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Carl-Wilhelm Reinhold de Boor

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Born
3 December 1937
Stolp, Germany (now Słupsk, Poland)
Summary
Carl de Boor is German born mathematician who has worked for most of his career in the United States. He has made remarkable contributions to the theory of splines and has won the John von Neumann Lecture Prize from the Society for Industrial and Applied Mathematics in 1996 and National Medal of Science in 2003.
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Biography

Carl de Boor is the son of Werner Hans Richard de Boor (1899-1976) and Toni Emma Schröder (1900-1979). Werner de Boor, born 24 November 1900 in Lüneburg, Germany, attended school in Marburg and, after serving in World War I in 1917-18, studies natural sciences in Marburg, then Protestant theology in Marburg, Tübingen and Erlangen. On 22 June 1922 he married Wilhelmine Berta Charlotte Friedrich (1903-1945) in Marburg; they had two sons, Joachim de Boor (1923-2007) and Wolfgang de Boor (1925-1945). Werner became a Lutheran minister and was divorced on 20 April 1926. He married Toni Emma Schröder on 21 May 1926; they had eight children, Peter de Boor (1927-1946); Wilhelm Herrmann de Boor (1929-2011); Anne de Boor; Hans de Boor (1930-2023); Friedrich de Boor (1933-2020), Elizabeth de Boor; and Carl-Wilhelm de Boor, the subject if this biography; and Tonimaria de Boor.

When Carl de Boor was born his father was a pastor at St John's Castle Church in Stolp, Pomerania. He was also a member of the Confessing Church, a Protestant resistance movement against Nazi control of the church, serving on its organising body the Council of Brethren. In 1937 he was one of 96 Protestant church leaders to sign a declaration against the Nazi theologian Alfred Rosenberg who held important roles in the Nazi government. At the end of the war in 1945 the family moved to Lübtheen, Wismar, Rostock and then in September 1946 to Schwerin, in East Germany, where Werner de Boor worked for the Department for Popular Mission of the Schwerin Church Council.

Carl de Boor suffered from poor health when he was a child. His parents had him learn to play the cornet to help him combat asthma. From that time on, he had a great love of music, especially classical music, for his whole life. He began his schooling at a junior high school in Schwerin then attended the Goethe School at Pfaffenteich in Schwerin, a secondary school on August-Bebel-Strasse. After graduating in 1955, he intended to continue his education and applied to the Humboldt University in East Berlin to study chemistry. He was able to obtain a one month visa to visit West Germany where he intended to spend the summer before beginning his studies at the Humboldt University. He travelled there on his bicycle knowing that there were people in West Germany who would support him.

The Friedrich family had members both in Germany and in the United States. Werner de Boor's first wife was a member of this family; she had a brother Otto Friedrich who was living in West Germany and a brother Carl Joachim Friedrich living in the United States. Otto Friedrich was an industrialist prominent in the German rubber industry in Hamburg while Carl Friedrich was a political scientist teaching at Harvard University. At this stage Carl de Boor wanted to study chemistry at university so, with help from Otto Friedrich, he found a job in a chemical laboratory in Hamburg. While there he learnt that his application to the Humboldt University had been refused so he decided to stay in West Berlin and study chemistry there. His East German high school diploma was not accepted by West Germany so he had to spend a year obtaining a West German high school diploma. Continuing his work at the chemical factory, he applied to Hamburg University to study chemistry but was told there were no laboratory places left for the first semester. They suggested he take the mathematics for chemists course in the first semester and delay his start in the chemical laboratory until the second semester. He explained in the interview [4]:-
This combination of taking the mathematics that the chemists have to learn and working in a chemistry laboratory was no contest, mathematics was much more intriguing - much - you could do it without any laboratory equipment. I could actually do it by myself, so I became intrigued, then I stayed in mathematics.
In 1957, while a mathematics undergraduate at Hamburg University, he met Matilda Cornwall Friedrich, the daughter of the professor of political science at Harvard, Carl Joachim Friedrich. Matilda, although born on 8 May 1938 in Locarno, Switzerland, was an American citizen. They were engaged in 1958. Matilda suggested that de Boor spend a year in the United States and get to know her family there. She asked her father if he could find a position for de Boor at Harvard for a year and he talked to his friend Garrett Birkhoff who offered de Boor a position as his research assistant for a year. This is quite surprising since at this stage de Boor only had a high school qualification and had spent three and a half years as an undergraduate but had not completed his course. In the interview [21] he explained how this happened. Carl Friedrich, when speaking to Birkhoff, had:-
... mentioned that I had worked as an "assistant" to Collatz who was at that time a main figure in numerical mathematics, at least in Germany. Now, I had indeed worked as a teaching assistant for Collatz and even done some calculations for him. But Birkhoff misunderstood "assistant" and thought that I had been an "Assistant". In the German system, an "Assistant" is someone close to a Ph.D. So, Birkhoff was very happy to give me this job. But it became clear very quickly that I was not at all qualified for it. Birkhoff was a very kind person. He did not kick me out, but he gave me a good problem, and I have never worked so hard in my life, trying to produce at least something.
De Boor had travelled by ship from Germany to the United States in 1959. He said in the interview [4]:-
In those days immigration was very much welcomed so it was very easy to get a visa and I worked for professor Garrett Birkhoff.
During his year as Birkhoff's assistant, he decided that American university life was preferable to that in Germany and decided he wanted to stay in America. During that year he married Matilda Friedrich, realised that a research assistantship did not pay enough to support a family, so asked Birkhoff's advice.

