# Oene Bottema

### Born: 25 December 1901 in Groningen, Netherlands

Died: 30 November 1992 in Delft, Netherlands

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**Oene Bottema**was the son of Rinze Wiltje Bottema (1872-1946) and Wijtske Hoekstra (1872-1951). Rinze Bottema had a position with the railways and was subsequently station manager at a few village stations in the north of the country. Rinze and Wijtske were married on 13 August 1898 at Leeuwarderadeel, The Netherlands. Their son was given the name Oene since this was his grandfather's name, Oene Wiltjes Bottema (1834-1897).

After attending elementary school, Bottema entered the Rijks Hogere Burgerschool in Groningen. This school had been founded in 1868 as a five year school to train pupils for business and industry. Up to 1917 the certificate earned by pupils from such schools did not allow for university entry, which was only possible for those attending a Gymnasium, but in 1917 the parliament passed a law allowing pupils with Hogere Burgerschool certificates to enter university to study sciences. Bottema was one of the first to benefit from this change, and in 1918 he entered the Department of Mathematics and Physics of the University of Groningen.

One of Bottema's professors at Groningen was Julius Wolff (1882-1945) who, after studying for a doctorate advised by Diederik Korteweg, had spent ten years as a school teacher, then was appointed professor of differential calculus, theory of functions and higher algebra at Groningen in 1917. Bottema was also taught by Johan Antony Barrau (1873-1953) who had also been advised by Korteweg for his doctorate. Barrau had taught at the University of Delft before being appointed professor of synthetic, analytical and descriptive differential geometry at Groningen in 1913. Another of Bottema's teachers, who only arrived in Groningen in 1923, was the number theorist Johannes Gaultherus van der Corput (1890-1975). Bottema was taught theoretical physics by Frits Zernike (1888-1966), an outstanding scientist who was awarded a Nobel Prize for physics in 1953. Bottema graduated from the University of Groningen in 1924 and began a career as a secondary school mathematics teacher.

After the award of his degree in mathematics, Bottema was appointed as a teacher at the Hogere Burgerschool in Hengelo. During his teaching at Hengelo, Bottema came into contact with Willem Van der Woude (1876-1974) from Leiden, who acted as a commissioner at his school. Van der Woude had studied for his doctorate at Groningen advised by Pieter Hendrik Schoute and, from 1916, was professor of mathematics and mechanics at the University of Leiden. Bottema had published a paper while still an undergraduate, namely

*Opmerking aangaande het artikel van N. R. Pekelharing-Azn: "Een toepassing van het lineair complex"*Ⓣ in which he showed that a geometrical theorem 'proved' by Pekelharing was untrue in certain cases. Bottema was keen to work towards his doctorate and, advised by Van der Woude, he undertook research while continuing to work full time as a mathematics teacher. He published three articles in Dutch in 1925, namely

*Over Brachistochronen*Ⓣ,

*Over het osculatievlak*Ⓣ, and

*Over de toevallige verdeeling van een lijnsegment*Ⓣ.

In 1927 Bottema was awarded a doctorate for his thesis

*De figuur van vier kruisende rechte lijnen*Ⓣ. He gives the following acknowledgements in the thesis:-

Teun Koetsier writes [6]:-Upon completing my dissertation I would like to thank you, dear teachers and dear former teachers of the Faculty of Physics at the University of Groningen, my warmest thanks for your teaching.

I am thinking in particular of you, Professor Barrau, whose lessons were of great importance to me and provided guidance for further study.

I owe a lot to you, Professors Wolff, Zernike and van der Corput.

Professor van der Woude, Dear Promoter, it is impossible to describe in a short sentence the thanks I owe to you. You have met me, who was never your pupil in a narrow sense, with an interest and helpfulness, which have forever obliged me to you.

The award of a doctorate did not mean that Bottema gave up being a school teacher. He remained active in secondary education for many years since from Hengelo he went to Groningen, and in 1933 he became headmaster of the Rijks Hogere Burgerschool in Sappemeer near Groningen; then he became director of the Rijks Hogere Burgerschool in Deventer in 1935 continuing in that role until 1941. At that time schools were much smaller than they are today and each headmaster also taught, so he remained a mathematics teacher.In the thesis Bottema deals with the projective properties of four mutually skew lines. Grassmann had discovered that the projective properties of such a figure are characterized by the so-called Grassmann harmonic ratio, a projective invariant for four mutually skew lines analogous to the harmonic ratio for four points on a line. In1878Voss had discovered that although a calculation by means of degrees of freedom suggests otherwise, in general there does not exist a third degree curve of double curvature that touches four given straight lines. And if there is such a curve there exist infinitely many of them. In this case the four lines form a Voss-quadruple. In the thesis Bottema studies such Voss-quadruples and other special quadruples of skew lines. In his thesis Bottema's elegant style in mathematics is already present.

