Ferdinand von Lindemann
Encyclopedia
Carl Louis Ferdinand von Lindemann (April 12, 1852 – March 6, 1939) was a German
mathematician
, noted for his proof, published in 1882, that π
(pi) is a transcendental number
, i.e., it is not a root of any polynomial
with rational
coefficients.
, the capital of the Kingdom of Hanover
. His father, Ferdinand Lindemann, taught modern languages at a Gymnasium
in Hanover. His mother, Emilie Crusius, was the daughter of the Gymnasium's headmaster. The family later moved to Schwerin
, where young Ferdinand attended school.
He studied mathematics at Göttingen
, Erlangen
, and Munich
. At Erlangen he received a doctorate, supervised by Felix Klein
, on non-Euclidean geometry
. Lindemann subsequently taught in Würzburg
and at the University of Freiburg
. During his time in Freiburg, Lindemann devised his proof that π is a transcendental number (see Lindemann–Weierstrass theorem
). After his time in Freiburg, Lindemann transferred to the University of Königsberg
. While a professor in Königsberg
, Lindemann acted as supervisor for the doctoral theses of David Hilbert
, Hermann Minkowski
, and Arnold Sommerfeld
.
of π. 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 π were transcendental, then the ancient and celebrated problem of squaring the circle
by compass and straightedge
would be solved in the negative.
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, noted for his proof, published in 1882, that π
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
(pi) is a transcendental number
Transcendental number
In mathematics, a transcendental number is a number that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e...
, i.e., it is not a root of any polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
with rational
Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...
coefficients.
Life and education
Lindemann was born in HanoverHanover
Hanover or Hannover, on the river Leine, is the capital of the federal state of Lower Saxony , Germany and was once by personal union the family seat of the Hanoverian Kings of Great Britain, under their title as the dukes of Brunswick-Lüneburg...
, the capital of the Kingdom of Hanover
Kingdom of Hanover
The Kingdom of Hanover was established in October 1814 by the Congress of Vienna, with the restoration of George III to his Hanoverian territories after the Napoleonic era. It succeeded the former Electorate of Brunswick-Lüneburg , and joined with 38 other sovereign states in the German...
. His father, Ferdinand Lindemann, taught modern languages at a Gymnasium
Gymnasium (school)
A gymnasium is a type of school providing secondary education in some parts of Europe, comparable to English grammar schools or sixth form colleges and U.S. college preparatory high schools. The word γυμνάσιον was used in Ancient Greece, meaning a locality for both physical and intellectual...
in Hanover. His mother, Emilie Crusius, was the daughter of the Gymnasium's headmaster. The family later moved to Schwerin
Schwerin
Schwerin is the capital and second-largest city of the northern German state of Mecklenburg-Vorpommern. The population, as of end of 2009, was 95,041.-History:...
, where young Ferdinand attended school.
He studied mathematics at Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
, Erlangen
Erlangen
Erlangen is a Middle Franconian city in Bavaria, Germany. It is located at the confluence of the river Regnitz and its large tributary, the Untere Schwabach.Erlangen has more than 100,000 inhabitants....
, and Munich
Munich
Munich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...
. At Erlangen he received a doctorate, supervised by Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
, on non-Euclidean geometry
Non-Euclidean geometry
Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
. Lindemann subsequently taught in Würzburg
Würzburg
Würzburg is a city in the region of Franconia which lies in the northern tip of Bavaria, Germany. Located at the Main River, it is the capital of the Regierungsbezirk Lower Franconia. The regional dialect is Franconian....
and at the University of Freiburg
University of Freiburg
The University of Freiburg , sometimes referred to in English as the Albert Ludwig University of Freiburg, is a public research university located in Freiburg im Breisgau, Baden-Württemberg, Germany.The university was founded in 1457 by the Habsburg dynasty as the...
. During his time in Freiburg, Lindemann devised his proof that π is a transcendental number (see Lindemann–Weierstrass theorem
Lindemann–Weierstrass theorem
In mathematics, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if 1, ..., are algebraic numbers which are linearly independent over the rational numbers ', then 1, ..., are algebraically...
). After his time in Freiburg, Lindemann transferred to the University of Königsberg
University of Königsberg
The University of Königsberg was the university of Königsberg in East Prussia. It was founded in 1544 as second Protestant academy by Duke Albert of Prussia, and was commonly known as the Albertina....
. While a professor in Königsberg
Königsberg
Königsberg was the capital of East Prussia from the Late Middle Ages until 1945 as well as the northernmost and easternmost German city with 286,666 inhabitants . Due to the multicultural society in and around the city, there are several local names for it...
, Lindemann acted as supervisor for the doctoral theses of David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
, Hermann Minkowski
Hermann Minkowski
Hermann Minkowski was a German mathematician of Ashkenazi Jewish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.- Life and work :Hermann Minkowski was born...
, and Arnold Sommerfeld
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...
.
Transcendence proof
In 1882, he published the result for which he is best known, the transcendenceTranscendental number
In mathematics, a transcendental number is a number that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e...
of π. His methods were similar to those used nine years earlier by Charles Hermite
Charles Hermite
Charles Hermite was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra....
to show that e, the base of natural logarithms
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
, is transcendental. Before the publication of Lindemann's proof, it was known that if π were transcendental, then the ancient and celebrated problem of squaring the circle
Squaring the circle
Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge...
by compass and straightedge
Compass and straightedge
Compass-and-straightedge or ruler-and-compass construction is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass....
would be solved in the negative.
External links
- Lindemann, F. "Über die Zahl π", Mathematische Annalen 20 (1882): pp. 213–225.