# Judita Cofman

### Born: 4 June 1936 in Vrsac, Vojvodina, Yugoslavia (now Serbia)

Died: 19 December 2001 in Debrecen, Hungary

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**Judita Cofman**was born in Vrsac, a town about 70 km north east of Belgrade and 100 km east of Novi Sad, in which, at the time she was born, roughly half the population spoke German and half a Yugoslav language. Her name in the official register of births is Judit Zoffmann, but she always used the Serbian form of Judita Cofman. Her father, Åkos Zoffmann (1910-1974), was brought up in an Hungarian speaking family but was educated in Germany. He was an expert in brewing beer and in wine production having his own brewery in Vrsac. Judita's mother, Lujza Kozics, came from a Hungarian family of lawyers on her father's side. The family spoke Hungarian at home.

Judita was only three years old when World War II broke out in 1939 and in 1941 German troops occupied the town of her birth. She began her primary education at a Hungarian school in Vrsac but there were large changes in 1944 when the defeated German troops left the town together with the citizens who were ethnically German. The Soviet troops moved in and the town became part of Socialist Yugoslavia. In 1946 the brewery which had been owned by the Zoffmann family for several generations was nationalised. There were no Hungarian secondary schools in Vrsac so Cofman attended a Serbian High School. Despite being brought up in a war-torn land, her upbringing was a happy one ([5] or [6]):-

Her schooling in two different languages was not a problem ([5] or [6]):-The family home, full of love and harmony, installed in her a great feeling that work, study, reading and knowledge of foreign languages are necessary preconditions for success in life.

The University of Novi Sad was founded on 28 June 1960 but some of its faculties were founded in Novi Sad before this date. The first two to begin operating were the Faculty of Philosophy and the Faculty of Agriculture, both in 1954. The Faculty of Philosophy taught six subjects in its first year: History, South Slavic Languages, South Slavic Literature, English Language and Literature, German Language and Literature, and Mathematics with Physics. Of course, only first year studies were taught in this first year of operation and the mathematics syllabus was essentially that of the first year at the University of Belgrade. Most of the teaching was by professors who were employed by the University of Belgrade. In this first year there were 66 students studying mathematics in the Faculty of Philosophy at Novi Sad, one of them being Cofman. All of the 66 which, may we suggest, is a surprising high number, were intending to become teachers of mathematics. As Cofman progressed at Novi Sad, the younger students came to rely on her help since their professors were living and teaching in Belgrade and only travelled to Novi Sad to carry out their teaching duties there. Aleksander M Nikolic writes ([5] or [6]):-Besides being gifted for mathematics, Judita had a talent for languages, so, besides her mother tongue of Hungarian and the official Serbian language, as a child she learned German, Russian and, which was rare at that time, English. She later learned French and Italian.

Mileva Prvanovic (born 16 July 1929) studied mathematics at the University of Belgrade from 1947 to 1951, then undertook research in geometry at the University of Zagreb being awarded a Ph.D. in 1955. From 1951 to 1955, she taught at the Mathematical Institute of the Serbian Academy of Sciences in Belgrade. In 1955 she was appointed to the Faculty of Philosophy in Novi Sad. There she taught Cofman who excelled in her studies and graduated with an outstanding degree in 1958. Following her graduation, Cofman taught at Zrenjanin High School. This school on Gimnazijska street in Zrenjanin, a town about 40 km east of Novi Sad, was founded in 1848 and enlarged in 1937. Cofman taught there for two years before returning to the Faculty of Philosophy in Novi Sad in 1960 when she was appointed as an assistant to Mileva Prvanovic. She taught ruler-and-compass construction and her lecture notes, entitledThe professional literature in the Serbian language was still insufficient at that time, and students could not use foreign titles because their knowledge of foreign languages was modest. The only person who was able to answer at any moment a variety of questions by curious students was Judita Cofman. As her knowledge of foreign languages was high, she was almost the only one among the students who could use German, English and Russian textbooks and widen her knowledge of mathematics, which she used to unselfishly share with her colleagues. They felt that she knew all there was to know about mathematics!

*Ruler-and-compass Constructions*, were published by the Faculty of Philosophy in Novi Sad. It was the first mathematics publication by the Faculty of Philosophy.

Cofman, advised by Prvanovic, was studying for a Ph.D. in finite geometries. In 1961 she went to Rome where she studied with Lucio Lombardo-Radice (1916-1982) who, only a couple of years earlier, had published

*Piani grafici finiti non desarguesiani*Ⓣ (1959) on finite non-desarguesian planes. Lombardo-Radice had been imprisoned during World War II for his opposition to the Fascist Regime but served as an assistant at La Sapienza University in Rome from 1945 to 1956 when he was appointed as an extraordinary professor at the University of Palermo. He had returned to La Sapienza in Rome in 1960 and he advised Cofman on her research into finite non-desarguesian planes. Cofman returned to Novi Sad in 1963 and submitted her Ph.D. thesis entitled

*Finite non-desarguesian planes generated by quadrangles*. She was examined by a committee consisting of Lucio Lombardo-Radice, Mirko Stojakovic (1915-1985) and Mileva Prvanovic. She was awarded the degree and became the first to be awarded a Ph.D. in mathematics from the University of Novi Sad.

Following the award of her Ph.D., Cofman spent the year 1964-65 at the University of Frankfurt am Main financed by an Alexander von Humboldt scholarship. From 1965 to 1970 she worked in England where she was a lecturer at Imperial College, University of London. There she continued her work on finite geometries and published papers such as:

*On a characterization of finite desarguesian projective planes*(1966);

*Double transitivity in finite affine planes*(1967);

*Triple transitivity in finite Möbius planes*(1967);

*Translations in finite Möbius planes*(1968);

*On Baer involutions of finite projective planes*(1970); and

*Simple groups and Möbius planes of even order*. During these years that Cofman worked at Imperial College, London, she returned to Novi Sad every Christmas and delivered lectures at the university.