Although Bottema taught in schools from 1924 to 1941, he also taught some university courses as a docent. In 1930 he was employed as a docent at the University of Groningen to teach the course 'Special chapters in geometry." On 20 October 1931 he delivered a public lecture

*De meetkunde als invariantentheorie*Ⓣ held at his acceptance of the position of docent at the University of Groningen. You can read our English version of this lecture at THIS LINK.

In 1930 Bottema married Femmina Catharina Johanna Berendsen on 21 August 1930 at Hengelo, Overijssel. Femmina, known as Femmy, was more than one year younger than Oene Bottema. She was the daughter of Jan Willem Berendsen, an office clerk born about 1876 in Enschede, Overijssel, and Willemina Luijerink, born about 1874 in Hengelo, Overijssel. Oene and Femmy Bottema had a daughter Willemina Wytske Bottema, born in Groningen, and a son born in Deventer.

In 1938 Bottema published his first book,

*De elementaire meetkunde van het platte vlak*Ⓣ. His aim was to write a book on plane geometry which was completely rigorous yet looked at interesting applications as well. The 328-page book looked at projective geometry as well as plane geometry and included a study of the theorems of Desargues, Pappus, Pascal and Gauss.

In 1941 Bottema left his position as director of the Rijks Hogere Burgerschool in Deventer when he was appointed as professor at the Technical University in Delft. The appointment was difficult since the vacancy occurred due to the German occupiers having dismissed the Jewish David van Dantzig. To avoid any bad feeling that might arise, the university decided to appoint Bottema to the chair which W A Versluys had held until 1935 but which had never been filled. N G de Bruijn writes in [2] (we have added full names and dates):-

Teun Koetsier writes [6]:-When Bottema took office in1941he thought it was just one boring job in the mathematics department, located in the emergency wooden buildings on Jaffalaan. His colleagues didn't go out much. One of the first things what he said to his assistant was: "I'm40, Charles Hendrik van Os(1891-1969)is50, and the rest are60." The rest consisted of Johannes George Rutgers(1880-1956), Hendrik Johan van Veen(1879-1962), Hendrik Bremekamp(1880-1963), Jan Arnoldus Schouten and Frederik Schuh(1875-1966). ... in1941Schouten was half-time being half on sick leave; he gradually disappeared from the scene. Schuh was still very active in writing textbooks but did not concern anyone.

N G de Bruijn writes [2]:-At the age of forty the name Bottema had become very well known among Dutch mathematicians. His scientific qualities were generally recognized and in1941he became full professor for pure and applied mathematics at the Technological University in Delft. From1951to1959he was rector magnificus(president or vice chancellor)of the university. He was a born manager, honest and hard working. As a rector he was admired and feared. He was, moreover, a gifted orator. The speeches that he gave as rector were works of art. It is also amazing that while rector he still managed to write45papers.

In 1944 he publishedHis style was what we call today "No nonsense, zero tolerance". The assistants and the serving staff were scared of him. He could say things mockingly, but everyone knew that he meant it. Nothing escaped him and his memory was phenomenal.

*Hoofdstukken uit de Elementaire Meetkunde*Ⓣ. A second edition was published in 1987 and this edition was translated into English and published as

