for the envisioned global WDML. In this paper, the results of the implementation of the digital mathematical library Lobachevsky-DML are presented. We describe the purpose of creating this digital library, methods of managing mathematical content based on semantic technologies. The following show how Lobachevskii DML interacts with the information systems of scientific journals. We also present a system of services to support the life cycle of a mathematical document and highlight technologies for supporting new forms of scientific publications and providing integration services with other digital mathematical archives and libraries.
Introduction
The creation and development of specialized digital
libraries (DL) are one of the directions for the formation
of a global scientific infrastructure. In the field of
mathematics, the problems of integrating knowledge
obtained over the entire “printed” period of the
development of this science have been considered in a number
of projects (see, for example, [
1
]). Even when such
projects were of a local nature, the methods and tools
developed during their implementation were oriented
towards a comprehensive integration of knowledge (see,
for example, [
2–4
]).
The modern vision of the tasks of forming a global
infrastructure of mathematical knowledge is reflected in
the documents of the World Digital Mathematics
Library (WDML) project [
5
]. In these documents, it was
noted that the leading role in the formation of digital
mathematical collections, the accompaniment of their
metadata (annotations, key words, etc.) is given by the
“smaller” DML.
The present work is devoted to the presentation of
Lobachevskii Digital Mathematics Library
(Lobachevskii DML, http://www.Lobachevskii-dml.ru/), which we
develop in accordance with the basic principles of
WDML. The digital mathematical library Lobachevskii
DML is another of the national initiatives that have
emerged in the past decade in different countries of the
world. During this time, the formed technical and
organizational conditions allowed making mathematicians’
dreams of a global WDML a reality. Following the
vision approved by the International Mathematical Union,
we started the Lobachevskii DML project in 2017 – the
year of the 225-th anniversary of the birth of the
brilliant mathematician Nikolai Ivanovich Lobachevskii,
the founder of non-Euclidean geometry, the rector (from
1827 to 1845) of the Kazan University. The year 2017
was announced at the Kazan University of as the “Year
of N. I. Lobachevskii”.
The main task of Lobachevskii DML project is the
development of such tools for managing mathematical
content, which take into account not only the specifics
of mathematical texts, but also the features of
processing Russian-language texts. A particular task of
creating this digital library is the integration of
mathematical resources of Kazan University. Therefore, the
original goal of the project was to build up a sound basis
for a digital archive comprising the relevant
mathematical literature published for 213 years of the existence of
Kazan University and stored in the libraries of the
University and Kazan. According to our assumption, the
digital library Lobachevskii DML should be endowed
with all conceivable necessary functions and services,
making it a comprehensive and up-to-date live DML,
generally respected and used by the local as well as the
global mathematical community. From the very
beginning, we had in mind that the Lobachevskii DML
should constitute a building block for the envisioned
global WDML.
In this paper, the results of the development of the
digital mathematical library Lobachevsky-DML are
presented. We describe the purpose of creating this
digital library, methods of managing mathematical content
based on semantic technologies. The following shows
how Lobachevskii DML interacts with the information
systems of scientific journals. We also present a system
of services to support the life cycle of a mathematical
document and highlight technologies for supporting new
forms of scientific publications and providing
integration services with other digital mathematical archives
and libraries.
1 Information Systems in Mathematics
Since inception of the first scientific information
systems, the community of mathematicians has been
involved in the full cycle of developing such systems,
from basic idea to full-scale implementation.
Wellknown examples are an open source system TeX [
6
] and
commercial systems Wolfram Mathematica and
WolframAlpha [
7, 8
]. With the help of communities of
mathematicians, tools for mathematical content
management are also actively developed. Examples are
MathJax system by American Mathematical Society,
information system Math-Net.Ru (http://www.mathnet.
ru), developed at the Steklov Mathematical Institute of
the Russian Academy of Sciences, and the collection of
publicly available preprints arXiv.org (https://arxiv.
org/). Now one of the largest digital mathematical
libraries is Mizar (http://www.mizar.org/). This is a
collection of papers prepared in the Mizar system of formal
language, containing definitions, theorems and proofs
[
9, 10
]. Mizar is one of the pioneering systems for
mathematics formalization, which still has an active
user community. The project has been in constant
development since 1973.
