Topics in History and Philosophy of Mathematics in which exists a contribution of our greatest scientists in the fields closest to Mathematics. In the History of Mathematics, main topics shall consist in editing, in the electronic form, of the masterpieces of our relevant scientists who worked in Mathematics and close to it Sciences and whose careers are situated in the period before the World War II. In Philosophy and Foundations of Mathematics, we are preparing to work in topics in Philosophy of mathematics in Ancient Greece, Byzantine mathematics and main topics of the contemporary Foundations of Mathematics.
History and Philosophy of Mathematics are huge disciplines and resources in Serbia don't allow research in all topics. Consequently, we choused two groups of topics which are also a priority of the national programme of research.
First group is the national History of Mathematics.
We are going to select and conserve the most important mathematical works of the Serbian mathematicians, which have been published until the World War II. Conservation shall be made in electronicaly-phototypical form, convenient for the presentation via electronic or optical media or via Internet.
Scientific contribution in these topics shall consist in comments of these works with biographies of authors and analysis of the context, either temporal or scientific, within which they originated.
This work we regard as a way of preserving a national cultural and scientific heritage and national identity but also as affirmation of our science and culture.
Second group of topics is the research of our scientists which is already underway and where we can expect a relevant scientific contribution. These topics are the Foundations of Mathematics, Philosophy and History of Mathematics in Antique and Byzantine Mathematics.
In the Foundations, the main research shall be about the concepts of infinity, continuum and continuity. This research is multidisciplinary as also Mechanics, Philosophy, Physics, Astronomy and History of Sciences are related to it.
Particular attention will be devoted to the contribution of our scientists in these topics (R. Boskovic, M. Petrovic, B. Petronijevic, D. Nesic, B. Gavrilovic etc.)
In Philosophy and History of Mathematics in Antique research shall focus on modern trends which are situating the emergence of mathematics as deductive and axiomatic science in the Athens of 4th century BC, i.e. in Plato's Academy. In nowadays the attitude that Mathematics has emerged as a product of philosophical requests of Platonic philosophy is prevailing.
Last but not least, international scientific community if poorly informed about Byzantine Mathematics in spite of the fact that the Byzant has played an important role in preservation and transfer of the Greek mathematical knowledge to the Renaissance Europe. The goal the topic is research in Byzantine Mathematics and its influence on the Mathematics of the relevant periods.
We expect the widening of the scope of our research but we think that we should not undertake efforts which can't be realized because of lack of resources.
Annotated editions of the main works of our greatest mathematicians in electronic form. New insights in Foundations of Mathematics, Philosophy of Mathematics in Antique and Byzantine Mathematics.
Editing, annotating and publishing in electronic form, as much as resources allow, of the main works of our mathematicians which have worked in the period before the World War II. Publishing in the form of papers and monographies of the results of the researchers participating in the Project. Organizing scientific gatherings where our scientific heritage can be presented.
History and Philosophy of Mathematics are huge scientific fields. Several tens of thousands various publications (papers, monographies, and books) appear every year in these fields. However, as already has been mentioned, because of resources, research on our Project shell concentrate on limited number of topics. Among these, the topics which are of universal importance (Foundations of Mathematics, problems related to infinity, continuum an continuity, Philosophy of Mathematics in Antique, origins of the mathematics of Plato's Academy) are widely treated in international mathematical publications. As in our country they are in the focal point of interest of the worldwide mathematical researchers. Obviously, the topics of national interest (annotated editions in the electronic form of the works of our mathematicians as also the influence of Byzantine Mathematics) are not at all or poorly appearing in international mathematical publications. As has been stated one of main goals of the Project is to make them present worldwide. However, it should be stressed that activities in the domain of the electronically archiving of the domestic scientific heritage are highly developed in the developed countries of the world. Almost all mathematical works of any relevance published in these countries are present as electronic archives, but not always annotated. In our neighborhood such projects are underway in Bulgaria, Hungary and Slovenia.
Organized research in History and Philosophy of Mathematics until now was within the project mathematics with Applications.Many various publications have appeared on basic topics. Generally it can be estimated that the research in History and Philosophy of Mathematics is on the equal footing with research in Mathematics as a whole. The research in electronically archiving the national mathematical heritage is still at the beginning. In the previous decade the task has been undertaken by Prof Zarko Mijajlovic with the support of the Mathematical Institute, but no official organizational form has existed. In spite of that important experience has been gathered. However, as the research has not been substantially supported by the State, the volume of the electronic archives is still modest but of the high quality.We believe that the institutionalization of State support in this project of the preservation of national cultural and scientific heritage is of the ultimate national importance.
As a main group of the Project results we expect a set of the electronic archives with annotated editions of the older important mathematical works. The technology and the methodology of creating such an archive (programming and media creation) can have applications in the numerous other scientific fields.
Electronic books are by itself already a product. Depending on the successfulness of the realization, the result of the Project can become directly commercially and mercantile attractive.