Natural Science

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ASTRONOMY AND ASTROPHYSICS IN CROATIA
FROM 1874 TO 1995

The oldest astronomical observatory in Croatia was established in Pula in 1871 as part of the Hydrographical Institute of the Imperial and Royal Navy. J. Palisa (1848-1925) discovered 28 planetoids from the Pula Observatory, three of which were named Polana, Adria and Istria. In 1883 the Croat Baron Ivo Benko of Bojnik (1851-1903) became head of the Pula Observatory. He developed systematic work on the meridian circle and compiled a catalogue of fundamental stars that was completed and published after his death. When Istria came under Italian administration (1918-1943) the astronomical instruments and the library were moved to Trieste, and in 1944 the Anglo-American air force destroyed the building. Today the Istra Amateur Astronomical Society works in the partly renovated north-west Observatory wing. The second observatory in Croatia was founded in 1893 on Mali Lošinj by Spiridon Gopcevia (pseudonym Leo Brenner, 1855-1928). This was Manora Observatory, named after his wife and equipped with a 175 mm refracting telescope. Gopcevia tried to observe the "canals" on Mars, and he also watched other planets, especially the rings of Saturn. Brenner Crater on the Moon was named after him. Between 1899 and 1908 he edited and published the popular scientific journal Astronomische Rundschau. In 1909 Gopcevia sold his instruments and closed Manora Observatory because of financial difficulties. In 196 ??? his telescope was bought by Don Nikola Milicevia (1887-1963), the last administrator of Blaca Hermitage on Brac, who had studied astronomy in Vienna. In Blaca he mostly analysed the problems of celestial mechanics, observed double stars, and searched for comets and new stars.

The Observatory in the Priests' Tower (Popov toranj) in Zagreb was founded in 1903 by the Croatian Natural History Society on the initiative of O. Kucera (1857-1931). Its main telescope had a 162 mm lens. This Observatory had been intended as a scientific-research institution, but due to bad observation conditions and a lack of researchers, it was used for popularizing natural science, especially astronomy, in Croatia. O. Kucera published a lot of popular-science books including Our Sky - Notes in Astronomy, which became a favourite. After 1945 the Observatory continued work on popularizing astronomy and it was often visited by secondary school pupils and students. Many prominent people worked there, including Slavko Rozgaj (1895-1978), whose best-known book was A Book About Stars, Josip Goldberg (1885-1960), who wrote the secondary-school text-book Astronomy, and Gabrijel Divjanovia (1913-1991), the head of the Observatory from 1954 to 1978, a prolific author of popular-science texts and long-time editor of the journal Èovjek i svemir (Man and the Universe), which came out in runs of 70,000 copies. The many years of systematic science popularization by the Zagreb Observatory were most effective, and today Croatia has about twenty amateur astronomical societies which form the Union of Amateur Astronomical Societies of Croatia. The Observatory greatly helped their foundation and further work. In 1966 the so-called Kucera Telescope was replaced by a Zeiss refractor with a 130 mm lens, and in 1992 a new dome was made. In 1937, on the initiative of N.P. Abakumov (1882-1965), an Astronomical Pavilion was built in Maksimir, in which astrogeodesic measurements were made.

In 1972, in cooperation of the Committee for Science of the SR Croatia and the Academy of Sciences of Czechoslovakia, Hvar Observatory of the Faculty of Geodesy of Zagreb University was founded. It is equipped with a double solar refracting telescope for observing the Sun's photosphere and chromosphere, and a 65 mm reflecting telescope for the photoelectric observation of variable stars. Astrophysical research in Croatia is centered around Hvar Observatory and has developed widespread international cooperation. Many noted international scientific symposiums and schools are organized, and the journal Hvar Observatory Bulletin published. We must finally mention that the Croatian Astronomical Society was founded in 1992, and became a member of the European Astronomical Society and of the International Astronomical Union.

