Carl Louis Ferdinand von Lindemann (12 April 1852 – 6 March 1939) was a German
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
, noted for his proof, published in 1882, that
(pi) is a
transcendental number
In mathematics, a transcendental number is a number that is not algebraic—that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are and .
Though only a few classes ...
, meaning it is not a
root
In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the sur ...
of any
polynomial
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...
with
rational
Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abi ...
coefficients
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves var ...
.
Life and education
Lindemann was born in
Hanover
Hanover (; german: Hannover ; nds, Hannober) is the capital and largest city of the German state of Lower Saxony. Its 535,932 (2021) inhabitants make it the 13th-largest city in Germany as well as the fourth-largest city in Northern Germany ...
, the capital of the
Kingdom of Hanover
The Kingdom of Hanover (german: Königreich Hannover) 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 Han ...
. 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
Schwerin (; Mecklenburgisch dialect, Mecklenburgian Low German: ''Swerin''; Latin: ''Suerina'', ''Suerinum'') is the Capital city, capital and List of cities and towns in Germany, second-largest city of the northeastern States of Germany, German ...
, where young Ferdinand attended school.
He
studied mathematics at
Göttingen
Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...
,
Erlangen
Erlangen (; East Franconian German, East Franconian: ''Erlang'', Bavarian language, Bavarian: ''Erlanga'') is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative d ...
, and
Munich
Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the States of Germany, German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the List of cities in Germany by popu ...
. At Erlangen he received a doctorate, supervised by
Felix Klein
Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group ...
,
on
non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geo ...
. Lindemann subsequently taught in
Würzburg
Würzburg (; Main-Franconian: ) is a city in the region of Franconia in the north of the German state of Bavaria. Würzburg is the administrative seat of the ''Regierungsbezirk'' Lower Franconia. It spans the banks of the Main River.
Würzburg is ...
and at the
University of Freiburg
The University of Freiburg (colloquially german: Uni Freiburg), officially the Albert Ludwig University of Freiburg (german: Albert-Ludwigs-Universität Freiburg), is a public university, public research university located in Freiburg im Breisg ...
. During his time in Freiburg, Lindemann devised his proof that is a transcendental number (see
Lindemann–Weierstrass theorem
In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following:
In other words, the extension field \mathbb(e^, \dots, e^) has transce ...
). After his time in Freiburg, Lindemann transferred to the
University of Königsberg
The University of Königsberg (german: Albertus-Universität Königsberg) was the university of Königsberg in East Prussia. It was founded in 1544 as the world's second Protestant academy (after the University of Marburg) by Duke Albert of Prussi ...
. While a professor in
Königsberg
Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was named ...
, Lindemann acted as supervisor for the doctoral theses of the mathematicians
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
,
Hermann Minkowski
Hermann Minkowski (; ; 22 June 1864 – 12 January 1909) was a German mathematician and professor at Königsberg, Zürich and Göttingen. He created and developed the geometry of numbers and used geometrical methods to solve problems in number t ...
, and
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretica ...
.
Transcendence proof
In 1882, Lindemann published the result for which he is best known, the
transcendence of
. His methods were similar to those used nine years earlier by
Charles Hermite
Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
Hermi ...
to show that
''e'', the base of natural logarithms, is transcendental. Before the publication of Lindemann's proof, it was known that ''if'' was transcendental, with
Johann Heinrich Lambert
Johann Heinrich Lambert (, ''Jean-Henri Lambert'' in French; 26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Swiss or French, who made important contributions to the subjec ...
as the
first to prove being irrational in the 1760s, along with the impossibility to
square the circle by
compass and straightedge
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an ideali ...
.
References
External links
*
*
*
* Lindemann, F.
Über die Zahl , ''Mathematische Annalen'' 20 (1882): pp. 213–225.
{{DEFAULTSORT:Lindemann, Ferdinand von
1852 births
1939 deaths
19th-century German mathematicians
20th-century German mathematicians
Squaring the circle
Number theorists
Scientists from Hanover
People from the Kingdom of Hanover
University of Göttingen alumni
University of Erlangen-Nuremberg alumni
Ludwig Maximilian University of Munich alumni
University of Königsberg faculty