Garrett Birkhoff began his consulting work with General Motors Research in 1959. David Young writes in [28]:-
One of the problems posed there was the mathematical representation of automobile surfaces in order to exploit the then new numerically controlled milling machines for the cutting of dies: these dies were needed for stamping of the outer and inner panels of automobiles. Garrett was quick to recommend the use of cubic splines (i.e. piecewise cubic polynomials with two continuous derivatives) for the representation of smooth curves.
When de Boor's time as Garrett Birkhoff's assistant ended he recommended de Boor for a position at General Motors Research to work on this problem. De Boor explained in his 2005 interview [4]:-
There was this wonderful situation; computers were ready to be used but the mathematics wasn't there. So even a failed graduate student could do fundamental work and that's what I did. I stayed at General Motors and it really was total luck, total luck. ... The problem at that time at General Motors was the following: A car has been designed, a wooden model has been put together and approved and now it is time to stamp the metal - the panels. For that you have to transfer the information from the wooden model to something called the die, a metal die, which is then used to stamp - you have to transfer. The transfer in those days was done this way. You had a machine, here was a drilling machine, here was the model and a guide would go along and the drill would cut the same path; a long and very arduous process. The idea was to describe this surface mathematically, compute the cutting paths from the mathematical formulas and in this way speed up the process. And what I did was to generate a method which now is so common it is not associated with my name any more.
De Boor's first publication was in 1962 when he published Bicubic spline interpolation. In 1963 de Boor published two papers, Best approximation properties of spline functions of odd degree, and (with John Rischard Rice) Chebyshev approximation by ∏x−rix−si\prod \Large\frac{x - r_i}{x -s_i} and application to ADI iteration. He gives his address on these papers as 'General Motors Research'. We note that John Rice (1934-2024) was a researcher at General Motors; he had been awarded a Ph.D. in 1959 from the California Institute of Technology having had Arthur Erdélyi as his thesis advisor.

The first of the 1963 papers we mentioned above was communicated by Garrett Birkhoff. De Boor and Garrett Birkhoff published the first of their three joint papers in 1964, namely Error Bounds for Spline Interpolation. De Boor's address on this paper is 'University of Michigan, Ann Arbor', for by that time he was studying for a Ph.D. at the University of Michigan. He had decided to continue his education and had applied to the University of Michigan to study for a PhD in numerical methods. He was able to go straight into the doctoral program without a having master's degree with the support of the numerical analyst Robert Bartels whom he had met previously at summer workshops for mathematics in industry.

He was awarded a Ph.D. from the University of Michigan in 1966 after submitting the thesis The method of projections as applied to the numerical solution of two point boundary value problems using cubic splines. The examining committee comprised: Professor Robert C F Bartels, Chairman; Assistant Professor William A Ericson; Professor Herbert P Galliher; Associate Professor Wilfred M Kincaid; and Research Mathematician John F Riordan. Although Robert Bartels, who was a numerical analyst running the Computing Center at the University of Michigan, had been his official thesis advisor, the thesis was based on work de Boor had done while at General Motors.