BIOLOGY IN CROATIA

In the middle of the nineteenth century the modern Croatian nation was being rapidly moulded and the feudal society was quickly transformed into a middle-class society. Croatian revivalists wanted the nation to advance in every field, including the economic, and this was closely linked with education and scientific development. With that purpose L. Gaj and his followers very early (1829) planned the foundation of some basic national health and cultural institutions (for example, public libraries, museums). On Gaj's proposal, the Croatian Parliament (1836) established a learned society, an academy. Gaj himself, while he was still at secondary school in Krapina, made a list of the plants of his region. Two interesting developments took place in this period. Many foreign schooled natural scientists came to Croatia and stayed there permanently, usually very quickly becoming Croats, and slowly but steadily the number of Croatian natural scientists, mostly amateurs, increased. There were differences between coastal and continental Croatia in this process. There were relatively more students from Croatian Dalmatian towns at various European universities. They studied science abroad and after graduating returned home. These included S. Brusina, and G. Bucia. Some well-known biologists, who also belong to the history of Croatian biology, were born in Croatia and spent not only their schooling but most of their professional life outside their homeland. These were R. Visiani, N. Host, R. Molin, P. Doderlin, J. Pancia, and I.P. Vlahovia. Finally, an important groups of biologists, like J.K. Schlosser, A. Alschinger, A. Praunsperger, B. Šulek, F. Erjavec, B. Jiruš, and J.K. Lorenz, came to Croatia from abroad as trained experts and remained there.

Until about the 1870s members of all the three groups had the traditional typological or physiological approach in which the appearance and form of organisms are usually statically described and less interest is paid to the causes of events that take place in them and among them. The goal was the condition, not the dynamism of the process. In the periodization of biology in Croatia this, and the biology of earlier centuries, was in fact a period of preparation. It had its stages of development and reached important results that paved the way for the beginning of modern dynamic biology which posed questions about the origin of organisms, and about the causes and nature of complex relations that are established among them, and with the environment.

The second, we might call it the phylogenetic period, developed with the foundation of the new University. This was in the early 1870s, and it coincided with the beginning of modern university teaching and with the appearance of Darwinism in Croatia. Life was now regarded as a sequence of cause and result, which had already come to expression in Scholsser's somewhat earlier attempt at plant geography (1867), in Brusina's idea about the development sequence of Slavonian vivipara (1874), and in L. Car's doctor's thesis about the origin of bird reptiles (Jena 1881). It reached its peak in the biological and palaeobiological (palaeontological) work of S. Brusina and in the palaeontological work of D. Gorjanovia-Kramberger at the end of the nineteenth century.

The beginning of the twentieth century brought the beginning of the third period of Croatian biology, the period of its first maturity. This lasted until the early 1920s, and its basic mark was a degree of synthesis in faunistics (Brusina, Kolombatovia, Katuria, Kostia etc.) and even more in floristics, i.e. phytogeography (Adamovia etc.).

The fourth period, from the 1920s to the early 1960s, was the period of phytocenology, systematization and genetics. Biology in Croatia now reached its peak and was in many cases on a world level (Heinz, Vouk, Horvat, Pevalek, Horvatia, Ercegovia, Šoljan, Jurilj, Horvatia, Lorkovia, Demerec, Travcar). And finally, in the last thirty years we have the fifth period. Since about 1960 the focus has been on keeping in touch with world results and on contributing to the development of ecology, animal and plant physiology, developmental biology, and genetic engineering. Great efforts are made to keep abreast of at least some of the main currents in world biology, but for understandable reasons success is modest. It is interesting that there is no research into the behaviour of organisms (aetiology).

THE DEVELOPMENT OF CROATIAN PHYSICS SINCE 1874

Physics has a long tradition at Zagreb University. In 1664 Stjepan Glavac taught physics as part of philosophy at the Jesuit Neoacademia Zagrebiensis. There was a great advance in 1875 when Vinko DvorÏak was appointed the first professor of physics at Zagreb University. After 1875 five Croatian physicists made a great contribution to physics on the world level: Vinko DvorÏak, Vladimir Varicak, Stjepan Mohorovicia, Vladimir Glaser and Gaja Alaga.