Cofman spent 1970 as a visiting professor funded by the Consiglio Nazionale delle Ricerche at the University of Perugia in Italy. The conference

*Geometria Combinatoria e sue Applicazioni*Ⓣ was held at this university from 11 to 17 September 1970. Cofman gave the lecture

*On automorphism groups of finite geometries*and it was published in the Proceedings of the conference which was published in 1971 by the Istituto di Matematica, Università degli Studi di Perugia. In 1971 she was appointed to the University of Tübingen in Germany and continued to undertake research in the same areas. Papers she published while at Tübingen include:

*Baer subplanes in finite projective and affine planes*(1972); and

*On subplanes of affine and projective planes*(1973). She attended the 'International Colloquium on the Theory of Combinatorics' in Rome in 1973 and gave the lecture

*On combinatorics of finite Sperner spaces*which was published in the proceedings of the conference. In the following year she attended the conference on the

*Foundations of geometry*at the University of Toronto in Canada. Her 38-page paper

*Configurational propositions in projective spaces*was published in the conference proceedings. By 1976 she had moved to the University of Mainz, publishing the paper

*On ternary rings of derivable planes*(1977). At this stage in her career, Cofman made a major change of direction when she became a school teacher and her research interests moved from finite geometries to mathematical education.

In 1978, at the age of 42, she became a teacher of mathematics at Putney High School, London. She remained there until 1993 and during these years she began publishing articles on mathematical education. For example, she published:

*Mathematics and the Christmas Tree (A Classroom Experience)*(1980);

*Play with tangram - The activities of a Maths Club*(1980),

*Tangram and Pangram (Experience of a Maths Club)*(1980); and

*Operations with Negative Numbers*(1981). You can read extracts from some of these papers as well as some extracts from Cofman's

*Role of Geometry in Contemporary Mathematical High School Education*(1996) at THIS LINK.

She also became involved in summer teaching camps which gave her the opportunity to experiment with getting talented children to cooperate rather than to compete. She wrote in [4]:-

In the Preface of her bookThe National Association for Gifted Children in Great Britain organizes residential courses for its "Explorers". In1981I was asked to conduct a week's course on mathematics for teenagers. This most interesting enterprise was followed by two more Explorers' courses in the two subsequent summers. It was encouraging to see a substantial number of participants returning from year to year. ... At the meeting in1983, participants asked for talks on various aspects of topology and quantum mechanics to be arranged; answers to specific questions on permutations were also in demand. In addition, two important decisions were made:(1)To extend the duration of next year's course from one week to a fortnight, and(2)to invite participants from abroad. ... At this stage we had to depart from the Explorers. Our wishes had become too specialized, and we had to prepare a "camp" in1984on our own. We were very fortunate to receive excellent response and generous aid from all the people we asked for support. Guest speakers, tutors and houseparents have done voluntary work sacrificing parts of their holidays, and this was greatly appreciated. We have spent a rewarding and inspiring time with thirty-three youngsters from nine countries. ... The second camp took place in the summer of1985; this time we met in Germany, since we felt that we would all benefit from "moving around". We had invaluable support from German University teachers. Professor Pickert from Giessen and Professor Hirzebruch from Bonn arranged various lectures at the camp and at the Max Planck Institute in Bonn where we spent a day.

*What to solve?*Cofman wrote about the problems posed to children at these summer camps. You can read extracts from this Preface at THIS LINK.

In 1993 Cofman left high school teaching and returned to universities when she was appointed as professor of didactics of mathematics at the University of Erlangen, Nürnberg. She became the head of the Department of Mathematics Teaching Methods. She worked there until 2001 when she was appointed as a professor in the Department of Postgraduate Studies for Mathematics Teaching Methods in the Faculty of Natural Sciences at Kossuth Lajos University in Debrecen, Hungary. She died a couple of months after taking up this appointment.

Mileva Prvanovic writes in [7] about Cofman's interest in educating young mathematicians:-

She published three books:Judita Cofman dedicated the greatest part of her work in mathematics to fostering young mathematicians. The results of such work were a great number of articles dedicated to mathematics teaching methods, which were published in several international journals. In the last decade of her professional career, Judita Cofman published three books for young mathematicians, where she presented various mathematical problems and tasks, experiences in their solving, as well as an outstanding methodical approach to solving non-standard mathematical problems.

*Problems for young mathematicians*(1981);

*What to solve? Problems and suggestions for young mathematicians*(1990);

*and Numbers and shapes revisited. More problems for young mathematicians*(1995).

*You can read extracts from some reviews of the second and third of these books at THIS LINK.*

You can read extracts from (A) the Preface, (B) the Acknowledgements, (C) Introduction to Chapter I, (D) Introduction to Chapter II, (E) Introduction to Chapter III, and (F) Introduction to Chapter IV of

*What to solve?*at THIS LINK.

Mileva Prvanovic also writes about her character [7]:-

Judita Cofman was adorned with the finest human characteristics. So greatly talented and educated(she spoke several languages), she was very modest, communicative, always ready to help, not only her friends and colleagues, but also anyone who would turn to her for help. She was always polite and considerate towards her colleagues as well as anyone coming into contact with her. She cared to keep every single promise she gave. Everyone admired her hard work and dedication, feeling her stimulating enthusiasm.

**Article by:** *J J O'Connor* and *E F Robertson*

**List of References** (7 books/articles)

**Mathematicians born in the same country**

**Additional Material in MacTutor**

**Other Web sites**