After the award of his Ph.D., de Boor was appointed as an Assistant Professor of Mathematics and Computer Science at Purdue University. His co-author John Rice was also working at Purdue University, in the recently founded Computer Science Department, having left General Motors in 1964. While at Purdue, de Boor had worked with Robert Emmett Lynch who was studying for a Ph.D. from Harvard with Garrett Birkhoff as his advisor. De Boor and Lynch published the joint paper On splines and their minimum properties (1966). Lynch joined the Department of Computer Science at Purdue University in 1967. In 1968 de Boor was promoted to Associate Professor of Mathematics and Computer Science at Purdue University. He became a citizen of the United States in 1969.

De Boor returned to the University of Michigan at Ann Arbor for the year 1970-71, and also at that time he was employed as a consultant at the Los Alamos laboratory. In fact he continued to hold the position at Los Alamos until 1995 where he worked on B-splines, weapons research and advanced computing.

After the year at Michigan, he returned with his family to Purdue for one more year when he was offered a position at the Mathematics Research Center at the University of Wisconsin-Madison. Isaac Schoenberg had initiated the study of splines while working at the Army's Ballistic Research Laboratory in Aberdeen, Maryland during World War II. In 1966 Schoenberg had moved from the University of Pennsylvania to the University of Wisconsin-Madison. In his 1964 paper On Interpolation by Spline Functions and its Minimal Properties he mentions de Boor's work on splines briefly in a "Note added in proof." The authors of [17] write:-
In fact, when informed by de Boor a few years later of his newly found recurrence relation for B-splines, Schoenberg was initially sceptical: while linear combinations of non-smooth functions could, accidentally, produce a function of greater smoothness, one should not expect such miracles to happen in a consistent way! Schoenberg's scepticism, however, was short-lived: in 1972, on his initiative, the University of Wisconsin hired de Boor at the rank of full professor.
De Boor's work on B-splines which impressed Schoenberg was explained in his paper On calculating with B-splines (1972). He writes in the Introduction to the paper [2]:-
In computational dealings with splines, the question of representation is of primary importance. For splines of fixed order on a fixed partition, this is a question of choice of basis, since such splines form a linear space. Only three kinds of bases for spline spaces have actually been given serious attention; those consisting of truncated power functions, of cardinal splines, and of B-splines. Truncated power bases are known to be open to severe ill-conditioning, while cardinal splines are difficult to calculate. By contrast, bases consisting of B-splines are well-conditioned, at least for orders < 20. Such bases are also local in the sense that at every point only a fixed number (equal to the order) of B-splines is nonzero. B-splines are also evaluated quite easily, using their definition as a divided difference of the truncated power function. Unfortunately, such calculations are ill-conditioned, particularly for partitions of widely varying interval lengths, as is indicated by the fact that special measures have to be taken in case of coincident knots. In this note, a different way of evaluating B-splines is discussed which is very well conditioned yet efficient, and which needs no special adjustments in case of coincident knots. It is also shown that the condition of the B-spline basis increases exponentially with the order.
For an excellent overview of de Boor's contributions to splines, see his own account in [3].

De Boor writes in [3] about his move to Madison:-
In 1972, I moved to Madison WI, to the Mathematics Research Center (MRC) funded since 1957 by the United States Army Research Office to carry out research in applied mathematics. It had an extensive postdoc and visitors program, the only fly in the ointment its location far from the centre of the University of Wisconsin-Madison because its former housing there was bombed in August 1970, as a protest against the Vietnam war, by people who took the very absence of any mention of military research in the semi-annual reports of that Army-financed institution as proof of the importance of the military research supposedly going on there. I had been hired at the time of I J Schoenberg's retirement from MRC.
De Boor was elected to the American Academy of Arts and Sciences in 1987, received the Humboldt Research Prize from the Humboldt Foundation Germany in 1992 and was elected to the National Academy of Engineering in 1993. He was awarded an honorary doctorate from Purdue University in 1993, was presented with the John von Neumann Prize by the Society for Industrial and Applied Mathematics in 1996, and became a member of the National Academy of Sciences in 1997. This achievement was recorded in the Van Vleck Notes of the Department of Mathematics, University of Wisconsin as follows [8]:-
Carl de Boor, Professor of Mathematics and Computer Sciences, was among the 60 scholars elected this year to the National Academy of Sciences. Carl grew up in East Germany and received the PhD from the University of Michigan in 1966. He was on the faculty of Purdue University when in 1972 he joined the Mathematics and Computer Sciences Departments at UW-Madison. He was named P L Chebyshev Professor of Mathematics and Computer Sciences in 1983 and Steenbock Professor of Mathematical Sciences in 1987. The Steenbock Award is for ten years, and Carl was given the award again in 1997. It is endowed through the generosity of Mrs Evelyn Steenbock and, according to the Graduate School Dean Virginia S Hinshaw, the "level and flexibility of this research support and the selection process places this professorship among the most prestigious ever awarded by this University."