Vinko DvorÏak (1848-1922) was a Czech-Croatian physicist, professor and rector of Zagreb University and a member of the Academy of Sciences and Arts. After obtaining his doctorate in Prague he came to Zagreb and founded the Physics Cabinet at the Faculty of Philosophy, where he worked for almost half a century. DvorÏak made many important discoveries in the field of experimental acoustics and optics, which are known as the DvorÏak-Rayleigh current, the DvorÏak acoustic repulsion, and the DvorÏak circuit. He was in constant contact with world scientists and quickly introduced new scientific results in Croatia. For example, in 1895 Roentgen discovered X-rays, and in 1896 DvorÏak already had an X-ray tube that he used in teaching and research at the Physics Cabinet of Zagreb University. In 1897, at the convention of the Alliance of Doctors in Zagreb, he made the first demonstration of the use of X-rays in medicine.

Vladimir Variaak (1865-1942), mathematician and physicist, professor and rector of Zagreb University and academician, made two very important discoveries in the theory of relativity. They were quoted by Nobel Prize winner Wolfgang Pauli, one of the greatest physicists of the twentieth century, in his famous review paper on the theory of relativity Relativitaetstheorie.

Stjepan Mohorovicia, a physicist, geophysicist and astronomer of world renown, a grammar-school teacher in Zagreb, was the first in the world to hypothesize about the existence of a new particle, the positronium. He published his results in 1934 in the renowned German scientific journal Astronomische Nachrichten. The positronium was experimentally discovered 17 years later, and a whole field of science has today developed around it. A large number of contemporary publications by world scientists stress that Mohorovicia was the first to hypothesize the existence of the positronium.

Vladimir Jurko Glaser (1924-1984) was a theoretical physicist or world renown in the field of quantum fields theory and the canonization of the analytic S-matrix, where he made some very important scientific discoveries. He was head of the Department of Theoretical Physics at the Ruder Boškovia Institute in Zagreb, and in 1957 he left Croatia and found permanent employment in one of the most renowned scientific institutions in the world, CERN in Geneva.

Gaja Alaga (1924-1988), a member of the Croatian nobility from Vojvodina, was professor at the Faculty of Science and Mathematics in Zagreb and an academician. In 1955, in cooperation with K. Alder from Switzerland, A. Bohr from Denmark and B. Mottelson from America, he discovered K-selection rules and intensity rules for beta- and gamma- transitions in deformed nuclei. This discovery became one of the fundaments in the development of the collective nuclear structure model, for which

A. Bohr and B. Mottelson were awarded the Nobel Prize in 1975.

The dynamic development of physics in Croatia began after the Second World War with the foundation of the Ruder Boškovia Institute, the Faculty of Science and Mathematics, the University Physics Institute, and physics institutes at the Faculties of Electrical Engineering, Medicine and Technology. It is especially important that Croatian physics was turned to intense international scientific cooperation, which led to the sudden growth of many physics sub-fields in Croatia and their development on a world level. For example, in 1977 Croatia reached a relatively high (35th) place among countries according to the production of scientific publications in physics. In the 1963-1993 period, 99 Croatian physicists were co-authors of 464 scientific papers written in cooperation with 492 American physicists, which illustrates their very dynamic international activity.

GEOPHYSICS

Geophysics is a natural science concerning the physical laws that govern the Earth as a whole or some large parts of it. Because of the great area involved and the wide range of phenomena, geophysics is divided into physical oceanography, geomagnetism and aeronomy, meteorology and seismology.

Physical oceanography studies the physical properties of the sea and marine motion. In Croatia it began to develop after G. Bucia researched the atmosphere and sea in Hvar in the mid-nineteenth century. In 1897 physical oceanography became a subject at Zagreb University, and in 1913/14 the first Croatian study trips on the ship Vila Velebita were organized.

In the period between the two world wars important contributions were made by A. Ercegovia from the Oceanographical Institute in Split, and J. Goldberg from the Geophysical Institute in Zagreb. After 1945 a network of mareographic stations was established, a series of study trips on research boats organized, and currents and waves measured. The analysis of data thus obtained and the development of the corresponding mathematical models greatly advanced knowledge about the Adriatic: geostrophic currents were charted, temperature and salinity changes through many years were analyzed, the influence of planetary atmospheric waves on the sea were observed, the reaction of the sea to the bura and jugo winds was researched, and so on.

