In 1882, he published the result for which he is best known, the transcendence of Pi. His methods were similar to those used nine years earlier by Charles Hermite to show that e, the base of natural logarithms, is transcendental. Before the publication of Lindemann's proof, it was known that if Pi is transcendental, then the ancient and celebrated problem of squaring the circle by compass and straightedge could not be solved.

...He was the first to prove that e, the base of natural logarithms, is a transcendental number. His methods were later used by Ferdinand von Lindemann to prove that π is transcendental....

...While a professor at the University of Königsberg, Lindemann acted as supervisor for the doctoral thesis of David Hilbert, Hermann Minkowski, and Arnold Sommerfeld.

...He was educated in Germany at the Albertina University of Königsberg, where he achieved his doctorate in 1885 under direction of Ferdinand von Lindemann. While still a student at Königsberg, in 1883 he was awarded the Mathematics Prize of the French Academy of Sciences for his manuscript on the theory of quadratic forms.

...While a professor at the University of Königsberg, Lindemann acted as supervisor for the doctoral thesis of David Hilbert, Hermann Minkowski, and Arnold Sommerfeld.

Arnold Sommerfeld studied mathematics and physical sciences at the University of his native city, Königsberg, East Prussia. His dissertation advisor was the mathematician Ferdinand von Lindemann, and he also benefited from classes with mathematicians Adolph Hurwitz and David Hilbert, and physicist Emil Wiechert...

...While a professor at the University of Königsberg, Lindemann acted as supervisor for the doctoral thesis of David Hilbert, Hermann Minkowski, and Arnold Sommerfeld.

...An intense and fruitful scientific exchange between the three began and especially Minkowski and Hilbert would exercise a reciprocal influence over each other at various times in their scientific careers. Hilbert obtained his doctorate in 1885, with a dissertation, written under Ferdinand von Lindemann, titled Über invariante Eigenschaften spezieller binärer Formen, insbesondere der Kugelfunktionen ("On the invariant properties of special binary forms, in particular the spherical harmonic functions")...

...He studied mathematics at Göttingen, Erlangen, and Munich. At Erlangen he received a doctorate, supervised by Felix Klein, on non-Euclidean geometry....

...If it were possible to calculate the area of each of those parts, then the area of the circle as a whole would be known too. Only much later was it proven (by Ferdinand von Lindemann, in 1882) that this approach had no chance of success, because the factor pi (π) is transcendental...