*Topics in Elementary Geometry*in 2008. The publisher,

*Springer*, gives the following information about the reprint:-

Bottema published around 200 papers during his career, but he also made contributions to high school mathematics. M C van Hoorn writes in [9]:-Oene Bottema(1901-1992)may not be so well known abroad, but in his own country he is "the great geometer". He graduated from the University of Groningen in1924and obtained his doctor's degree from Leiden University in1927. He spent his early years as a high school teacher and administrator. He published extensively, and as his ability became known, he was made professor at the Technical University of Delft in1941, and later rector of that university(1951-1959). With his encyclopaedic knowledge of19th-century geometry and his training in20th-century rigour, he was able to make many contributions to elementary geometry, even as that subject was eclipsed by the modern emphasis on abstract mathematical structures. He also had a fruitful collaboration with engineers and made substantial contributions to kinematics, culminating in the book Theoretical Kinematics, with Bernard Roth, in1979. Throughout his life he was inspired by geometry and poetry, and favoured elegant succinct proofs. This little book, first published in1944, then in a second expanded edition in1987, gives us a glimpse into his way of thinking. It is a series of vignettes, each crafted with elegance and economy. See, for example, his proof of the Pythagorean theorem(1.2), which requires only one additional line to be drawn. And who can imagine a simpler proof of the nine-point circle(4.1)? There is ample coverage of the modern geometry of the triangle: the Simson line, Morley's theorem, isogonal conjugates, the symmedian point, and so forth.

In October 1950 the Board of the Koninklijke Wiskundig Genootschap (Dutch Mathematical Society) appointed a small committee with the task of drawing up a report on the structure and regulations for the International Congress of Mathematicians to be held in Amsterdam in 1954. H D Kloosterman was chair of this committee with Haantjes as its secretary and Bottema as one of the three other members.During the entire existence of the Hogere Burgerschool, commissioners were active during the final examinations, usually doctoral students with a PhD, who co-assessed the written work and took the oral examinations together with the examiner. In this way, Bottema, while still a teacher, came into contact with Van der Woude. A smaller group of experts took care of the examination assignments. It is the latter in which Bottema was involved, possibly since the1940s. Nowhere is this activity written. When I visited him in1975, he casually told me that he had prepared examination papers. I might have had to ask about it, although Bottema was not someone who let go more than he intended. At the time, little was known about the way in which the examination assignments were made. The assignments were there and who drafted them was irrelevant. Bottema was perfect for this work and thus certainly exerted his influence on secondary education.

Bottema retired in 1971 at the age of 70. His wife Femmy had begun to suffer from multiple sclerosis in around 1950 and her health deteriorated so that she was confined to a wheelchair. She became totally dependent on Bottema who took care of her in the most loving way. Femmy died in 1981. After retiring, Bottema continued to produce research papers, the last appearing in 2001 nearly 10 years after his death. This last paper,

*The Malfatti problem*, has the following summary:-

Bottema received many honours for his contributions. He was elected to the Paris Academy of Sciences in 1954. In 1958 he was honoured by his country when he was made Knight of the Order of the Nederlandsche Leeuw and, in 1959, he became Commander of the Order of Orange Nassau. He received an honorary doctorate from the University of Leeds, England, in 1958. He was also made an honorary member of the Dutch Mathematical Society and the International Federation for the Theory of Machines and Mechanisms. When he retired in 1971 he was presented with the Gold Medal of the city of Delft.A solution is given of Steiner's variation of the classical Malfatti problem in which the triangle is replaced by three circles mutually tangent to each other externally. The two circles tangent to the three given ones, presently known as Soddy's circles, are encountered as well.

Let us end this biography with T Koetsier's description of Bottema's character and interests [6]:-

One final amusing story from [2]. Bottema attended N G de Bruijn's public defence of his thesis at the University of Amsterdam in 1943:-Bottema was an erudite man, the opposite of a man only occupied with mathematics. He had a vast knowledge of history and literature, which is obvious from his public lectures and articles in literary journals. On his seventieth birthday his friends gave him a book, which he had in fact written himself. It contains a selection of his best public addresses and literary articles. The title of the book 'Steen en Schelp'(Stone and Shell)was taken from an address with the same title. Bottema admired Wordsworth, who in Book V of 'The Prelude' uses the stone and the shell to represent respectively geometrical truth and poetry. For Bottema the unshakable argument of geometry and the inspiration of poetry were the two indispensable guides in life. He disdained belaboured and messy solutions in his mathematics and in all other aspects of his life. As a mathematician, an administrator and a human being, Bottema always attempted to create a good balance between content and form. That is how we remember him; mathematics, poetry and, of course, the presence of his inseparable pipe.

It was a public promotion and Bottema would ask a question from the audience. However, because he did not understand the thesis("It is still tied up in my cupboard," he said), de Bruijn had written the question for him. And because he did not want to look as if he was reading from notes, he had learned the text that de Bruijn had given him before. So nothing could go wrong. But what was revealed by de Bruijn's acceptance speech? Bottema had learned his lesson too well and in addition to the question he gave the answer(that de Bruijn had written for the sake of completeness). A nice directing error.

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

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