A. Kugler made the first systematic geomagnetic measurements in Croatia in 1915 and 1916 on 80 sites between the Koprivnica-Zagreb and Vukovar-Îupanja lines. In 1949 the magnetic declination of the east Adriatic coast and the Adriatic islands was measured. Measurement time reductions were made on the basis of registration in relatively distant foreign magnetic observatories, so it is necessary to establish a geomagnetic observatory in Croatia.

Aeronomy studies physical and chemical processes in the upper atmosphere. The parameters of atmospheric tidal oscillations were established, and the influence of the eclipse of the Sun on 15 February 1961 on the Earth's electric field. The rather rare phenomenon of stratospheric ozone intrusion deep into the lower troposphere was recorded and studied above Zagreb.

In Croatia, as elsewhere in the world, meteorology began to develop as an exact natural science in the nineteenth century. The work of I. StoÏir and A. Mohorovicia was very important in this field.

Croatian meteorologists often studied the bura, a north wind that blows on the Croatian coast (B. Makjania). The World Meteorological Organization organized a special international project, the ALPEX, to study the bura in 1982. At present this wind is being studied in the American-Croatian project The Nature and Theory of Severe Bura.

Special attention was paid to the study of precipitation, especially to dry and rainy periods. Most research into the climate of Croatia (S. Škreb) is part of the UN Environment Programme. A very sensitive model was developed for isentropic weather forecasting, which is used by some European services. The planetary border layer is researched in connection with atmospheric pollution. There are studies about the harnessing of solar and wind energy. Problems of human meteorology and bioclimate are analyzed. J. Goldberg began to study climatic changes in Croatia.

The development of seismology in Croatia was initiated as a result of serious earthquakes, especially that on 8 October 1909 whose epicentre was in the valley of the river Kupa (A. Mohorovicia, the Mohorovicia Discontinuity). Seismological research includes: generalization of earthquake frequency distribution in relation to magnitude, the distribution of extreme earthquake values, the quantitative relationship between ground movements, earthquake magnitude and strength, seismic zoning, the evaluation of favourable locations for new stations. Process characteristics and spatial earthquake generation in the Earth's crust are determined to define seismic hazard and specific earthquake forecasting. Shift mechanisms in the foci of Croatian earthquakes are linked with geological parameters, the characteristic wave codes of local earthquakes are theoretically interpreted, problems of earthquake quantification are discussed. The procedure for determining earthquake magnitude is constantly modified. New seismological models of the Earth's crust and mantle are introduced.

GEOGRAPHY

Geography first became a university study in Croatia in 1883 in the Faculty of Philosophy. Its later development may be divided into three stages:

1. Before the First World War. The formation of a university department made it possible to educate teachers of the subject in Croatian for later work in schools. Research work also began to be developed. Petar Matkovic, founder of the department, was the first university teacher of geography. He was also the first to produce an atlas in Croatian and founded the Croatian statistical service. In 1899 his place was taken by Hinko Hranilovic and his, in 1918, by Milan Senoa. In 1900 Hranilovic and Hirc began publication of Zemljopisa Hrvatske (Croatian Geography) and Hirc in 1905 published Prirodni zemljopis Hrvatske (the Natural Geography of Croatia).

2.. Between the two world wars: After the First World War (1922) Senoa founded the geographical institute which concentrated on human geography, in 1927 the department of physical geography was taken over by Artur Gavazzi. In this way a dualism developed in the organization and teaching of geography in Zagreb which lasted down to the end of the Second World War even after Senoa, in 1940, had been replaced by Otto Opiz and Gavazzi, in 1944, by Zvonimir Dugacki. Between 1929 to 1939 Gavazzi published 10 numbers of the Geographic Herald. These same years saw considerable enrichment in number of specialist books available the most important being: F.Balenovic Opca Geografija (General Geography, 1923), F.Lukas Ekonomska geografija ( Economic Geography 1923/24), A.Gavazze Astronomska geographija (Astronomic Geography), Lukas and .N.Peric wrote a geography of SHS and published the Minerva atlas, S.Ratkovic wrote Zemljopis Banovine Hrvatske (Geography of the Banovina of Croatia). During the war F.Lukas and N.Peric wrote the first Zemljopis NDH (Geography of NDH) and, together with Dugacki, Zemljopis Hrvatske (Geography of Croatia).

