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Michiel Hazewinkel

Michiel Hazewinkel: A Dutch Luminary in Mathematics

Michiel Hazewinkel, born on June 22, 1943, in the bustling city of Amsterdam, stands as a prominent Dutch mathematician. His academic journey has been marked by significant contributions, particularly in the realm of formal groups and their myriad applications. For years, he held the esteemed position of Emeritus Professor of Mathematics at both the Centre for Mathematics and Computer Science (CWI) and the prestigious University of Amsterdam. His 1978 seminal work, Formal groups and applications, and his extensive editorial role in the monumental Encyclopedia of Mathematics have cemented his legacy within the mathematical community.

Biography

Born to Jan Hazewinkel and Geertrude Hendrika Werner, Hazewinkel’s intellectual curiosity was nurtured from an early age in Amsterdam. He embarked on his academic pursuits at the University of Amsterdam, a decision that would shape the trajectory of his illustrious career. In 1963, he earned his Bachelor of Arts degree, a dual major in mathematics and physics, demonstrating an early aptitude for the rigorous and the abstract. His thirst for knowledge continued, culminating in a Master of Arts in mathematics in 1965, with a focused minor in philosophy, a testament to his desire to understand the underlying principles and implications of mathematical thought.

The year 1969 marked a significant milestone as Hazewinkel completed his doctoral studies. Under the tutelage of distinguished scholars Frans Oort and Albert Menalda, he defended his thesis, "Maximal Abelian Extensions of Local Fields," a work that delved into complex algebraic structures and laid the groundwork for future explorations.

Following his graduation, Hazewinkel commenced his academic career in earnest, joining the faculty of the University of Amsterdam as an assistant professor in 1969. The following year, he transitioned to the Erasmus University Rotterdam, where he quickly ascended through the ranks, becoming an associate professor in 1970. By 1972, his contributions were recognized with an appointment as a full professor of mathematics at the Econometric Institute. During his tenure at Erasmus University, he guided the doctoral research of several promising mathematicians, including Roelof Stroeker (1975), M. van de Vel (1975), Jo Ritzen (1977), and Gerard van der Hoek (1980). His influence extended beyond Rotterdam, as he also held a professorship at the Universitaire Instelling Antwerpen from 1973 to 1975, where Marcel van de Vel was among his PhD students.

The period between 1982 and 1985 proved to be a dynamic phase in Hazewinkel's career. He held a dual appointment, serving as a part-time professor extraordinarius in mathematics at the Erasmus Universiteit Rotterdam while simultaneously heading the Department of Pure Mathematics at the Centre for Mathematics and Computer (CWI) in Amsterdam. This period of leadership at CWI foreshadowed his later, more extensive involvement with the institution. In 1985, he further expanded his academic reach with an appointment as professor extraordinarius in mathematics at the University of Utrecht. There, he supervised the doctoral promotions of Frank Kouwenhoven (1986), Huib-Jan Imbens (1989), J. Scholma (1990), and F. Wainschtein (1992), nurturing the next generation of mathematical minds.

His association with the Centre for Mathematics and Computer Science (CWI) in Amsterdam solidified in 1988 when he was appointed professor of mathematics and head of the Department of Algebra, Analysis and Geometry. He continued to lead and contribute to this department until his retirement in 2008, leaving an indelible mark on the institution.

Beyond his direct professorial roles, Hazewinkel has been a pivotal figure in the dissemination and advancement of mathematical knowledge through his extensive editorial work. Since 1977, he has served as a managing editor for the esteemed journal Nieuw Archief voor Wiskunde. From its inception in 1983, he has been instrumental as an editor for Acta Applicandae Mathematicae. His association with Chaos, Solitons & Fractals began in 1991, where he served as an associate editor. His leadership extended to major book series and encyclopedic projects. From 1977, he managed the book series Mathematics and Its Applications for Kluwer Academic Publishers. In 1981, he took on a similar role for Mathematics and Geophysics at Reidel Publishing. His most significant editorial undertaking was perhaps his tenure as managing editor for the Encyclopedia of Mathematics from 1987 to 1994, a colossal project that aimed to compile and present a comprehensive overview of mathematical knowledge. Furthermore, he oversaw the ambitious six-volume Handbook of Algebra for Elsevier Science Publishers from 1995 to 2009.

