# Johannes Gaultherus van der Corput

### Quick Info

Rotterdam, The Netherlands

Amsterdam, The Netherlands

**Johannes van der Corput**was a Dutch mathematician who worked in the field of analytic number theory.

### Biography

**Johannes van der Corput**'s parents were Gualtherus Johannes van der Corput (10 January 1847, Oostrhout - 16 April 1916) and Anna Maria Blomjous (17 February 1850, Tilburg - 10 March 1937, Rotterdam). Gualtherus, who had a grocery selling colonial products, married Anna on 19 April 1882 in Tilburg. They had six children: Hendrika Cornelia Adriana van der Corput (born 1883); Cornelis Adrianus Walterus van der Corput (born 1884); Adriana Henrica Cornelia van der Corput (born 1885); Josephus Walterus van der Corput (born 1887); Johannes Gualtherus van der Corput (the subject of this biography) (born 1890); and Gualtherus Adrianus Henricus van der Corput (born 1892). Johannes was always known as Jan by his friends and colleagues.

Jan's father, Gualtherus Johannes van der Corput, does not appear to have had any particular mathematical skills but there were other van der Corput's who did have strong mathematical connections. For example Johannes de Corput (1542-1611), also known as Johannes Corputius, was a Dutch engineer, cartographer and military leader. He is best known for his beautiful map of Duisburg completed in 1566. Anna Maria van der Corput (1599-1645) married Jacob Witt (1589-1674) and they had eight children including the two mathematicians and statesmen Jan de Witt and Cornelius de Witt. Jan van der Corput was not the only one of the six children to become a mathematician, for his brother Cornelis Adrianus Walterus van der Corput studied at Delft and became a secondary-school teacher of mathematics.

Jan attended primary school in Rotterdam before studying at the Gymnasium Erasmianum in Rotterdam. This famous Gymnasium, the second oldest in the Netherlands, was founded in 1328. At the time that van der Corput studied there it was situated at the corner of the Coolsingel and the Laurensstraat. He graduated from this school in 1908 and, after much deliberation as to what subject he should study, chose mathematics. Jacob Korevaar writes in [4]:-

His family wanted him to study medicine and he himself considered history (in which he always maintained a lively interest) and the Dutch language. In the end the recommendation of his secondary-school teacher, R H van Dorsten, was decisive: Jan should study mathematics, pure mathematics.Van der Corput entered the University of Leiden where Jan Cornelis Kluyver (1860-1932) was the professor with research interests in analysis, differential geometry and number theory. Kluyver, who originally undertook research on geometry, had, after his appointment in 1892 as Professor of Mathematical Analysis at Leiden, changed his research efforts to analysis, and in a relatively short time brought analysis teaching to a level that had not previously been reached in the Netherlands. We are now accustomed to analysis being presented according to very rigorous rules, but before Kluyver's time, analysis in the Netherlands was still almost at the level of the 18th century. Despite the improvement in the level of analysis teaching that Kluyver was making at Leiden, van der Corput did, later in his life, sometimes make critical comments about the level of Kluyver's courses and research. Despite this, he must have found Kluyver's number theory interesting since, after graduating in 1914, he decided to undertake research at Leiden for a Ph.D. advised by Kluyver.

Before van der Corput had started his research, on 28 July 1914, the Austro-Hungarian Empire declared war on Serbia. Two days later, the Dutch declared themselves neutral and, as further nations joined the war in August 1914, the Dutch repeated their declaration of neutrality on each occasion. Despite this position of neutrality, nevertheless they mobilised the Royal Netherlands Army throughout the war years 1914-18. Van der Corput was called up for military service and served as a captain. He became interested in horseback riding during these years of service. His position in the middle of his education allowed him to leave the Army before the standard demobilisation at the end of the war, and he taught mathematics in secondary schools in Leeuwarden from 1917 to 1919 while, at the same time, he undertook research for his Ph.D. advised by Kluyver.

In 1919 he submitted his thesis

*Over roosterpunten in het platte vlak. De beteekenis van de methoden van Voronoi en Pfeiffer*Ⓣ (1919). This thesis, on lattice points in the plane, studied problems which had interested number theorists for quite a while. Gauss had posed the problem, known as the "circle problem", to determine the number of integer lattice points that are in a circle with centre at the origin and radius $√r$. Since the equation of the circle is $x^{2} + y^{2} = r$, the problem is to find how many pairs of integers $m$ and $n$ there are such that

$m^{2} + n^{2} ≤ r$.

