Births on January 10

Heinrich Behmann, German mathematician and academic (d. 1970)

Heinrich Behmann: A German Mathematician's Contributions to Logic and His Complex History

Heinrich Behmann, born on 10 January 1891 in Bremen-Aumund, Germany, and also passing away in his hometown on 3 February 1970, was a prominent German mathematician whose significant work advanced the fields of set theory and predicate logic. His career, marked by pivotal academic achievements, was also influenced by the turbulent historical events of 20th-century Germany, leading to a complex legacy.

Early Life, Education, and Wartime Service

Behmann pursued his advanced mathematical studies at renowned German universities, including Tübingen, Leipzig, and particularly Göttingen. Göttingen, often considered a "mathematical Mecca" during that era, was a leading global center for mathematics, attracting brilliant minds like David Hilbert and Emmy Noether and serving as a crucible for foundational ideas in logic and mathematics. His academic journey was interrupted by World War I, during which he served and was wounded, subsequently being awarded the Iron Cross 2nd Class, a military decoration of the Kingdom of Prussia and later Germany, recognizing bravery or leadership on the battlefield.

Doctoral Research Under David Hilbert and Foundational Contributions

A pivotal moment in Behmann's academic career was the supervision of his doctoral thesis by the eminent mathematician David Hilbert. Hilbert, a foundational figure in mathematics, was instrumental in shaping 20th-century mathematical thought, particularly through his work on the foundations of mathematics and logic. Behmann's thesis, titled "Die Antinomie der transfiniten Zahl und ihre Auflösung durch die Theorie von Russell und Whitehead" (The Antinomy of the Transfinite Number and its Resolution through the Theory of Russell and Whitehead), delved into critical foundational issues of mathematics. The "antinomy of the transfinite number" refers to paradoxes arising in set theory, a field pioneered by Georg Cantor, which deals with collections of objects. Such paradoxes, like Russell's Paradox, highlighted inconsistencies within naive set theory, prompting a search for rigorous foundations. Behmann's thesis explored how the groundbreaking work of Bertrand Russell and Alfred North Whitehead, especially their monumental three-volume *Principia Mathematica* (published 1910–1913), offered a potential resolution to these foundational crises by attempting to reduce all mathematics to logic.

Groundbreaking Work on Decidability in Logic

Beyond his doctoral work, Heinrich Behmann made a significant and lasting contribution to mathematical logic in 1922 by proving the decidability of the monadic predicate calculus. In the context of logic, "decidability" refers to the existence of an effective algorithm that can determine, for any given formula in that logical system, whether it is true (or valid). The monadic predicate calculus is a specific fragment of first-order logic where predicates (properties or relations) can only take a single argument. Behmann's proof demonstrated that there is an algorithmic procedure to decide the validity of any formula expressible within this logical system. This was a crucial result in the early development of computability theory and laid groundwork for understanding the limits of automated reasoning.

Later Career and Post-War Dismissal

In 1938, Heinrich Behmann attained a significant academic position, securing a professorial chair in mathematics at the University of Halle (Saale). However, his career took a dramatic turn after World War II. In 1945, in the wake of Germany's defeat and the subsequent denazification efforts by the Allied powers, Behmann was dismissed from his professorship. This dismissal was a direct consequence of his membership in the Nationalsozialistische Deutsche Arbeiterpartei (NSDAP), commonly known as the Nazi Party. Such dismissals were a widespread measure across various public sectors in post-war Germany, aimed at removing individuals associated with the Nazi regime from positions of influence and responsibility.

Frequently Asked Questions About Heinrich Behmann

Who was Heinrich Behmann?

Heinrich Behmann (1891–1970) was a German mathematician known for his research in set theory and predicate logic, and for proving the decidability of the monadic predicate calculus.

What was the significance of his doctoral thesis?

His doctoral thesis, supervised by David Hilbert, addressed the "Antinomy of the Transfinite Number," a paradox in set theory, and explored its resolution through the foundational work of Russell and Whitehead, particularly their *Principia Mathematica*.

What is the monadic predicate calculus and why was its decidability proof important?

The monadic predicate calculus is a specific part of first-order logic where predicates have only one argument. Behmann's proof in 1922 showed that there's an algorithm to determine the truth or validity of any statement in this system, which was a fundamental result for early computability theory and automated reasoning.

Why was Heinrich Behmann dismissed from his professorship in 1945?

He was dismissed from his professorial chair at Halle (Saale) in 1945 as part of the post-World War II denazification process in Germany, due to his membership in the NSDAP (Nazi Party).