---

About the Man Who Showed us the Transcendence of π.

On the 6th of March 1939, in the German city of Munich, the great German mathematician Ferdinand von Lindemann passed away. Although he was a very prolific mathematician, Von Lindemann is actually famous in the world of mathematics and science in general for his greatest work, that is, the mathematical demonstration of the transcendentality of the number π, a demonstration that he achieved around 1882. This problem related to the transcendentality of π, and the absence of a proof, had puzzled mathematicians for centuries. His contributions to mathematics were fundamental to the advancement of number theory and a better understanding of the behaviour of number structures.

---

Main Mathematical Contributions.

---

• Mathematical Proof of the Transcendence of π :
  Essentially, Lindemann's mathematical proof consisted of proving that π is not a root of any polynomial equation with rational coefficients, which means that π is a transcendent number. In addition, this mathematical proof managed to solve an open problem in mathematics related to the squaring of the circle, which consists in the study of the possibility of constructing a square with the same area of a given circle, using only a ruler and compasses.

• Lindemann-Weirstrass Theorem:
  Together with Weierstrass, Lindemann made an important contribution to the conception of the Lindemann-Weierstrass theorem, which turns out to be a fundamental theorem in the study of transcendental number theory.

---

Life and Performance.

---

Von Lindemann was born on 12 April 1852 in Hanover, Germany. He studied mathematics at the famous universities of Göttingen, Erlangen and Munich, where he obtained his doctorate from the University of Erlangen in 1873.

He had an outstanding career as a professor of mathematics, becoming professor of mathematics at the universities of Freiburg, Konigsberg and Munich, where he also became the academic tutor of other mathematicians of great importance in the history of mathematics, such as David Hilbert and Hermann Minkowski, to name but a few. Professor Lindemann married Elizabeth Küssner, the daughter of a high school teacher.

Key Publications:

• ‘Über die Zahl π’ (About the number π) (1882).
  This is his most important work, among all his very important contributions to mathematics. In this work lies the proof of the transcendence of π.

---

Finally, it is safe to say that Ferdinand Von Lindemann's work will never be forgotten, for in accomplishing the titanic task of closing an open problem in mathematics as important as proving the significance of the number π , Lindemann's work will be fundamental to a deep understanding of an important area of number theory and mathematics in general.

Thank you for your work, Professor Lindemann.

Some of His Contributions.

---

---

Ferdinand Von Lindemann Portrait Image Source

Note: All the images related to Lindemann Contributions are crafted by me using the text editor based on LaTeX: Beamer. The Structure of this article is by my authorship too.

Regards.

References

A. Baker, Transcendental Number Theory, Cambridge University Press, 1990.

Gelfond, A.O. (2015) [1960], Transcendental and Algebraic Numbers, Dover Books on Mathematics, translated by Boron, Leo F., New York: Dover Publications, ISBN 978-0-486-49526-2, MR 0057921

---

---