3. After the Second World War. In 1947 the study of geography began to take place in a separate department of the newly organized Faculty of Mathematics and Natural Sciences.. Josip Roglic became head of the department with Ivo Rubic as his deputy. Roglic intensified the study of physical geography, especially geomorphology, and as part of it inaugurated serious study of the karst regions and other human and regional geographical areas. Together with previous students such as Crkvencic other fields of study were developed such as: Crkvencic - social and especially agrarian geography; Roglic - principles of regionalization and history of geography; Segota - climatology; Baucic - labour migrations; Sic - transport geography; Friganovic - demography; Ridanovic - hydrogeography; Pepeonik - geography and tourism; Novosel-Zic - cartography; Vrsk - urban geography; Bognar - geomorphology; Feletar - industrial geography; Malic - agricultural and transport geography; Brazda and Pejnovic - teaching methods. All members of the department also worked on the study of some region of the world or Croatia.

Since the reform of the university in 1995 until today (1996) the department of geography has had 10 professors, 6 assistant professors and 11 researchers.. In the academic year 1995/96 there were 448 students of whom 179 were geography majors and the rest took another subject such a history or geology. Since 1952 there have been 1,464 geography graduates. In 1964 graduate studies were organized at which 110 students gained a master's degree and 55 a Ph.D.

The department of geography publishes two periodicals Acta Geographica Croatica (previously Radovi), from 1958 (29 numbers in all) and since 1970 Geographical Papers in English (so far 8 numbers). The members of the department are the main organizers of the Croatian Geographical Society and in the publication of the Geografski glasnik (Geography Herald, since 1945) and Geografski horizont (Geographical Horizons since 1955). They all take part in one of the current research projects of which there are at present three: production of a geomorphic atlas of Croatia, the geographic aspects of urbanization in Croatia and the geographic aspects of social and economic development in Croatia.

GEOLOGY

In Croatia geology began to develop systematically when Gjuro Pilar was appointed the first professor of geology and mineralogy at Zagreb University in 1875. Before that Pilar was assistant professor at Brussels University, where he had attained his Ph.D. (1869). In 1877 his doctor's thesis was translated into English and published by the Smithsonian Institution in Washington. Pilar was active in all fields of geology, and was also the first professor of astronomy. After his death (1893) his department was divided into geology- palaeontology, headed by Dragutin Gorjanovia-Kramberger, and mineralogy-petrography, headed by Mijo Kišpatia. Dragutin Gorjanovia-Kramberger (1856-1936) gained a lasting place in world science by the discovery and analysis of the fossils of the Krapina Prehistoric Man. It was his results that finally convinced the world public of the existence of "prehistoric men" - hominids who preceded our present species. Placing man in the context of evolution meant a radical and for many people an unacceptable change in the existing world outlook. In 1909 Gorjanovia founded a Geological Commission for Croatia and Slavonia, whose immediate successor is today's Institute for Geological Research in Zagreb.

Mijo Kišpatia (1851-1926) contributed to structuring modern petrology as a complex science about rocks. His research into the ophiolithic zone in Bosnia is of pioneer importance. He was also very successful in popularizing science.

Between 1918 and 1939 there were no important changes, although the factography was expanded and enriched. Stagnation reached its peak in 1931 when the Institute of Geology in Zagreb and its entire documentation were removed to Belgrade in the era of King Alexander's centralism. Fran Tuaan, who trained many petrologists and mineralogists, and Marijan Salopek, who introduced group field research, made a positive contribution in that period. Salopek's geological charts are still a model of the lithostratigraphic approach in geological map-making, which was not reaffirmed until 1985.

