Died: 24 March 1945 in Budapest, Hungary

**Leopold Klug**'s name is also written **Lipót Klug**; the first version being German while the second version is Hungarian. His parents were Miksa Klug and Hani Neufeld; the family was Jewish. He attended the gymnasium in his hometown and entered the University of Budapest in 1872. After he graduated from the University on 16 July 1874 with a teaching diploma, he was appointed on 25 September as a high school teacher in the Science High School in Pozsony (Bratislava). He taught there between 1874 and 1893, writing his first books on geometry, after which he taught at a secondary school in Budapest. During these years he undertook research, first for his diploma which was awarded in 1882, then for his habilitation. He also taught as a privatdocent in Synthetic Geometry at the University of Budapest from 1891. During these years, he was greatly influenced by Gyula König who taught at the Technical University of Budapest from the early 1870s. After the award of his habilitation, Klug was appointed to the Joseph Franz University of Kolozsvár (now Cluj) as an extraordinary professor in Descriptive Geometry. After two years he was appointed to the chair of Descriptive Geometry at the University of Kolozsvár, a position he held for nearly twenty years, until 1917, when he retired and moved back to Budapest.

Soon after he retired, Klug wrote to Leopold Fejér and the letter contains interesting information about Klug's family (see [2]):-

I'm telling you what you already know, that I retired, and that my daughter obtained the Music Teacher's Diploma. She's learning her eighth language, namely Turkish, because she has been reading novels and epic poems in Spanish and Russian for a long time.

He spent his years in retirement continuing to undertake scientific work and publishing the fruits of his efforts; it is no accident that the Technical University of Vienna keeps a whole box containing his works. However, his eyes must have troubled him for he wrote in a letter in April 1918 (see [2]):-

I don't intend to write more because my eyes have became weak because of the reading and writing I've done in all these years. Now I'm not allowed to tire them with geometry work.

During his retirement, he put in much effort encouraging young talents such as Ferenc Kárteszi (1907-1989) and Edward Teller (1908-2003), the 'father of the hydrogen bomb'. Back in Budapest after his retirement, Klug lived on Kertesz Street, 38, I/4, in the 7^{th} District of Budapest; the Tellers also lived there. We quote from an interview by Teller in which he talks of the influence that Klug had on him:-

When I was ten years old, my father, who had really no understanding of how and why I would be interested[in mathematics], did see that I was. And he had an older friend who was a retired mathematics professor. His name was Leopold Klug. And he is probably the man who had the greatest influence on my life. I did not see him often, half a dozen times, a dozen times. He was a retired mathematics professor, and he did two things. One is, he got me a book. The title was 'Algebra', the author was Leonhard Euler. ... It was a very elementary book, starting from questions why to add, and why to multiply, and why minus one times minus one is plus one. All the way up to the solving of fourth order algebraic equations. The fifth order had not been solved at that time. And at the time of Euler, it was not known that the equations above the fourth order cannot be solved. That was shown much later, by a very young Frenchman, Évariste Galois. Klug gave me that book, and I read it. It was my favourite book.

Klug had a favourite subject, and that was projective geometry. Projective plane geometry. What happens if you take a drawing in a plane, and project it on another plane. What are the properties that remain unchanged? For instance, a line will remain a line. A triangle will remain a triangle. But an equilateral triangle will not remain an equilateral triangle. A circle may become a hyperbola. What is the similarity between these curves? What remains unchanged? I was ten years old, and the problems that came up were too difficult for me to solve, but not too difficult to understand. And there was a human element in it which impressed me.

I found that the grown-ups had a terrible time, everybody got tired of what they were doing. Klug was the first grown-up who I met who loved what he was doing, who did not get tired, and who even enjoyed explaining things to me. That I think is when I made up my mind, very firmly, that I wanted to do something that I really did want to do. Not for anyone else's sake, not for what it may lead to, but because of my inherent interest in the subject.

Klug died in Budapest towards the end of 1944 but the circumstances of his death have been unclear up to now. In 1944, with the Red Army and the Romanian Army approaching Budapest, the ninety-year-old mathematician walked out of his home in Budapest and he never came back. Probably he was the victim of a racially motivated attack.

