Winfried Scharlau (1940–2020) was a distinguished German mathematician whose work bridged the rigorous world of algebraic number theory with the narrative world of mathematical history. A central figure in the "Münster School" of mathematics, Scharlau is best remembered for his definitive contributions to the theory of quadratic forms and his exhaustive, multi-volume biography of the computer science pioneer Alan Turing.
1. Biography: Early Life and Academic Trajectory
Winfried Scharlau was born on August 12, 1940, in Berlin, Germany. He grew up in a post-war Germany that was rapidly rebuilding its intellectual institutions. He pursued his university studies at the University of Bonn and the University of Zurich, eventually returning to Bonn to complete his doctorate in 1966.
His doctoral advisor was the legendary Friedrich Hirzebruch, one of the most influential mathematicians of the 20th century. Under Hirzebruch’s mentorship, Scharlau developed a deep interest in the intersection of algebra and topology. After a productive period as a research fellow at the Institute for Advanced Study in Princeton (1969–1970)—a global hub for mathematical excellence—he returned to Germany to complete his Habilitation at the University of Münster.
In 1970, at the remarkably young age of 30, he was appointed Professor of Mathematics at the Westfälische Wilhelms-Universität Münster. He remained there for the rest of his career, serving as a pillar of the faculty until his retirement in 2005. Scharlau passed away on November 26, 2020.
2. Major Contributions: Quadratic Forms and "Scharlau’s Transfer"
Scharlau’s primary mathematical legacy lies in the algebraic theory of quadratic forms. A quadratic form is a polynomial where every term has a degree of two (for example, $f(x, y) = ax^2 + bxy + cy^2$). While these objects have been studied since the time of Gauss, Scharlau helped revolutionize the field using modern algebraic tools.
- Scharlau’s Transfer: His most famous technical contribution is a mapping technique known as "Scharlau’s Transfer." This tool allows mathematicians to "transfer" information about quadratic forms from a field extension back to the original base field. This proved crucial in the study of the Witt ring, an algebraic structure that classifies quadratic forms.
- Hermitian Forms: He extended the study of quadratic forms to Hermitian forms (which involve complex conjugation), providing a unified framework that linked number theory, algebra, and topology.
- Classification Theorems: Scharlau was instrumental in developing the classification of these forms over various types of fields, providing a clearer map of how these mathematical objects behave under different conditions.
3. Notable Publications
Scharlau was a prolific writer known for his clarity and structural elegance. His bibliography includes both technical masterpieces and accessible textbooks.
- Quadratic and Hermitian Forms (1985): This is widely considered the "Bible" of the field. It remains a standard reference for researchers, lauded for its comprehensive coverage and rigorous proofs.
- Algebra: Eine Einführung (Algebra: An Introduction) (with Siegfried Bosch): A staple in German universities, this textbook introduced generations of students to the fundamentals of modern algebra.
- Alan Turing 1912–1954 (Multiple Volumes): In his later years, Scharlau turned to biography. This exhaustive work (published in several volumes, including Turing: Biography and Turing: The Novel) is one of the most detailed accounts of the life of the British codebreaker.
- The Mathematical Correspondence of Rudolf Lipschitz (1986): Scharlau edited the letters of this 19th-century mathematician, contributing significantly to the history of science.
4. Awards and Recognition
While Scharlau did not seek the limelight of international prizes like the Fields Medal, he was held in the highest esteem within the German academic hierarchy:
- Member of the Akademie der Wissenschaften zu Göttingen: Election to this academy is one of the highest honors for a German scholar.
- Editorial Leadership: He served as an editor for prestigious journals, including Manuscripta Mathematica, influencing the direction of mathematical publishing in Europe.
- Honorary Symposia: Upon his retirement and subsequent birthdays, the international mathematical community organized several colloquia in his honor, reflecting his status as a "mathematician’s mathematician."
5. Impact and Legacy
Scharlau’s impact is twofold: pedagogical and structural.
Pedagogically, he modernized the way algebra was taught in Germany, moving away from dry, computational methods toward a more structural, "Bourbaki-style" approach that emphasized the underlying patterns of mathematical systems.
Scientifically, his work on the Witt ring and transfer maps laid the groundwork for the "Milnor Conjecture" (later proven by Vladimir Voevodsky), which earned a Fields Medal in 2002. Scharlau’s tools were the essential scaffolding upon which these later, more famous breakthroughs were built.
6. Collaborations and Students
Scharlau was a central node in a vast network of algebraic researchers.
- The Münster School: He mentored dozens of PhD students, many of whom became professors across Europe and North America, including figures like Eva Bayer-Fluckiger and Detlev Hoffmann.
- Key Partners: He collaborated frequently with Albrecht Pfister, another giant of quadratic form theory, and Tsit Yuen Lam. These collaborations helped define the "Golden Age" of quadratic forms in the 1970s and 80s.
7. Lesser-Known Facts
- The "Turing Project": Scharlau became so obsessed with Alan Turing that he spent years traveling the world to interview people who had known Turing personally. He even wrote a novel about Turing (Das Glück der Welt) to explore the emotional truths that a standard biography could not capture.
- The Arboretum: Scharlau was a passionate amateur dendrologist (a scientist of trees). On his property near Münster, he planted a massive collection of rare trees from around the world, creating a private arboretum that he maintained with the same precision he applied to his equations.
- Fiction Writer: Late in life, he transitioned into a novelist, writing historical fiction that explored the intellectual and moral dilemmas of scientists throughout history.
Winfried Scharlau’s life was a testament to the idea that mathematics is not an isolated discipline but a deeply human endeavor, connected to history, biography, and the natural world.