Ulf Grenander (23 July 1923 – 12 May 2016) was a Swedish mathematician and statistician, born in Västervik, Sweden, to Sven Grenander, who later died in Providence, Rhode Island, United States.^{[1,2,4,29,30,28,9]} He began his higher education at Uppsala University, receiving a filosofie kandidat in 1946, and completed his postgraduate education at Stockholm University (Stockholms högskola), earning a filosofie licentiat in 1948 and defending his doctoral dissertation on stochastic processes and statistical inference in 1950 under the supervision of Harald Cramér.^[3,9,30] His doctoral students included Sven Erlander and Per Martin-Löf.

Grenander served as a docent and lecturer at Stockholm University from 1950 to 1951, before working as an assistant professor at the University of Chicago in 1951–1952. He was at the University of California (Berkeley) as an associate professor in 1953 according to German Wikipedia, or during 1952–1953 according to Swedish Wikipedia, and subsequently lectured at Stockholm University from 1954 to 1957 (or 1953 to 1957 according to Swedish Wikipedia). After serving as a professor at Brown University in 1957–1958, he returned to Stockholm University from 1959 to 1966 according to German Wikipedia, or from 1958 to 1966 according to Swedish Wikipedia, succeeding Harald Cramér in 1959 as professor of actuarial mathematics and mathematical statistics. From 1966 until his retirement, Grenander was a professor at Brown University, where he held the title of L. Herbert Ballou University Professor of Applied Mathematics. Concurrently, from 1969 to 1974, he was also professor of applied mathematics at the Royal Institute of Technology (Kungliga Tekniska högskolan) in Stockholm.^[31,8]

Grenander's scientific contributions spanned mathematics, statistics, and computer science. His early research focused on probability theory, stochastic processes, time series analysis, and statistical theory, where he introduced the sieve estimator (particularly for the order-constrained estimation of cumulative distribution functions) and investigated the maximum subarray problem.^[5] In subsequent decades, Grenander contributed to computational statistics, image processing, pattern recognition, artificial intelligence, and computational anatomy.^[5] He coined the term 'pattern theory' to distinguish it from pattern recognition and pursued this statistical theory of shape and pattern recognition at Brown University starting in the early 1970s, an approach also pursued by David Mumford.^[1,2,6,5] Applications pursued by his research group included computer vision, natural language processing, automatic target recognition, and the recognition of anatomical patterns from computed tomography data of the brain.

In 1998, he was an invited speaker at the International Congress of Mathematicians in Berlin, delivering a lecture titled 'Strategies of seeing'. Grenander was awarded honorary doctorates by the University of Chicago in 1994 and by the Royal Institute of Technology (Kungliga Tekniska högskolan) in 2005.^[31,8] He was elected a member of the Royal Swedish Academy of Sciences in 1966, the American Academy of Arts and Sciences, and the National Academy of Sciences in 1996. He was also an honorary member of the Royal Statistical Society and a Fellow of the Institute of Mathematical Statistics.

Grenander earned his undergraduate degree at Uppsala University.^[9] He earned his Ph.D. at Stockholm University in 1950 under the supervision of Harald Cramér.^[10]

He studied at Uppsala University and Stockholm University and worked in the field of mathematical analysis and probability theory. He was active as an Associate Professor at Stockholm University from 1950 to 1951, at the University of Chicago from 1951 to 1952, at the University of California–Berkeley from 1952 to 1953, and at Stockholm University from 1953 to 1957. He was at Brown University from 1957 to 1958 and again at Stockholm University from 1958 to 1966, where in 1959 he succeeded Harald Cramér as the Professor in actuarial science and mathematical statistics. From 1966 until his retirement, Grenander was L. Herbert Ballou University Professor at Brown University. In 1969–1974, he was also professor of Applied Mathematics at the Royal Institute of Technology.

In 1966 Grenander was elected to the Royal Academy of Sciences of Sweden, and in 1996 to the US National Academy of Sciences. In 1998, he was an Invited Speaker of the International Congress of Mathematicians in Berlin.^[7] He received an honorary doctorate in 1994 from the University of Chicago, and in 2005 from the Royal Institute of Technology of Stockholm, Sweden.^[8,11]

Grenander co-authored Statistical Analysis of Stationary Time Series with Murray Rosenblatt, published by the American Mathematical Society in 1957 and reviewed in the Bulletin of the American Mathematical Society in 1958. With Gábor Szegő, he published Toeplitz Forms and Their Applications through Chelsea in 1958, which received a review in the Bulletin of the American Mathematical Society in 1959. In 1959, he published Probability and Statistics: The Harald Cramér Volume with Wiley. His subsequent works with Wiley include Probabilities on Algebraic Structures in 1963, reviewed in the Bulletin of the American Mathematical Society in 1965, and Abstract Inference in 1981. Grenander's Mathematical Experiments on the Computer was published by Academic Press in 1982 and reviewed in the Bulletin of the American Mathematical Society (New Series) in 1985.

His publications on pattern theory comprise General Pattern Theory (Oxford Science Publications, 1994), Elements of Pattern Theory (Johns Hopkins University Press, 1996), and Pattern Theory: From Representation to Inference (Oxford University Press, 2007). In 2012, World Scientific Publishing released his work A Calculus of Ideas: A Mathematical Study of Human Thought.

External links include the homepage of Ulf Grenander at Brown University. They also feature a video lecture by David Mumford titled "Pattern Theory: Grenander's Ideas and Examples". An additional listing includes 13664.