Barna Szénássy [1] sums up Klug's mathematical contributions:-

At the beginning of his activity spanning more than fifty years, Lipót Klug turned to problems studied by Gyula Vályi, consistently ignoring analytic methods. Later he studies more diverse fields with success.

We should now look at the Klug Foundation which he set up at the University of Kolozsvár (Cluj) with money which he saved from his pension during the years of his retirement in Budapest. In August 1942, two years before Klug died, the following report appeared in the *Hungarian Jewish Journal* [3]:-

Prof Dr Leopold Klug

In the Hungarian Scientific circles it has been enthusiastically discussed for weeks that Prof Dr Leopold Klug, internationally recognized mathematician, has set up a foundation of ten thousand Hungarian pengö at the University of Kolozsvár (Cluj), where he was ordinary public teacher before the Romanian occupation.

The news proved to be true. The offer of the substantial foundation really has taken place. The Council of the University of Kolozsvár(Cluj)accepted with thanks the gesture of patronage from the Jewish scientist. The Ministry of Religion and Education approved the constitution of the foundation.

From the foundation of Leopold Klug - according to our information - the first aim will be to reward those students who have undertaken excellent work in the seminar in the field of Descriptive Geometry. The second aim will be to reward those who show extraordinary interest and special talent in Geometry. This subject was Dr Leopold Klug's favourite.

Dr Leopold Klug, the new patron of a university foundation, was born in Gyöngyös in1854, as a child of a Jewish family; in1891he became a privatdocent in synthetic geometry at the University of Budapest, and in1897he became an extraordinary professor at the University of Kolozsvár(Cluj). In1900he became ordinary professor at the University of Kolozsvár(Cluj). He published his work entitled "The Elements of the Projective Geometry" with the support of the Hungarian Academy of Sciences. Several of his works were published in German by the Akademie der Wissenschaften in Wien(Austrian Academy of Sciences).

His students became the future generations of mathematicians. His work is comparable maybe only to that of Dr Leopold Fejér, who also pursued his first scientific research at the old University of Kolozsvár (Cluj).

Dr Leopold Klug, at the age of a patriarch, living permanently in Budapest but spending each summer in the emergent Kolozsvár(Cluj), now wishes to serve Hungarian science by financially supporting the first steps of talented mathematicians and geometers at his former place of employment.

The first winner of the Leopold Klug Prize was Ferenc Zigány in 1943. He was awarded the prize because of his report reviewing the scientific contributions made by Leopold Klug. Here is a short quote from Zigány's report (see [2]):-

With time things change, and scientific research is no exception. Its diverse problems are sometimes in vogue, but sometimes pushed into the background giving space for new ones. While in the past two centuries geometers chose their themes from the field of Projective Geometry, particularly from the domain of second degree curves and surfaces, interest in this topic has significantly decreased nowadays. Leopold Klug was an enthusiast for the flourishing of Projective Geometry, and within that, the synthetic method which inspired many great minds in the past. As big as the love was with which he promoted projective geometry based on the synthetical method, equally big was the bitterness after he realized the decrease of interest in it.

The highlight of his work is represented by two textbooks: 'The Elements of Projective Geometry' and 'Projective Geometry' (1903). The first describes the problems in the plane while the second extends the study to problems in 3-dimensional space. A very interesting and more extensively worked out detail of the first book is the different projectivities and involutions, and the relations of some of these (for example, the adjuncteds), as well as the conic with double tangential point. Both of these topics were Klug's favourites and several of his dissertations deal with them. A beautiful detail from of the second book is the part concerning the polaric tetraeder in the chapter entitled 'Hyperboloid', and in the chapter entitled 'The Third Order Space Curve'. The relation of this curve to the 0 system and the components of the hyperboloid intersecting the curve are studied. In the third place there is his textbook entitled 'Descriptive Geometry', a work written with an excellent pedagogical sense and with a great choice of material, then the fourth one: 'A Synthetic Discussion of Third-Order Space Curves' (1881).

Besides these textbooks a large number of his articles enrich our geometry literature.

We should note that Leopold Klug Prize was only awarded in 1943. The prize was divided between Ferenc Zigány and László Fejes (Tóth) for his successful geometrical research.

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

**November 2010**

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Klug.html]