De Boor's speciality is approximation by spline functions. Splines were introduced in the 40's (by the late I J Schoenberg of Wisconsin) as a means for approximating discrete data by curves. Their practical application was delayed almost twenty years until computers became powerful enough to handle the requisite computations. Since then they have become indispensable tools in computer-aided design and manufacture (cars and airplanes, in particular), in the production of printer's typesets, in automated cartography, and in many other areas, often concealed at the core of elaborate software packages, Carl is the worldwide leader and authority in the theory and applications of spline functions. His contributions have been more fundamental and numerous than any other researcher in this field, ranging from rigorous theories through highly efficient and reliable algorithms to complete software packages. Carl has made UW-Madison a major international centre in approximation theory and numerical analysis, attracting students, faculty, and visitors from all over the world. He is also a thoughtful teacher and has a tremendous ability to pass on his vast knowledge and understanding, and is always among the first to adapt and to promote new instructional tools.
He became a member of the German Academy of Scientists Leopoldina in 1998 and of the Polish Academy of Sciences in 2000. He was awarded an honorary degree by Technion (the Israel Institute of Technology) in 2002, received the Hilldale Award from the University of Wisconsin in 2002, and received the 2003 National Medal of Science in 2005. He was elected a fellow of the Society for Industrial and Applied Mathematics in 2009 and presented with the John A Gregory Memorial Award from the University of Florida in 2011 for:-
... fundamental contributions to the field of geometric modelling.
De Boor is the author of several important books. For example (with S D Conte) Elementary numerical analysis. An algorithmic approach (Second Edition) (1972), A practical guide to splines (1978), Splinefunktionen (1990), and (with K Höllig and S Riemenschneider) Box splines (1993). You can read more information about these books at THIS LINK.

Let us make a few comments about the de Boor family. Carl de Boor had a substantial pay rise in 1981 as reported in [27]:-
Following is a list of the top dollar raises of at least $5,200 given to 28 members of the UW Madison faculty for the 1981-82 school year: ... Carl De Boor, computer sciences and math, $5,200.
After the family moved to Madison all the children of Carl and Matilda de Boor attended West High School, Madison. Consulting the West High School Yearbooks, we find: Carl Thomas de Boor, born about 1960, in 1976, 1977 and 1978 Yearbooks, four-year National Merit Scholarships for undergraduate study 1978, Gisholt award from the John A Johnson Foundation 1978; Thomas De Boor, born about 1961, in 1975, 1976 and 1978 Yearbooks; Elizabeth (Lisa) de Boor, born about 1963, in the 1978, 1979 and 1980 Yearbooks; Peter de Boor, born about 1966, in 1982, 1983 and 1984 Yearbooks; and Adam R de Boor, born about 1967, in 1981, 1982, 1983 and 1984 Yearbooks, finalist in the 1984 Merit Scholarship competition. Carl and Matilda de Boor were divorced on 12 September 1984. On 2 January 1991 de Boor married Helen Lucille Bee in Madison. Helen Bee, born in April 1939 in Tacoma, Washington, had two children from a previous marriage to George C Douglas. She is a psychologist and the author of books on human development which have run to many editions.

De Boor retired in 2003 and went to live in Washington State. He continued to undertake research and published many articles over the next 15 years. While living on Orcas Island, he soon became involved in the musical life there [7]:-
Carl has served on the Investment Committee of the Orcas Island Community Foundation and is president of the Buck Ridge NW & Sucia Water Users Association. After joining the Orcas Island Chamber Music Festival Board in 2010, he was appointed treasurer in 2012 and has vastly contributed to financial innovations throughout his tenure. As treasurer, he also currently serves on the finance and ad hoc compensation committees. Carl is an avid Orcas Island Chamber Music Festival supporter, attending all of the concerts, hosting artist homestays, and traveling to Austin, Texas, to hear the Miró Quartet play.
Other Mathematicians born in Poland
A Poster of Carl de Boor

References (show)

