Ludwig Bieberbach: The owner of the conjecture that has puzzled the mathematics community for over 60 years
In the history of complex analysis, there was a problem that challenged mathematicians around the world for several decades before it was proven. This is the conjecture named after Ludwig Georg Elias Moses Bieberbach, a German mathematician who passed away on September 1, 1982, in Oberaudorf, Upper Bavaria, West Germany.
Early life and academic path
Bieberbach was born on December 4, 1886, in the town of Goddelau, near Darmstadt, Germany. He was interested in mathematics since high school, inspired by an excellent mathematics teacher. He studied at Heidelberg University before moving on to study under Felix Klein, a great mathematician at the University of Göttingen, and received his doctorate in 1910 with a dissertation on the theory of automorphic functions.
Bieberbach held a professorship at the University of Frankfurt and the University of Berlin, and he had students who later became many famous mathematicians, such as Heinz Hopf, a pioneer of topology.
Bieberbach's predictive message
The work that made Bieberbach's name most recognized in the field of mathematics is the Bieberbach conjecture, which he proposed in 1916. This conjecture concerns the coefficients of the power series of a univalent holomorphic function defined on the unit disk, by setting an upper bound on the absolute value of each coefficient in that series.
Even though Bieberbach successfully proved the case of the second coefficient, the general problem for all coefficients remained a puzzle that would challenge mathematicians around the world for many decades. Many mathematicians attempted to prove this conjecture for various specific cases, resulting in numerous new results and techniques in the field of geometric function theory along the way.
The proof by Louis de Broglie
Eventually, Bieberbach's conjecture was completely proven in 1985 by Louis de Branges, a French-American mathematician, after the problem had remained unsolved for nearly 70 years. De Branges' proof used sophisticated and unexpected techniques, connecting with Hilbert space theory, and at first, even de Branges himself had difficulties convincing fellow mathematicians that his proof was correct. It was not until a group of Soviet mathematicians reviewed and confirmed the validity of the proof that it gained acceptance. This proof is considered one of the most significant achievements in complex analysis in the 20th century.
The Dark Side of History: Bieberbach and Nazism
Apart from his mathematical work, Bieberbach is also known in the history of mathematics as an active supporter of the Nazi ideology. He was one of the key leaders of the movement called 'German Mathematics' (Deutsche Mathematik), which attempted to segregate mathematics according to race, promoting the idea that there was a 'German' way of mathematical thinking that was different and superior to the abstract style he accused of being 'Jewish.' He even founded a journal called Deutsche Mathematik to disseminate this idea. Bieberbach's openly anti-Jewish attitude caused significant damage to the German mathematical community at the time and is part of the dark history in which many mathematicians were expelled or killed during the Nazi regime.
Complex academic heritage
Bieberbach passed away on September 1, 1982, at the age of 95. His name is still mentioned in the field of mathematics through academic works, such as the Bieberbach conjecture and the Fatou–Bieberbach domain. At the same time, his history remains an important example that serves as a reminder of the harmful impact that political ideologies can have on academia.