Since, on average, each unit square contains one lattice point, the number of lattice points in the circle will be $\pi r + R$ where, $R$ is the remainder term. Gauss had shown that $R$ is at most of order $√r$ and Sierpinski had improved the remainder term to be of order $r^{1/3}$. Edmund Landau in Göttingen, and G H Hardy and J E Littlewood in Cambridge, England, had all been interested in this problem and written papers which gave a lower bound of $r^{1/4}$ for the remainder. These papers led van der Corput to try to improve the remainder term and also to look at the number of lattice points inside other figures in the plane, in particular in the region between an orthogonal hyperbola and its asymptote (known as the Dirichlet problem).
While working on his thesis, van der Corput had made contact with Edmund Landau who was greatly impressed with his work. After graduating he taught mathematics at a secondary school in Utrecht for the year 1919-20 and then spent the summer of 1920 working with Edmund Landau in Göttingen. The result of this summer research visit was the joint paper E Landau and J G van der Corput,

*Über Gitterpunkte in ebenen Bereichen*Ⓣ (1920) and two single authored papers by van der Corput, namely

*Über Gitterpunkte in der Ebene*Ⓣ (1920) and

*Zahlentheoretische Abschätzungen*Ⓣ (1921).

In 1920 van der Corput was appointed as an assistant to Arnaud Denjoy at the University of Utrecht. Denjoy was a French mathematician, who had studied and worked in France until 1917 when he was appointed to a professorship at the University of Utrecht. He would only remain in Utrecht until 1922 when he returned to a professorship at the University of Paris. Van der Corput was his assistant for the final two years of Denjoy's stay in Utrecht then, in 1922, van der Corput was appointed as professor at the University of Fribourg in Switzerland.

Let us return to the 1921 paper mentioned above. In it he introduced the method of exponential sums which was a new method for making number-theoretic estimates. It led to a breakthrough when he was able to improve the remainder term in the circle problem from $r^{1/3}$ to $r^{33/100}$. This might not seem a large improvement but it was highly significant in that many who had worked on the topic were coming to believe that $r^{1/3}$ was the correct answer.

Van der Corput only spent one year at the University of Fribourg before accepting a professorship at the University of Groningen in 1923. For some years he continued to undertake research on number theory problems associated with his earlier work on lattice points in the plane, continuing to develop and refine his method of exponential sums. In the 1930s his research interests broadened, partly because of the courses that he was giving at the University of Groningen but mainly, it seems, because he had to find topics for around fifteen Ph.D. students. He undertook research on the asymptotic evaluation of general types of integrals publishing

*Zur Methode der stationären Phase. I: Einfache Integrale*Ⓣ (1934) and

*Zur Methode der stationären Phase. II: Wiederum einfache Integrale*Ⓣ (1936).

Van der Corput attended the International Congress of Mathematicians in Strasbourg in September 1920, the International Congress of Mathematicians in Zurich in September 1932, and was a plenary lecturer at the International Congress of Mathematicians in Oslo in July 1936 delivering the lecture

*Diophantische Approximationen*Ⓣ on 17 July.

You can read his introduction to his plenary lecture at THIS LINK.

In Germany the Nazis came to power in 1933 and over the following years it was clear to almost everyone that they were preparing for war. Van der Corput was strongly opposed to the Nazis and, in a letter to Bartel van der Waerden in 1945 explained his attitude towards Germany [5]:-

Concerning me personally, in January 1939 I turned down Erich Hecke's invitation, passed on to me by Harald Bohr, to give one or more lectures, because I refused to come to Germany as long as Hitler was in power. Consequently I have not been in Germany after 1932.He had also resigned from

*Zentralblatt für Mathematik*in 1938 after Tullio Levi-Civita, as a Jew, was dismissed from the board following the passing of the September 1938 Racial Laws. Van der Corput wrote in a 1945 letter [5]:-

Speaking of Jews, when Levi-Civita was thrown out of 'Zentralblatt für Mathematik', I withdrew as an associate (while giving my reasons) and suggested all Dutch associates to do the same and to become associates for the 'Mathematical Reviews'.It appears that the rise of the Nazis and then their occupation of the Netherlands, led to a change in van der Corput lifestyle [3]:-

In the late thirties and the years 1940-45 of the German occupation of the Netherlands there was a big change in van der Corput's orientation. Exaggerating a little, one might say that before the war he had lived only for mathematics, whereas in this period he became much more socially engaged. Still a bachelor, he met a remarkable woman, Jeannette Cornelia Houwink (1898-1989). She had obtained a law doctorate at Groningen and married fellow-student H W O ten Cate in 1920, worked at the tax department for a while, had three children and became a writer. After her divorce, van der Corput married her on 31 August 1942, the birthday of the Dutch queen in exile. She would strongly support him in his activities (and share his frugality when it concerned themselves). He played an active role in the university opposition to the German occupants, for which he regularly travelled to Amsterdam. In their home, he and his wife provided shelter for persons hiding from the enemy. They also assisted Jewish mathematicians from abroad. At the beginning of 1945 van der Corput and two persons hiding at his house were arrested, but thanks to the help of some unknown person, he was released after three anxious weeks.In a letter to Bartel van der Waerden in July 1945, van der Corput gives more details [5]:-