  1. D W Arthur, Review: Elementary numerical analysis. An algorithmic approach, by S D Conte and Carl de Boor, The Mathematical Gazette 59 (410) (1975), 295-296.
  2. C de Boor, On calculating with B-splines, Journal of Approximation Theory 6 (1972), 50-62.
  3. C de Boor, The way things were in multivariate splines: A personal view, in R DeVore and A Kunoth (eds.), Multiscale, Nonlinear and Adaptive Approximation (Springer-Verlag, Berlin Heidelberg, 2009), 19-38.
  4. Carl de Boor - National Medal of Science, 2005, Wikimedia Commons (2025).
    https://commons.wikimedia.org/wiki/File:Carl_de_Boor_-_National_Medal_of_Science,_2005.webm
  5. Carl de Boor receives Hilldale Award and an Honorary Doctorate of Science from the Technion (Israel), Department of Mathematics, University of Washington (2025).
    https://web.math.wisc.edu/oldnews/2003/awards.html
  6. Carl de Boor, Professor Emeritus, Department of Mathematics, University of Wisconsin-Madison (2025).
    https://math.wisc.edu/staff/de-boor-carl/
  7. Carl de Boor, Orcas Island Chamber Music Festival (2025).
    https://oicmf.org/carl-de-boor/
  8. Carl De Boor Elected to the National Academy of Sciences and Receives Steenbock Professorship, Van Vleck Notes, Department of Mathematics, University of Wisconsin (Fall 1997).
  9. Carl R de Boor, Department of Applied Mathematics, University of Washington (2025).
    https://amath.washington.edu/people/carl-r-de-boor
  10. Carl R de Boor, National Academy of Sciences (2025).
    https://www.nasonline.org/directory-entry/carl-r-de-boor-glsp1y/
  11. Carl W R DeBoor, mathematics, Journal and Courier from Lafayette, Indiana (Friday, 15 March 1968), 14.
  12. Carl Wilhelm R De Boor, ancestry.com (2025).
  13. C K Chui, Review: Box splines, by C de Boor, K Höllig and S Riemenschneider, Mathematical Reviews MR1243635 (94k:65004).
  14. Curriculum Vitae: Carl(-Wilhelm Reinhold) de Boor, Department of Computer Sciences, University of Wisconsin-Madison (2025).
    https://pages.cs.wisc.edu/~deboor/cv.pdf
  15. de Boor and Luce receive National Medal of Science, Notices of the American Mathematical Society 52 (6) (2005), 634.
  16. de Boor, Carl, ISI HighlyCited.com (14 February 2003).
    https://web.archive.org/web/20060304073635/http://hcr3.isiknowledge.com/author.cgi?&link1=Browse&link2=Results&id=2487
  17. R DeVore and A Ron, Developing a Computation-Friendly Mathematical Foundation for Spline Functions, SIAM News 38 (4) (2005), 71-72.
  18. E W Grafarend, Review: Splinefunktionen, by Carl de Boor, Mathematical Reviews MR1212083 (95k:41002).
  19. J Gordon, Carl R de Boor, National Medal of Science, National Science & Technology Medals Foundation (2025).
    https://nationalmedals.org/laureate/carl-r-de-boor/
  20. R Lange, Interview of Carl de Boor, Oral History Project, University of Wisconsin-Madison (25 April 2007).
  21. Y K Leong, Carl de Boor: On wings of splines, Newsletter of Institute for Mathematical Sciences National University of Singapore 5 (2004), 16-20.
  22. G Merz, Review: A practical guide to splines, by Carl de Boor, Mathematical Reviews MR0507062 (80a:65027).
  23. G Plonka, Review: A practical guide to splines. Revised Edition, by Carl de Boor, Mathematical Reviews MR1900298 (2003f:41001).
  24. J R, Review: A practical guide to splines, by Carl de Boor, Mathematics of Computation 34 (149) (1980), 325-326.
  25. P W Smith, Review: A practical guide to splines, by Carl de Boor, SIAM Review 22 (4) (1980), 520-521.
  26. Workshop on Spline Approximation and its Applications on Carl de Boor's 80th Birthday, Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne (December 2017).
    https://bigwww.epfl.ch/events/de-boor-80.pdf
  27. UW faculty pay increases, The Capital Times from Madison, Wisconsin (Tuesday, 22 September 1981), 1, 4.
  28. D M Young, Garrett Birkhoff and applied mathematics, Notices of the American Mathematical Society 44 (11) (1997), 1446-1450.

Additional Resources (show)

Other pages about Carl de Boor:

  1. Carl de Boor Books

Other websites about Carl de Boor:

  1. Mathematical Genealogy Project
  2. MathSciNet Author profile
  3. zbMATH entry

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update December 2025