Hazewinkel's dedication to the mathematical community is evident in his active participation in numerous professional organizations. He was a member of 15 professional societies dedicated to mathematics, engaging in a wide array of administrative duties. These included serving on institute boards, program committees, steering committees, consortia, and various councils. His commitment to the broader scientific landscape was further recognized in 1994 when he was elected as a member of the International Academy of Computer Sciences and Systems.

Publications

Michiel Hazewinkel's prolific output includes a substantial body of authored and edited books, alongside a vast collection of articles. His written works have significantly shaped discourse and understanding in various branches of mathematics.

Books, a selection:

  • 1970. Géométrie algébrique-généralités-groupes commutatifs. Co-authored with Michel Demazure and Pierre Gabriel. Published by Masson & Cie. This foundational text explored the general principles of algebraic geometry, with a specific focus on commutative groups, a critical area for understanding advanced algebraic structures.
  • 1976. On invariants, canonical forms and moduli for linear, constant, finite dimensional, dynamical systems. Co-authored with Rudolf E. Kálmán. Published by Springer Berlin Heidelberg. This work delved into the intricate relationship between invariants, canonical forms, and moduli within the context of linear dynamical systems, a topic with deep implications in control theory and systems analysis.
  • 1978. Formal groups and applications. Vol. 78. Published by Elsevier. This is arguably his most renowned work, a comprehensive treatise that systematically explored the theory of formal groups and their diverse applications across various mathematical disciplines. Its impact on algebraic geometry and related fields cannot be overstated.
  • 1993. Encyclopaedia of Mathematics. Edited. Vol. 9. Published by Springer. This volume represents a significant contribution to a larger collaborative effort to create a definitive reference work for the mathematical sciences, reflecting Hazewinkel's commitment to accessible and comprehensive mathematical knowledge.

Articles, a selection:

  • Hazewinkel, Michiel (1976). "Moduli and canonical forms for linear dynamical systems II: The topological case". Mathematical Systems Theory. 10 (1): 363–385. The paper, with its doi of 10.1007/BF01683285 and S2CID 25234632, further explored the topological aspects of moduli and canonical forms for linear dynamical systems, building upon previous work and offering new insights into the structure of these systems. The original document was archived from the PDF on December 12, 2013.
  • Hazewinkel, Michiel; Marcus, Steven I. (1982). "On Lie algebras and finite dimensional filtering". Stochastics. 7 (1–2): 29–62. This article, accessible via doi 10.1080/17442508208833212 and identified by S2CID 119818672, investigated the connections between Lie algebras and the theory of finite-dimensional filtering, a crucial area in signal processing and statistical estimation. The PDF was archived on December 12, 2013.
  • Hazewinkel, M.; Marcus, S. I.; Sussmann, H. J. (1983). "Nonexistence of finite-dimensional filters for conditional statistics of the cubic sensor problem". Systems & Control Letters. 3 (6): 331–340. With doi 10.1016/0167-6911(83)90074-9 and S2CID 122766978, this paper addressed a fundamental question regarding the existence of finite-dimensional filters for a specific, challenging problem involving cubic sensors. The PDF was archived on December 12, 2013, and retrieved on September 10, 2013.
  • Hazewinkel, Michiel (2001). "The algebra of quasi-symmetric functions is free over the integers". Advances in Mathematics. 164 (2): 283–300. This publication, carrying the doi 10.1006/aima.2001.2017, presented a significant result concerning the algebraic structure of quasi-symmetric functions, demonstrating their freeness over the integers.