At present, scientific research in the field of
mathematics is increasingly associated with the use of modern
information technologies (cloud, semantic technologies,
etc.). These technologies are used in research conducted
by distributed scientific groups, the preparation and
dissemination of mathematical knowledge in electronic
form, the formation of mathematical digital libraries and
intellectual processing of their contents. Particular
attention is paid to creating a single information space by
integrating existing and organizing new digital
mathematical libraries (DML). Description of existing digital
mathematical libraries with the indication of the
purposes and principles of their construction, as well as
services for managing scientific content is contained in
[
11
]. Implementation and development of digital
mathematical libraries are associated with the development
of special tools and the continuous improvement of their
functionality.
Since the beginning of the 21st century, a number of
developers have created information systems for the
management of electronic scientific journals. We
compared these systems according to the selected criteria
[
12
]. As a result, the OJS system was recognized as the
optimal [
13
]. We successfully implemented this
information platform in the journals Lobachevskii Journal of
Mathematics (LJM, http://ljm.kpfu.ru/)/), one of the first
Russian electronic mathematical journals, and Russian
Digital Libraries (http://ojs.kpfu.ru/index.php/elbib). To
manage digital content, we also developed a number of
tools that automate a whole series of editorial processes.
These include, in particular, the choice of
recommendations for the selection of reviewers, style validation of
author's documents, search tools, article design services,
etc. These tools served as the technological basis for the
Lobachevskii DML developed by us (see Section 3).
Let us also pay attention to important results related
to the formalization of the of mathematical articles
representations. For these purposes, specialized formal
languages for the presentation of mathematical texts
have been developed (see, for example, [
14–18
]). These
technologies are also used to construct a mathematical
ontology and create a semantic search service [
19–22
].
The above, as well as many other implemented
mathematical projects paved the way for the realization
of a new idea – the creation of the World Digital
Mathematical Library (WDML).
The idea of creating a WDML arose in 2002. The
initial aim of this project was digitizing the entire set of
mathematical literature (both modern and historical),
link it to the present literature, and make it clickable
(see [
1, 23–28
]). As noted in [
25
], the success of this
project and its further impact on mathematics, science
and education could be the most significant event after
the invention of scientific journals and to become a
prototype for a new model of scientific and technical
cooperation, a new paradigm for future science in the
electronic world. At the same time, the implementation of
such a large project will inevitably cause a series of
problems. These problems and ways to overcome them
were analyzed in [
27
]. In particular, one of the
recommendations was the proposal to develop and coordinate
some local projects of creating DML (see ([
27, 28
]).
Basic plans for the construction of WDML in
20142015 were discussed by various mathematical
communities and fixed in a number of documents (see [
5, 29
]).
In particular, it was noted that the next step in the
development of the WDML project would be building
information networks, knowledge-based, which are
contained in mathematical publications. Many of the
research groups of mathematicians throughout the world
took part in the discussion of these ideas, including our
group, which represented Kazan University.
In February 2016, in the Fields Institute (Toronto,
Ontario) by the Wolfram Foundation, the Fields
Institute and the International Mathematical Union working
group for the creation WDML, a Seminar on the
Semantic Representation of Mathematical Knowledge was
organized (https://www.fields.utoronto.ca/Programs/
science/15-16/semantic/). Our report on this symposium
was devoted to modeling and software solutions in the
area of semantic representation of mathematical
knowledge [
30
]. These results correspond to the general
ideology of the WDML-project in terms of semantic
representation and processing of mathematical
knowledge and are a strategic direction of our group's
research. In particular, they are connected to the project
for the construction of the digital mathematical library
Lobachevskii DML, which is described below.