People were in hiding in my house throughout the entire war, 23 in total, of which 5 were Jews; I was a representative at Groningen of the Professors Resistance Group. When I was arrested in February 1945, they found two people in hiding in my house, of which one was Jewish. I was suffering from angina and was released from prison after a week. My house and all my furniture were impounded [by the authorities] but we moved back on the day of liberation . . . I was on the Board of Vrij-Nederland [Free Netherlands] and was arrested for disseminating illegal literature.During the war a number of the professors at Groningen had formed a small group to discuss how universities, in a post-war situation, could be independent of authoritarian threats. Van der Corput was a member of this group as was Gerardus J van der Leeuw, a professor of history and religion at Groningen. After the war ended in 1945, van der Leeuw was appointed as Minister of Education for The Netherlands. He appointed van der Corput to be the chair of the Committee for the Coordination and Reorganization of Higher Education in Mathematics in The Netherlands. Other members of the committee were David van Dantzig, Jan A Schouten, Jurjen Koksma (who had been a doctoral student of van der Corput), Hendrik Kramers and the astrophysicist Marcel G J Minnaert (1893-1970). The Committee became known as "The Van der Corput Committee." In a letter to Bartel van der Waerden on 29 July 1945, van der Corput writes [5]:-

I have been appointed chairman of a commission to reorganise higher education in mathematics in the Netherlands, which will have as its primary duty to offer advice for the filling of vacancies in mathematics.The Committee discussed setting up a Mathematical Centre for Research and Development at either Utrecht or Amsterdam. This idea was strongly pushed by van der Corput and, when the City of Amsterdam showed that it was very positive in its support, they decided on that city. On 24 October 1945 van der Corput writes in a letter [5]:-

This week I received an invitation from the Faculty of Natural Sciences at Amsterdam to become Weitzenböck's replacement. ... I do not know what I am going to do. Personally, I like Utrecht better, but maybe I can do more for mathematics in Amsterdam ...We note that Roland Weitzenböck (1885-1955) was a differential geometer who was the professor of mathematics at the University of Amsterdam from 1923 until he retired in 1945.

The Mathematical Centre opened on 11 February 1946 and van der Corput became its first director. Taking up his professorship at the University of Amsterdam, van der Corput delivered his inaugural lecture

*Het Mathematisch Centrum*Ⓣ. In this he said:-

The only explanation of why someone chooses to study mathematics is that he gets caught by this science. No one should become a mathematician in search of personal success, but only to contribute to the expansion of a science which is of great importance to mankind. In doing the latter he will become a happy man, because he will enjoy what he does. But he will do this not only for joy, but also for a sense of duty, for society sustaining him has a right to demand that he spends his talents to its interest. Hardy may say that it is not that bad if a few university dons spend their lives on unimportant things, but I think it is bad for society.The Mathematical Centre set up a computing department, a department of mathematical physics, a statistics department and a pure mathematics department [5]:-

Van der Corput considered it as part of the Centre's mission to provide advanced mathematics courses and lectures for persons around the country who had been unable to obtain a university education. Many Dutch mathematicians participated in this program sponsored by the Centre, which also included summer courses for secondary-school teachers of mathematics. The Centre furthermore provided positions for promising young Dutch mathematicians who were likely to obtain a university appointment after a few years. Lively contacts developed with mathematicians from abroad. Paul Erdős lectured here in 1948 on his "elementary" proof of the prime number theorem (which he had found jointly with A Selberg); Van der Corput prepared an early Centre publication of the famous proof.Van der Corput delivered the Rouse Ball Lecture at the University of Cambridge in 1948. He was a Visiting Professor at Stanford University from 1950 to 1952, and after returning to Amsterdam he became somewhat disappointed that the atmosphere there was not as conducive to research as it had been in the United States. This led him to leave Amsterdam in 1954 and accept a permanent position at the University of California at Berkeley. He was on the faculty at Berkeley until 1958 but continued to have Berkeley as his main residence until 1966. He had various visiting positions in the years 1958-66, at Mathematics Research Center in Madison, Wisconsin, and in Rome. In 1966 van der Corput returned to Europe where he lived part of the time in Amsterdam and part in Antwerp.

Among the many honours which van der Corput received we mention his election to the Netherlands Academy of Sciences (1929) and to the Royal Belgium Academy of Science (1932). He was awarded an honorary doctorate by the University of Bordeaux (1952) and by the Technical University at Delft (1966). Let us also note that van der Corput was an editor of

*Acta Arithmetica*from the time the journal was founded in 1936.

### References (show)

- N G de Bruijn, Johannes G van der Corput, A biographical note,
*Acta Arithmetica***32**(1977), 207-208. - H J A. Duparc and J Korevaar, Johannes Gualtherus van der Corput,
*Nieuw Archief voor Wiskunde*(3)**30**(1982), 1-39. - Johannes Gualtherus van der Corput,
*Bernoulli Institute for Mathematics, University of Groningen*. http://www.cs.rug.nl/jbi/History/Corput - J Korevaar, Levensbericht van Johannes Gualtherus van der Corput (4 september 1890-13 september 1975),
*Jaarboek*(Amsterdam, 1975), 198-203. - A Soifer, Van der Waerden and Van der Corput: Dialog in Letters, in
*The Scholar and the State: In Search of Van der Waerden*(Birkhäuser, Basel, 2015), 233-254.

### Additional Resources (show)

Other pages about Johannes van der Corput:

Other websites about Johannes van der Corput:

### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update April 2020

Last Update April 2020