Field research obviously decreased in the period from 1939 to 1945, although the Institute of Geology was renewed in Zagreb when the Croatian Banovina was established. After 1945 the Faculty of Science and Mathematics became independent and the study of applied geology was introduced at the Technological Faculty (later the Faculty of Mining, Geology and Petroleum Engineering). The geological map of Croatia was systematically drawn, tectogenetic karst classification was born and was applied in the construction of the first karst water reservoirs in the world. Independent disciplines developed: the science of ore deposits, petroleum and gas geology, hydrogeology, engineering geology, micropalaeontology, and so on. Since 1990 research in all fields has continued, although in a limited area. The newest results, including those of a theoretic nature, are applied in practice.

CHEMISTRY IN CROATIA (AFTER 1874)

Aleksandar Veljkov (1847-1878) founded the first Chemical Institute of the Faculty of Philosophy, and was the first professor of chemistry. He taught at Nova ves 1 in Zagreb. Gustav Janecek (1848-1929) inaugurated the teaching of chemistry at the university and was the first Croatian chemist according to European standards of that time. He was at the head of the Chemical Institute for 45 years, and wrote many text-books. In 1884 he built the first building for the needs of chemistry in this part of Europe on today's Strossmayer Square in Zagreb. In 1919, in cooperation with Julije Domac (1853-1928), he built a second building on Marulia Square. This building was later assigned to the newly-founded Technical College (from 1926 the Technical Faculty, today the Faculty of Chemical Engineering and Technology). Between 1886 and 1924 about twenty students of G. Janecek became the first Croatian doctors of chemistry.

After the First World War new faculties were established (Medical, Technical, Veterinary, Agricultural, Economics) and new chemical industries with well-equipped laboratories. In the period between the two world wars Nikolaj Antonovia Pušin (1875-1947), Gilbert Flumiani (1889-1976) and Ivan Plotnikov (1878-1955) contributed most to teaching and research work in the field of physical chemistry. Plotnikov was elected (1921) professor of physics and physical chemistry at the Technical College, and was known for his papers and books in the field of photochemistry. Mladen DeÏelia (1890-1989) taught at the Faculties of Medicine, Pharmacy and Philosophy. After 1949 he was professor at the Faculty of Philosophy in Sarajevo and founder of chemistry in Bosnia and Herzegovina. Fran Bubanovia (1883-1956) was professor of chemistry at the Medical Faculty in Zagreb, the founder of physiological chemistry, and author of the first Croatian university text-book (Chemistry for Students of Chemistry, Medicine, Veterinary Medicine and Pharmacy, 1930-31). Tomislav Pinter (1899-1980) taught physical chemistry at the Medical Faculty (from 1936). Vladimir Njegovan (1884-1971) played an important role in anorganic and analytical chemistry at the Technical College, later the Technical Faculty. His field was anorganic analysis and he greatly contributed to teaching analytical chemistry, the development of chemical terminology, and the popularization of chemistry. Organic chemistry was neglected in Croatia for a long time. Ivan Marek (1863-1936) was the first professor of organic chemistry at the Technical College (1920), known in the world for the construction of a special stove for elementary organic analysis. He was succeeded by Vladimir Prelog (1906) who made the greatest contribution to the development of organic chemistry in Croatia. Although he moved to the Technical School in Zurich in 1941, where he received the Nobel Prize in 1975, he founded a school of organic chemistry in Zagreb whose influence is still very strong. Prelog introduced new views about the structure of molecules, resonance theory and the concept of wave mechanics. His first synthesis of adamantane is important, his work on determining the structure of natural compounds, and stereochemistry. The other Croatian Nobel Prize winner, Lavoslav RuÏicka (1887-1976), received the prize in 1939 for work on the synthesis of sex hormones androsterone and testosterone.