2 Object Approach to the Scientific DigitalContent Management
Managing of digital mathematical documents is a
unique and complex task. This is due both to the
processing of mathematical formulas and to the specific
structure of a mathematical document consisting of a
logically connected sequence of definitions, theorems,
proofs and references. The key idea identified in the
WDML project documents is the development of object
classes for adequate description and research of
mathematical content: a new paradigm for representing digital
mathematical content based on elements (classes) and
their interrelations is proposed. The selection of classes
of mathematical objects and the formation on their basis
of ontologies of knowledge areas will allow creating
new tools for processing information, in particular,
extracting and processing formulas, searching for similar
results, and so on.
In our works [
31–33
], methods of structural analysis
of mathematical documents and the selection of objects
from them are proposed. In [
22, 34
], the digital
ecosystem OntoMath is described, consisting of ontologies,
text analytics tools and applications, designed to control
mathematical knowledge. Semantic annotation of
mathematical texts is based on the ontology constructed
within the framework of the Mocassin project, and
ontology of professional mathematics OntoMathPRO [
35
].
An important application developed on the basis of
these ontologies is a special software platform for
preparing a mathematical set of related data for publication
in the LOD cloud. Another important tool is the
semantic search service by mathematical formulas [
34
].
Another application of the OntoMath ecosystem is a
recommendation system for collections of physical and
mathematical documents. In particular, for a given
document based on selected objects of mathematical
knowledge, this system allows you to create a list of
“similar” documents (see [
36
]). These tools are included
in the services of the Lobachevskii DML.
3 Content, Structure and Services of Lobachevskii DML
3.1 Content and structure of the digital library
Mathematical literature that has been published in
Kazan University for more than two centuries of its
existence is fairly varied. All these publications have been
fully preserved in Scientific Library of Kazan
University. The Great Russian scientist N. I. Lobachevskii
played a great role in the development of this library. In
1825, he was elected a librarian and managed the library
until 1835, combining these duties with the duties of the
rector. With him, the scientific foundations of the
collection of Library funds were laid, the compilation of
single catalogs began, Library has become public,
accessible to residents of the city, and a special building
was erected for it. Today our library is named after
N. I. Lobachevskii. With nearly 6 million publications,
it is one of the largest libraries in Russia.
The main goal of creating the Lobachevskii DML
was to not only create an archive of specialized
literature for mathematics researchers, but also to form an
open extensive mathematical library for a wide range of
users, possessing a wide range of information
processing tools, including search tools. Of course, the
basis of the Lobachevskii DML were research journals, as
well as selected conference materials and monographs.
The main emphasis in the selection of documents was
made on the relevance and scientific novelty of
materials included in the library.
The informational basis of digital collections in the
Lobachevskii DML was printed mathematical books
prepared at the Kazan University. At first, these editions
were translated into digital format: the result of
scanning was a set of pdf-files containing articles from
scientific journals, proceedings of conferences, and
monographs.
Scientific journals are not only the most important
section of the generated DML, but also collections, the
easiest to process in DML, because these articles have a
uniform structure and a standard set of metadata.
terials of international conferences on mathematics and
mechanics;
• the digital collection of articles from the journal
“Russian Mathematics (Iz. VUZ)”;
• the digital collection of articles from the journal
“Uchenye Zapiski Kazanskogo Universiteta. Seriya
Fiziko-Matematicheskie Nauki (Proceedings of Kazan
University. Physics and Mathematics Series).
The digital collections of Lobachevskii DML are
shown in Figure 3.
When designing Lobachevskii DML, we used the
results we obtained earlier on the management of
mathematical knowledge, as well as the developed methods of
structural and semantic analysis of mathematical
documents [
22, 31–36
].
