Carl Louis Ferdinand von Lindemann | Biography

The classic problem of squaring the circle had intrigued mathematicians since the time of Euclid. Only in 1882, however, when Ferdinand Lindemann proved that is a transcendental number, was this problem finally resolved. While Lindemann is best known for this one result, he also played an important role in the development of mathematics in Germany during the turn of the 20th century.

Lindemann was born in Hanover, Germany, on April 12, 1852. His father was a teacher of modern languages and later a manager of a gas works while his mother was the daughter of a famous teacher of classical languages, so it is not surprising that their son finished first in his class upon graduating from his gymnasium in 1870. France and Germany had recently gone to war, but Lindemann's poor health prevented him from being called into the army. Instead, he enrolled at the University of Göttingen to study mathematics.

Göttingen attracted many of Europe's leading mathematicians. During his time there Lindemann attended lectures by Alfred Clebsch on analytic spatial geometry, algebraic curves, elliptic functions, and the theory of algebraic forms. He also met Felix Klein, who was then a lecturer at the university. In 1872 Klein became a full professor at the University of Erlangen; Lindemann joined him as Klein's second Ph.D. student, receiving his degree in 1873 with a thesis on non-Euclidean geometry and its connection with mechanics. In addition, after Clebsch's sudden death in 1872 and with Klein's encouragement, Lindemann edited and revised Clebsch's geometry lectures which he published as a textbook in 1876. The Clebsch-Lindemann text won wide acclaim and was used for several decades.

Proves Is Transcendental

Lindemann spent part of the 1876-77 academic year in Paris, where he began a long friendship with Charles Hermite. Because of the success of the Clebsch-Lindemann text, he was introduced to many of the leading French mathematicians. He returned from Paris to become associate professor at the University of Freiburg after a promised position at the University of Würzburg never materialized. During his six years at Freiburg, Lindemann published several minor papers on special functions and Fourier series, and also wrote a paper on the vibration of strings, inspired by the recent invention of the microphone. But his main success came with his work on the number . During Lindemann's visit to Paris in 1876, Hermite had shown him his proof that the number e is transcendental, that is, that e is not the root of any polynomial with integer coefficients. Building upon his friend's earlier work, Lindemann finally succeeded in 1882 in proving that is also transcendental. He sent his paper "Über die Zahl " (Concerning the number ) to Klein for publication in the Mathematische Annalen. Klein sent the paper to Georg Cantor, who could find no errors, and who passed the paper on to Karl Weierstrass in Berlin for final verification of the proof. With Lindemann's permission, on June 22, 1882, Weierstrass presented the result to the Berlin Academy of Sciences to great acclaim.

The problem of squaring the circle, that is, constructing a square with the same area as that of a given circle, fascinated mathematicians for more than two thousand years. A solution had been found by Dinostratus around 350 B.C., but no one had ever been able to find a solution using just the classical Euclidean tools of the straightedge and compass. Mathematicians knew that if a number was transcendental, and hence not algebraic, then no line of that length could be constructed using these tools. Lindemann's proof that was transcendental, and hence unconstructible, finally established unequivocally that the squaring of the circle was impossible by means of straightedge and compass alone.

Teacher, Advisor, and Adminstrator

With the fame of his work on freshly behind him, Lindemann accepted an appointment as full professor at the University of Königsberg in 1883. After ten years, he moved one final time to take a chair in mathematics at the University of Munich. He never again published a paper to rival the importance of his work on . Nevertheless, Lindemann had a successful career as a teacher, an advisor of students, and an administrator. He supervised more than 60 German and foreign Ph.D. students, including Hermann Minkowski and David Hilbert. During his years in Munich, Lindemann served as dean of the arts and sciences, as rector of the university (an elected position comparable to that of president), and for 25 years as the director of the university's administrative committee. For several years Lindemann was also a confidential advisor to the king's court. In 1918, he received the Knight's Cross of the Order of the Bavarian Crown, an honor that granted nobility and the right to be known as Ferdinand Ritter von Lindemann.

In 1887, Lindemann married Lisbeth Küssner, a successful actress from Königsberg. They had two children, both born in Königberg, a son in 1889 and a daughter in 1891. Their son died tragically at the age of 22 during a mountain climbing accident in the Alps. Lisbeth apparently had mathematical as well as acting talents as she collaborated with her husband in translating and revising some of the works of the French mathematician Henri Poincaré. Lindemann died on March 6, 1939, three years after his wife. In his article on the man who discovered the transcendence of , Fritsch writes that "he still published mathematical papers and thought about problems up to the day before his death."