After the Second World War many faculties became autonomous (Pharmacy, Science and Mathematics, Technology, Textile Technology, Food Science and Biotechnology) and new ones were formed - in Zagreb, Sisak, Split, Rijeka and Osijek. The Ruder Boškovia Institute (founded in 1950) made the greatest contribution to world science. Outstanding in that period was the work of Hrvoje Ivekovia (1901-199 ??? ), Eugen Cerkovnikov (1904-1985), Stanko Borcia (1931-1994), Karlo Weber (1902-1978), Miroslav Karšulin (1904-1984), Vjera Marjanovia-Krajovan (1898-1988), Viktor Hahn (1912-1970), Mihovil Proštenik (1916-1994), Adolf ReÏek (1902-1980), Zvonimir Pucar (1922-1990), Zdenko Majerski (1939-1988), Zvonimir Ban (1934-1989) and BoÏo TeÏak (1907-1980). Croatian chemists attained world results especially in determining anorganic compounds structure, colloid and intersurface chemistry, electrochemistry, synthetic and physical-organic chemistry, stereochemistry and the chemistry of natural compounds, biochemistry and the field of molecular spectroscopy. The Croatian (formerly Yugoslav) Academy of Sciences and Arts, founded in 1866, played a great role in the development of chemistry, and so did the Croatian Chemical Society (1926) and the journal Croatica Chemica Acta (1927), the Croatian Society of Chemical Engineers and Technologists and the journal Kemija u industriji.

MATHEMATICS

Organized scientific mathematical research in Croatia began with the establishment in 1876/77 of the Department of Mathematics and the Natural Sciences within the Faculty of Philosophy of Zagreb University. The first professor was the Czech mathematician Karel Zahradnik (1848-1916). In his 23 years of productive activity in Zagreb he wrote several scholarly works, mainly concerned with algebraic curves, and in the same period the first Ph. D. theses in Zagreb were defended (D.Segan 1889, V.Varicak 1891).

Vladimir Varicak (1865-1942) was particularly outstanding among Zahradnik's successors, his most important work being the interpretation of the special theory of relativity in the Lobovceski space. Juraj Majcen (1875-1924) and Stjepan Bohnicek (1872-1956) were also among outstanding early Croatian mathematicians. Maths was also studied in the technical college under Marija Kiseljak (1883-1947) and later Zeljka Markovic (1889-1974) well known for research into the mathemtics of Plato and Aristotle and the life and works of Ruder Boskovic. Vladimir Vranic (1896-1976) was the first in Croatia to introduce the study of probability and statistics, mathematical methods, econometrics, numerical mathematics and the use of computers. Other important names for the furthering of research and the university study of mathematics between the wars were Rudolf Cesarec (1889-1972), Vladimir Vrkljan (1894-1974) and Duro Kurepa (1907-1993). Kurepa's work of tree theory was especially important. Among the most active in the fifties were Vilko Nice (1902- 1987) and Danilo Blanusa (1903-1987). Of especial note was Blanusa's work on isometric embedding of manifolds with constant curvature and similar manifolds. Zlatko Jankovic (1916-1987) was active in applied mathematics especially theories of mechanics and mathematical physics.

The second half of the twentieth century saw great intensification and expansion of studies at both secondary and university level and in research possibilities. The conditions were created for the formation of new centres of mathemtics in Rijeka, Split and Osijek. An important part in this was played by the Society of Mathematicians and Physicists of SR Croatia (1946), later the Croatian Mathematical Society (1990). In the Society's periodical Mathematics, Physics and Astronomy Herald (1946-1965) later Mathematics Herald (1966) has published many works by foreign mathematicians and more then 500 from Croatia. From 1961 to 1974 research has been organized at the university Institute of Mathematics, about 300 degrees of M.A. have been conferred and several hundred Ph.D. degrees.

The results achieved in the last twenty years are those of still living mathematicians working in the following branches:

1. Mathematical logic and the basis of Mathematics, 2. Algebra and the theory of numbers, 3. Geometry, 4. Topography, 5.Left groups and theory of representation, 6. Analysis and functional analysis, 7. The theory of probability and mathematical statistics, 8. Differential equations and mathematical physics, 9.Combinational and discreet mathematics, 10. Numerical mathematics, 11. Optomization, 12. Computer science, 13. History of mathematics.

A great contribution to the study and research in science has been made by Croatian mathematicians abroad. The most outstanding among them is Vilim Feller (1906-1970), Princeton University, who is one of the founders of contemporary theories of relativity.