For the semantic presentation of documents included
in the digital library Lobachevskii DML, we developed
an XML-language consisting of a set of tags; the rules
for filling them in the form of DTD and XML Schema
(see [
14
]). The XML-file describing each collection of
scientific documents was formed in several stages. Each
of them assumed the development of a special software
tool that eliminates or simplifies the manual processing
of a set of digitized documents [
31–33, 37, 38
]. This
XML-file was supplemented with a bibliographic
description of the articles contained in the digitized edition
(data on the journal number, the title of the conference
proceedings, etc.) were added. The most difficult task in
Figure 3 Mathematical collections (https://lobachevskii-dml.ru/collections/)
this case was the selection of a range of pages for each
3.2 Services of Lobachevskii DML article included in the publication. Based on the
described information, the general file of the processed
edition in automatic mode was divided into files
containing information about a separate article. Then, in the
XML-file that characterizes the collection as a whole, a
link to the file describing the article was added.
One of the new search services implemented in
Lobachevskii DML is OntoMath Formula Search Engine
(http://lobachevskii-dml.ru:8890/mathsearch/). It is a
single-page web application that interacts through the
SPARQL endpoint with a semantic view of publications
using OpenLink Virtuoso (https://virtuoso.openlinksw.
com/). This semantic representation is constructed using
a semantic publication platform [
34
]. OntoMath
Formula Search finds mathematical formulas containing
variables that denote a given mathematical concept. The
search is performed in the collection of mathematical
documents presented in Lobachevskii DML (Figure 4).
Currently, a new environment of scientific and
educational activities is being actively formed, based on the
use of Internet technologies. In this regard, along with
traditional forms of scientific exchange, focused mainly
on printed publications or their electronic versions, new
forms of scientific communications are emerging. As
the most notable, we note digital presentations as a
necessary attribute of reports at scientific conferences,
scientific forums and blogs, electronic preprints, webinars
and video lectures [
39
].
The Internet activity of a scientist, often considered
as his duty (see, for example, [
40
]), involves the
involvement of all possible means of communication. The
use of new forms of scientific exchange should not
violate the established traditions of the scientific
community, providing for the evaluation of scientific work in the
form of peer review, citation system, etc. Consequently,
a scientific document of any form should have a
bibliographic description and a set of metadata. For example,
for “live publications” it is suggested to include in the
description the date of the last edition [
41
]. A successful
example of the implementation of the “live
publications” model is the Stanford Philosophical Encyclopedia
(https://plato.stanford.edu/). All the articles of this
encyclopedia were written by specialists in the relevant
disciplines and passed the review procedure. The
authors maintain the articles up-to-date, periodically
updating them. Each new update of the article again
undergoes a review procedure, and the history of the
publication versions is maintained (it is possible to refer to
both the last and any of the previous versions of the
article).
Another means of supporting the Internet activity of
a scientist are blogs (see, for example, [
42, 43
]). An
example is the blog of modern mathematician Stephen
Wolfram (http://blog.stephenwolfram.com/). Another
example is the WDML project blog
(https://blog.wiasberlin.de/ imu-icm-panel-wdml/). Blogs can be used as
a means of organizing open scientific peer review. Such
a review, in addition to the traditional one, avoids
conflicts of interest and draws a wider circle of experts to
the examination. One of the types of open peer review is
crowdsourcing-review, in which any representative of
the scientific community can take part in the review
process.
4 Conclusion
A new digital mathematical library Lobachevskii
DML is presented. It is organized based on object
management, which corresponds to the paradigm of the
World Digital Mathematics Library project. The
services for managing mathematical knowledge,
implemented in Lobachevskii DML, are described.
This work was funded by the subsidy allocated to
Kazan Federal University for the state assignment in the
sphere of scientific activities, grant agreement no.
1.2368.2017) and with partial financial support of the
Russian Foundation for Basic Research and the
Government of the Republic of Tatarstan, within the
framework of scientific projects Nos. 15-07-08522,
15-4702472.
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